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Recent advances in the science of Champagne bubbles

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The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the fine interplay between CO(2)-dissolved gas molecules, tiny air pockets trapped within microscopic particles during the pouring process, and some liquid properties. This critical review summarizes recent advances obtained during the past decade concerning the physicochemical processes behind the nucleation, rise, and burst of bubbles found in glasses poured with champagne and sparkling wines. Those phenomena observed in close-up through high-speed photography are often visually appealing. Let's hope that your enjoyment of champagne will be enhanced after reading this fully illustrated review dedicated to the deep beauties of nature often hidden behind many everyday phenomena (51 references).
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Volume 37 | Number 11 | 2008 Chem Soc Rev Pages 2361–2580
ISSN 0306-0012
0306-0012(2008)37:11;1-T
www.rsc.org/chemsocrev Volume 37 | Number 11 | November 2008 | Pages 2361–2580
Chemical Society Reviews
TUTORIAL REVIEW
Ariel Fernández and
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Protein wrapping: a molecular
marker for association, aggregation
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CRITICAL REVIEW
Gérard Liger-Belair, Guillaume Polidori
and Philippe Jeandet
Recent advances in the science of
champagne bubbles
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Recent advances in the science of champagne bubbles
Ge
´rard Liger-Belair,*
a
Guillaume Polidori
b
and Philippe Jeandet
a
Received 8th July 2008
First published as an Advance Article on the web 5th September 2008
DOI: 10.1039/b717798b
The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the
result of the fine interplay between CO
2
-dissolved gas molecules, tiny air pockets trapped within
microscopic particles during the pouring process, and some liquid properties. This critical review
summarizes recent advances obtained during the past decade concerning the physicochemical
processes behind the nucleation, rise, and burst of bubbles found in glasses poured with
champagne and sparkling wines. Those phenomena observed in close-up through high-speed
photography are often visually appealing. Let’s hope that your enjoyment of champagne will be
enhanced after reading this fully illustrated review dedicated to the deep beauties of nature often
hidden behind many everyday phenomena (51 references).
1. Introduction
From a strictly chemical point of view, champagne and spark-
ling wines are multicomponent hydroalcoholic systems
supersaturated with CO
2
-dissolved gas molecules (formed
together with ethanol during the fermentation process).
1
As
soon as a bottle of champagne or sparkling wine is uncorked,
the progressive release of CO
2
-dissolved gas molecules is re-
sponsible for bubble formation, the so-called effervescence
process. It is worth noting that approximately five litres of
CO
2
must escape from a typical 0.75 L champagne bottle. To
get an idea of how many bubbles are potentially involved
throughout the degassing process from this single bottle, we
can divide this volume of CO
2
to be released by the average
volume of a typical bubble of 0.5 mm in diameter. A huge
number close to 10
8
is found! Actually, champagne and spark-
ling wine tasting mainly differs from still non-effervescent wine
tasting due to the presence of those myriad of bubbles con-
tinuously rising through the liquid medium. This is the reason
why considerable efforts have been conducted the past few years
in order to better illustrate, detect, understand and finally
control each and every parameter involved in the bubbling
process. Without bubbles, champagne and other sparkling
wines would be unrecognizable as such (see Fig. 1), but the
role of effervescence goes far beyond the solely aesthetical point
of view... This critical review covers recent progress in the field
of champagne science.
2. Within a champagne bottle
2.1. Where do CO
2
molecules dissolved in champagne come
from?
The modern production of champagne is not so far removed
from that empirically developed by the Benedictine monk dom
Pierre Pe
´rignon in the late 17th century. This method is also
used outside the Champagne region. Sparkling wines
produced as such are labelled me
´thode traditionnelle. Indeed,
most American and Australian sparkling winemakers use this
method to elaborate their own sparkling wines. This method
involves several distinct steps:
A first alcoholic fermentation. Three types of noble grapes
are grown in the 75 000 acres of the Champagne vineyards:
a
Laboratoire d’Œnologie et Chimie Applique
´e, Unite
´de Recherche sur
la Vigne et le Vin de Champagne (URVVC), Universite
´de Reims
Champagne-Ardenne, B.P. 1039, 51687 Reims Cedex 2, France.
E-mail: gerard.liger-belair@univ-reims.fr;
Fax: 00 (33)3 26 91 86 14; Tel: 00 (33)3 26 91 86 14
b
Laboratoire de Thermome
´canique, Groupe de Recherche en Sciences
Pour l’Inge
´nieur (GRESPI), Universite
´de Reims Champagne-
Ardenne, B.P. 1039, 51687 Reims Cedex 2, France
Ge
´rard Liger-Belair was born
in Beyrouth (Lebanon) in
1970. He studied Fundamental
Physics in Paris VI University.
He received his PhD in Physi-
cal Sciences in 2001, from
Reims University, where he
was appointed Associate
Professor in 2002 and full
Professor of Chemical Physics
in 2007. He is presently the
leader of the ‘‘Bubble Team’’
in the Laboratory of Enology
and Applied Chemistry. He has
been researching the physics and chemistry behind the
bubbling properties of carbonated beverages (including
champagne, sparkling wines, beers and fizzy waters) for several
years. He is the author or co-author of many articles and books
upon the subject. He is the recipients of several scientific awards
and recognitions, including the 2004 Award for Professional/
Scholarly book in Physics from the Association of American
Publishers for his book ‘‘Uncorked, the science of champagne’’,
published in 2004 by Princeton University Press. He also
has a passion for micro-photography. His series of ‘‘bubble’’
photographs, at the juncture between pure Science and modern
Art, have appeared in numerous exhibitions and art galleries.
His current interests include the science of bubbles, foams and
thin films, and their broad interdisciplinary applications.
Ge
´rard Liger-Belair
2490 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
CRITICAL REVIEW www.rsc.org/csr |Chemical Society Reviews
View Article Online
Chardonnay (a white grape), Pinot Meunier, and Pinot Noir
(both dark grapes). Usually around mid-September, the
grapes harvested from these vineyards are pressed to make a
juice, called ‘‘the grape must’’. After pressing, the must is
transferred into an open vat where yeast (a kind of fungus
called Saccharomyces cerevisiae) is added. Generally speaking,
the key chemical reaction of winemaking is alcoholic fermen-
tation: the conversion of sugars into ethanol and carbon
dioxide by yeast. The process of fermentation was first
scientifically described by the French chemist Joseph-Louis
Gay Lussac, in 1810, when he demonstrated that glucose is the
basic starting block for producing ethanol:
C
6
H
12
O
6
-2CH
3
CH
2
OH + 2CO
2
(1)
The manner in which yeast contributes to the fermentation
process was not clearly understood until 1857, when the
French microbiologist Louis Pasteur discovered that not only
does the fermentation process not require any oxygen, but
alcohol yield is actually reduced by its presence. The amount of
ethanol generated by this first alcoholic fermentation is about
11%. At this step, ‘‘champagne’’ is still actually a non-
effervescent white wine, because the carbon dioxide produced
during the first alcoholic fermentation is allowed to escape into
the atmosphere.
The art of blending. Because it is rare that a single wine of a
single vintage from a single vineyard and grape variety will
provide the perfect balance of flavour, sugar level, and acidity
necessary for making a fine champagne, winemakers will often
mix several different still wines. This is called the assemblage
(or blending) step, and it is carried out directly after the first
alcoholic fermentation is complete. Blending is considered the
key to the art of champagne-making. A cellar master will
sometimes blend up to 80 different wines from various grape
varieties, vineyards and vintages to produce one champagne.
The blending of still wines originally made from the three
kinds of grapes forms a base wine, which will then undergo a
second fermentation—the key step in producing the ‘‘sparkle’’
in champagne and sparkling wines.
The prise de mousse: a second alcoholic fermentation. Once
the base wine is created, sugar (about 24 grams per litre) and
yeast are added. The entire concoction is put into thick-walled
glass bottles and sealed with caps. The bottles are then placed
in a cool cellar (12 to 14 1C), and the wine is allowed to slowly
ferment for a second time, producing alcohol and carbon
dioxide again. Actually, during this second fermentation
process which occurs in cool cellars, the bottles are sealed,
so that the CO
2
molecules cannot escape and they progres-
sively dissolve into the wine. Therefore, CO
2
-dissolved mole-
cules in the wine and gaseous CO
2
molecules under the cork
progressively establish an equilibrium—an application of
Henry’s law which states that the partial pressure of a given
gas above a solution is proportional to the concentration of
the gas dissolved in the solution, as expressed by the following
relationship:
c=k
H
P
CO
2
(2)
where cis the concentration of dissolved CO
2
molecules, P
CO
2
is the partial pressure of CO
2
molecules in the vapor phase,
and k
H
is the Henry’s law constant. For a given gas, k
H
is
strongly temperature-dependent. The lower the temperature,
the higher the Henry’s law constant, and therefore the higher
the solubility.
In champagne and sparkling wines, Agabaliantz thoroughly
examined the solubility of dissolved CO
2
molecules as a func-
tion of both temperature and wine parameters.
2
His empirical
relationships are still used nowadays by champagne and spark-
ling winemakers. For a typical sparkling wine elaborated
according to the me
´thode traditionnelle, Agabaliantz established
the temperature dependence of the Henry’s law constant, which
is displayed in Table 1. Thermodynamically speaking, the
behaviour of Henry’s law constant as a function of temperature
can be conveniently expressed with a Van’t Hoff like equation
as follows:
kHðyÞ¼k298 K exp DHdiss
<
1
y1
298

ð3Þ
where DH
diss
is the dissolution enthalpy of CO
2
molecules in the
liquid medium (in J mol
1
), <is the ideal gas constant
(8.31 J K
1
mol
1
), and yis the absolute temperature (in K).
By fitting Agabaliantz data with the latter equation, it is worth
noting that the dissolution enthalpy of CO
2
molecules in
champagne may be evaluated.
3
The best fit to Agabaliantz data
was found with DH
diss
E24 800 J mol
1
(see Fig. 2). In
comparison, the dissolution enthalpy of CO
2
molecules in pure
water is about 19 900 J mol
1
.
4
2.2. The pressure under the cork
Following eqn (1), 24 grams per litre of sugar added in closed
bottles to promote the second alcoholic fermentation produce
approximately 11.8 grams per litre of CO
2
within each bottle.
Therefore, a typical 75 cL champagne bottle contains close to
9 g of CO
2
molecules. By use of the molar mass of CO
2
Fig. 1 Photograph of a typical flute poured with champagne (a), and
close-up on particles acting as bubble nucleation sites freely floating in
the bulk of the flute (called fliers), thus creating charming bubble trains
in motion in the champagne bulk (b) (rAlain Cornu/Collection
CIVC).
This journal is cThe Royal Society of Chemistry 2008 Chem.Soc.Rev., 2008, 37, 2490–2511 |2491
View Article Online
(44 g mol
1
), and the molar volume of an ideal gas (close to
24 L mol
1
at 12 1C), it can be deduced that about 5 L of
gaseous CO
2
are trapped into a single bottle of champagne
(i.e., 6 times its own volume!).
Because the solubility of CO
2
strongly depends on the
champagne temperature, the pressure of gaseous CO
2
under
the cork also strongly depends, in turn, on the champagne
temperature. The physicochemical equilibrium of CO
2
mole-
cules within a champagne bottle is ruled by both Henry’s law
(for CO
2
-dissolved gas molecules) and the ideal gas law (for
the gaseous CO
2
in the headspace under the cork). Moreover,
the conservation of the total mass of CO
2
molecules (dissolved
into the wine and in the vapor phase under the cork) applies,
since bottles are hermetically closed. Therefore, by combining
the two above-mentioned laws with mass conservation, the
following relationship can easily be determined which links the
pressure Pof gaseous CO
2
under the cork (in bars) with both
temperature and the bottle’s parameters as:
Pm<y
4:4103vþðkH<yÞVð4Þ
where mis the total mass of CO
2
within the bottle (in grams), y
is the champagne temperature (in K), <is the ideal gas
constant (8.31 J K
1
mol
1
), k
H
is the Henry’s law constant
given in Table 1 (in grams per litre per bar), Vis volume of
champagne within the bottle (in litres), and vis the volume of
the gaseous headspace under the cork (in litres).
For a typical champagne bottle with V= 75 cL, a volume in
the headspace of v= 25 mL, and a total mass of CO
2
trapped
within the bottle of m= 9 g, the variation in the pressure P
under the cork with the champagne temperature yis displayed
in Fig. 3. At the temperature of champagne tasting (usually
between 8 and 10 1C), the pressure within a typical 75 cL
champagne bottle is close to 5 bars (i.e.,510
5
Nm
2
).
2.3. The chemical composition of champagne
From the point of view of the chemist, champagne can indeed
be viewed as a multicomponent aqueous solution. The fine
chemical composition of a typical Champagne wine is reported
in Table 2.
5
Actually, gases like CO
2
undergo specific reactions
with water. Equilibrium is established between the dissolved
(CO
2
)
aq
and H
2
CO
3
, the carbonic acid:
(CO
2
)
aq
+H
2
O2H
2
CO
3
(5)
Moreover, carbonic acid is a weak acid that dissociates in two
steps:
Fig. 2 Henry’s law constant as a function of temperature (J)
(redrawn from Agabaliantz data
2
); the line is the best fit to
Agabaliantz data, drawn with the Van’t Hoff like eqn (3) and with
DH
diss
E24 800 J mol
1
.
Fig. 3 Pressure of gaseous CO
2
under the cork of a typical 75 cL
champagne bottle as a function of champagne temperature.
Table 1 Henry’s law constant for CO
2
in champagne as a function of
temperature, for a typical champagne with 12.5% (v/v) of ethanol and
10 g L
1
of sugars (compiled from the data by Agabaliantz
2
)
Temperature/1C
Henry’s law constant
k
H
/kg m
3
atm
1
0 2.98
1 2.88
2 2.78
3 2.68
4 2.59
5 2.49
6 2.41
7 2.32
8 2.23
9 2.16
10 2.07
11 2.00
12 1.93
13 1.86
14 1.79
15 1.73
16 1.67
17 1.60
18 1.54
19 1.48
20 1.44
21 1.40
22 1.34
23 1.29
24 1.25
25 1.21
2492 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
View Article Online
H
2
CO
3
+H
2
O2H
3
O
+
+ HCO
3
pK
a1
(at 25 1C) = 6.37 (6)
HCO
3
+H
2
O2H
3
O
+
+CO
32
pK
a2
(at 25 1C) = 10.25 (7)
However, as the pH of champagne and sparkling wines is
relatively low (in the order of 3.2), no carbonated species
(CO
32
, HCO
3
) should coexist with dissolved CO
2
. Recently,
the
13
C nuclear magnetic resonance (NMR) spectroscopy
technique was used as an unintrusive and non-destructive
method to determine the amount of CO
2
dissolved in closed
bottles of champagne and sparkling wines.
6
Different well-
separated peaks were recorded in a
13
C spectrum, as can be
seen in Fig. 4: (i) the quadruplet of CH
3
group of ethanol
appears at 17.9 ppm, (ii) the triplet of the CH
2
(–OH) group of
ethanol at 57.3 ppm, and (iii) the singlet of CO
2
appears at
124.4 ppm, thus confirming the absence of other carbonated
species (CO
32
, HCO
3
) in the liquid matrix (contrary to fizzy
waters for example, where pH values near neutrality enable the
above mentioned carbonated species to cohabit with
CO
2
-dissolved gas molecules).
2.4. Uncorking the bottle
Have you ever thought about the velocity reached by an
uncontrolled champagne cork popping out of a bottle?
Measurements conducted in our laboratory in Reims led to
typical velocities ranging from 50 to 60 km h
1
.
1
So, if it hits
someone in the eye, it could do some serious harm and
dramatically change the course of any romantic evening you
might have planned... When opening a bottle of champagne
(or carbonated beverage in general), everyone would have
already noticed the cloud of fog forming right above the bottle
neck (as wonderfully illustrated by the photograph displayed
in Fig. 5 taken by Jacques Honvault, a master of high-speed
photography). This cloud of fog is due to a significant drop in
temperature in the headspace below the champagne surface,
caused by the sudden gas expansion when the bottle is
uncorked. Actually, this sudden temperature drop is respon-
sible for the instantaneous condensation of water vapor into
the form of this characteristic cloud of fog. Assuming an
adiabatic expansion experienced by the gas volume of the
headspace (from about 5 atm to 1 atm), the corresponding
theoretical drop in temperature experienced by the gas volume
may easily be accessed by the following and well-known
relationship:
P
(1 G)
y
G
= constant (8)
where P,y, and Gare the pressure, temperature, and ratio of
specific heats of the gas volume experiencing adiabatic expan-
sion, respectively. With the ratio of specific heats for CO
2
Table 2 Average composition of a typical Champagne wine.
5
Typically, pH E3.2 and the ionic strength is 0.02 M
Compound Quantity
Ethanol E12.5% v/v
CO
2
10–12 g L
1
Glycerol E5gL
1
Tartaric acid E2.5 to 4 g L
1
Lactic acid E4gL
1
Sugars 10–50 g L
1
Proteins 5–10 mg L
1
Polysaccharides E200 mg L
1
Polyphenols E100 mg L
1
Amino acids 0.8–2 mg L
1
Volatile organic compounds (VOC) E700 mg L
1
Lipids E10 mg L
1
K
+
200–450 mg L
1
Ca
2+
60–120 mg L
1
Mg
2+
50–90 mg L
1
SO
42
E200 mg L
1
Cl
E10 mg L
1
Fig. 4
13
C spectrum recorded to measure the CO
2
concentration in a
typical Champagne wine;
6
it is clear that no carbonated species
(CO
32
, HCO
3
) coexist with dissolved CO
2
.
Fig. 5 Uncontrolled champagne cork popping out of a bottle; the
cloud of fog forming right above the bottle neck clearly appears.
(Photograph by Jacques Honvault.)
This journal is cThe Royal Society of Chemistry 2008 Chem.Soc.Rev., 2008, 37, 2490–2511 |2493
View Article Online
molecules being 1.3, an adiabatic expansion from about 5 atm
to 1 atm when uncorking the bottle corresponds to a theore-
tical drop in temperature close to 90 1C! No wonder traces of
water vapor immediately condensate into the form of a small
cloud.
In addition to this sudden temperature drop experienced by
gases from the headspace, the fall of CO
2
partial pressure
above the champagne surface linked with bottle uncorking
leads to a huge consequence concerning the thermodynamic
equilibrium of CO
2
-dissolved molecules. Since the partial
pressure of CO
2
falls above the champagne surface, the CO
2
dissolved in champagne is not in equilibrium any longer with
its partial pressure in the vapor phase. Champagne enters a
metastable state, i.e., it contains CO
2
molecules in excess in
comparison with what Henry’s law states. To recover a new
stable thermodynamic state corresponding to the partial
pressure of CO
2
molecules in the atmosphere (about only
3.5 10
4
atm), almost all the carbon dioxide molecules
dissolved in the champagne must escape. The champagne
becomes supersaturated with CO
2
. Before proceeding further,
it is important to define the supersaturating ratio, used for
quantifying CO
2
molecules in excess in a carbonated liquid.
The supersaturating ratio Sis defined as follows:
7
S¼cL
c0
1ð9Þ
where c
L
is the concentration of CO
2
in the liquid bulk, and c
0
is the equilibrium concentration of CO
2
corresponding to a
partial pressure of gaseous CO
2
of 1 atm.
As soon as S40, a supersaturated liquid enters a meta-
stable state and must degas to recover a supersaturating ratio
equal to zero. In the case of Champagne wines, just after
uncorking the bottle, c
L
is the equilibrium concentration of
CO
2
in the liquid bulk corresponding to a partial pressure of
CO
2
of about 5 atm. Because there is a strict proportionality
between the concentration of dissolved CO
2
and its partial
pressure in the vapor phase (as expressed by Henry’s law),
c
L
/c
0
E5. Therefore, just after uncorking the bottle, the
supersaturating ratio of champagne is approximately SE4,
and champagne must degas. Actually, there are two mechan-
isms for gas loss: (i) losses due to diffusion through the surface
of the liquid (invisible to the naked eye), and (ii) losses due to
bubbling (the so-called effervescence process). But, how and
where do all these bubbles form, or nucleate?
3. The bubble nucleation process
3.1. The critical radius required for bubble nucleation
Generally speaking, carbonated beverages are weakly super-
saturated with CO
2
-dissolved gas molecules. In weakly super-
saturated liquids such as champagne and sparkling wines,
bubbles do not just pop into existence ex nihilo. Actually, to
cluster into the form of bubbles, CO
2
-dissolved gas molecules
must cluster together and push their way through the liquid
molecules that are held together by Van der Waals attractive
forces. Bubble formation is therefore limited by an energy
barrier (for a complete review see the paper by Lugli and
Zerbetto
8
). This is the reason why in weakly supersaturated
liquids, bubble formation and growing require preexisting gas
cavities with radii of curvature large enough to overcome the
nucleation energy barrier and grow freely.
9,10
This critical
radius, denoted r*, can easily be accessed by using standard
thermodynamic arguments, or by using simple arguments
based on classical diffusion principles. The critical radius r*
of gas pockets required to enable bubble production in a
carbonated beverage is expressed as follows (see ref. 11 and
references therein),
r2g
P0Sð10Þ
where gis the surface tension of the liquid medium (in the
order of 50 mN m
1
in champagne and sparkling wines
5
), and
P
0
is the atmospheric pressure (P
0
E10
5
Nm
2
). At the
opening of a champagne bottle, because SE4, the critical
radius required to enable bubble nucleation is in the order of
0.25 mm.
Jones et al. made a classification of the broad range of
nucleation likely to be encountered in liquids supersaturated
with dissolved gas molecules.
9
Bubble formation from
preexisting gas cavities larger than the critical size is referred
to as non-classical heterogeneous bubble nucleation (type IV
bubble nucleation, following their nomenclature). Generally
speaking, effervescence in a glass of champagne or sparkling
wine may have two distinct origins. It can be ‘‘natural’’ or
‘‘artificial’’.
3.2. ‘‘Natural’’ bubble nucleation
Natural effervescence is related to the bubbling process from a
glass which has not experienced any specific surface treatment.
Closer inspection of such glasses poured with champagne and
sparkling wines revealed that most of the bubble nucleation
sites were found to be located on preexisting gas cavities
trapped inside hollow and roughly cylindrical cellulose-
fibre-made structures on the order of 100 mm long with a
cavity mouth of several micrometres (see Fig. 6).
11–14
The
hollow cavity (a kind of tiny channel within the fibres) where a
gas pocket is trapped during the pouring process is called the
lumen. It can be clearly noticed from Fig. 6 that the radii of
curvature of gas pockets trapped inside the fibre’s lumen are
Fig. 6 Three typical cellulose fibres adsorbed on the wall of a glass
poured with champagne; the gas pockets trapped inside the fibres
lumens and responsible for bubble formation clearly appear (bar =
50 mm). (Photographs by Ge
´rard Liger-Belair.)
2494 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
View Article Online
much higher than the above-mentioned critical radius r*.
Fibres probably adhere on the flute wall due to electrostatic
forces (especially if the glass or the flute is vigorously wiped by
a towel). Natural effervescence may also arise from gas
pockets trapped inside tartrate crystals precipitated on the
glass wall and resulting from the evaporation process after
rinsing the glass with tap water. Therefore, there is a
substantial variation concerning the ‘‘natural’’ effervescence
between flutes depending on how the flute was cleaned and
how and where it was left before serving.
The mechanism of bubble release from a fibre’s lumen has
already been described in recent papers.
14–17
In short, after
opening a bottle of champagne or sparkling wine, the thermo-
dynamic equilibrium of CO
2
molecules dissolved in the liquid
medium is broken. CO
2
-dissolved molecules become in excess
in comparison with what the liquid medium can withstand.
Therefore, CO
2
molecules will escape from the liquid medium
through every available gas/liquid interface to reach a vapor
phase. Actually, once the sparkling beverage is poured into a
glass, the tiny air pockets trapped inside the collection of fibres
adsorbed on the glass wall offer gas/liquid interfaces to CO
2
dissolved molecules, which cross the interface toward the gas
pockets. In turn, the gas pockets grow inside the fibres’
lumens. When a gas pocket reaches the tip of a fibre, a bubble
is ejected, but a portion of the gas pocket remains trapped
inside the fibre’s lumen, shrinks back to its initial position, and
the cycle starts again until bubble production stops through
lack of dissolved gas molecules (see the very typical time
sequence displayed in Fig. 7). The fibre displayed in Fig. 7 is
a sort of textbook case, the behaviour of which was recently
understood and modelled.
14,16
3.3. Entrapping an air pocket within a fibre
Cellulose fibres are in the form of hollow tubes of several
hundreds of micrometres long and with a cavity mouth of
several micrometres wide. The fibre wall section consists of
densely packed cellulose micro fibrils, with a preferential
orientation along the fibre axis. Cellulose micro fibrils consist
of glucose units bounded in a b-conformation favouring
straight polymer chains. The different structural levels of a
cellulose fibre are presented in Fig. 8. For a current review on
the molecular and supramolecular structures of cellulose, see
the article by O’Sullivan
18
and references therein.
From the physics point of view, cellulose fibres can indeed
be considered as tiny roughly cylindrical capillary tubes of
radius rand length h. Consequently, a wetting liquid placed
into contact with this highly hydrophilic material penetrates it
by capillary action. Actually, in capillaries with radii much
smaller than the capillary length, gravity may be neglected.
Therefore, with Zbeing the viscosity of the liquid phase, g
being the surface tension of the liquid, zbeing the distance of
Fig. 7 Time-sequence illustrating one period of the cycle of bubble
production from the lumen of a typical hollow cellulose fibre adsorbed
on the wall of a glass poured with champagne; from frame 1 to frame
5, the time interval between successive frames is about 200 ms, but
from frame 5 to frame 6, the time interval is only 1 ms (bar = 50 mm).
(Photographs by Ce
´dric Voisin and Ge
´rard Liger-Belair.)
Fig. 8 The different structural levels of a typical cellulose fibre; the
fibre wall consists of closely packed cellulose micro fibrils oriented
mainly in the direction of the fibre.
18
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penetration at time t, and ythe effective contact angle between
the liquid and the capillary wall, the overall balance of forces
on the liquid in the capillary may be expressed as,
rzd2z
dt2þdz
dt

2
"#
¼2gcos y
r8Zz
r2
dz
dtð11Þ
The left-hand side of eqn (11) is related to the liquid inertia,
whereas both terms in the right-hand side are related to
capillarity (the driving force), and viscous resistance, respec-
tively. Under steady state conditions, capillarity is balanced by
the viscous drag of the liquid, and the famous Lucas–
Washburn equation can be derived:
19,20
z2¼rgcos y
2Ztð12Þ
Let’s imagine a liquid edge spreading with a velocity valong
a solid surface where cellulose fibres are adsorbed. This is
basically what happens when you fill a glass with a liquid.
Actually, a liquid edge progressively advances along the
vertical glass wall at a velocity vin the order of several cm
s
1
. As soon as the wetting liquid gets in touch with the fibre,
some liquid progressively penetrates and fills the fibre’s lumen
by capillary rise. Finally, a gas pocket may be trapped within
the fibre if the time ttaken by the liquid to completely fill the
lumen by capillary action is greater than the characteristic time
Ttaken by the liquid edge to completely submerge the fibre
inside the liquid (see the scheme displayed in Fig. 9).
By retrieving eqn (12) with the characteristic fibre’s para-
meters defined in Fig. 9, the characteristic time required to
completely fill the fibre’s lumen by capillary action may be
expressed as,
t¼2Zh2
rgcos yð13Þ
Considering a fibre with a length h, inclined by an angle awith
regard to the liquid edge advancing over it at a velocity v, leads
to the following time required for the fibre to be completely
submerged:
T¼hsin a
vð14Þ
The condition of gas entrapment inside the fibre therefore is
expressed as t4T,i.e.,
2Zh2
rgcos y4hsin a
vð15Þ
Because cellulose is a highly hydrophilic material, the contact
angle of an aqueous liquid on it is relatively small (about 301
with pure water). Consequently, cos yE1. Finally, the
condition of entrapment may be rewritten as follows,
h
rsin a4g
2Zvð16Þ
with the geometric parameters of the cellulose fibre lying on
the left-hand side of eqn (16), and the liquid parameters lying
on the right-hand side of eqn (16).
The entrapment of an air pocket inside the lumen of a fibre
during the filling of a glass is therefore favoured by the
following conditions, depending on both fibre and liquid
parameters: (i) as elongated fibres as possible (hlong), (ii)
small lumen radii r, (iii) fibres as horizontal as possible with
regard to the liquid edge (i.e., sin asmall), (iv) liquids with a
small surface tension g, (v) and a high viscosity Z, and finally
(vi) a high velocity for the liquid edge advancing along the
glass wall. It is worth noting that both conditions (iv) and (v)
imply that hydroalcoholic carbonated beverages are more
favourable than fizzy waters to entrap air pockets inside
cellulose fibres during the pouring process. Actually, the
surface tension of champagne and beer is in the order of
50 mN m
1
(i.e., about 20 mN m
1
less than the surface
tension of pure water), and their dynamic viscosity is about
50% higher than that of pure water.
3.4. Modelling the repetitive bubble nucleation from a cellulose
fibre
As seen in Fig. 7, the whole process leading to the production
of a bubble from a cellulose fibre’s tip can be coarsely divided
in two main steps: (i) the growth of the gas pocket trapped
inside the fibre’s lumen (from frame 1 to frame 5), and (ii) the
bubble detachment as the gas pocket reaches the fibre’s tip
(from frame 5 to frame 6). Actually, it is clear from the
numerous close-up time sequences taken with the high-speed
video camera that the time scale of the bubble detachment is
always very small (E1 ms) compared with the relatively slow
growth of the gas pocket (several tens to several hundreds of
ms). Therefore, the whole cycle of bubble production seems to
be largely governed by the growth of the gas pocket trapped
inside the fibre’s lumen. This tiny gas pocket was modelled as a
slug-bubble growing trapped inside an ideal cylindrical micro
channel and being fed with CO
2
-dissolved molecules diffusing
(i) directly from both ends of the gas pocket, and (ii) through
the fibre wall, which consists of closely packed cellulose micro
fibrils oriented mainly in the direction of the fibre.
21
A scheme
is displayed in Fig. 10, where the geometrical parameters of the
tiny gas pocket growing by diffusion are defined.
Fig. 9 From the physics point of view, a fibre may be seen as a tiny
capillary tube which gets invaded by a wetting liquid placed into
contact with one of the fibre’s tip; vis the velocity of the liquid edge
advancing over the fibre, and uis the velocity at which the meniscus
advances inside the fibre’s lumen by capillary action.
2496 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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Taking into account the diffusion of CO
2
-dissolved mole-
cules from the liquid bulk to the gas pocket via the two ways
defined above, the growth of this gas pocket with time twas
linked with both liquid and fibre parameters as follows:
14
zðtÞðz0þAtÞexpðt=tÞAt
with t¼ðPþ2g=rÞrl
2<yD?Dc;and A¼4<yD0Dc
ðPþ2g=rÞl
8
<
:
ð17Þ
where zis the length of the gas pocket, z
0
is the initial length of
the gas pocket before it starts its growth through the lumen, at
each cycle of bubble production (see for example frame 1 and
frame 6 in Fig. 7), Pis the ambient pressure, D
0
is the diffusion
coefficient of CO
2
-dissolved molecules in the liquid bulk, D
>
is
the diffusion coefficient of CO
2
-dissolved molecules through the
fibre wall (and therefore perpendicular to the cellulose micro
fibrils), Dc=c
L
c
B
=c
L
k
H
P
B
=c
L
k
H
(P
0
+2g/r)isthe
difference in CO
2
-dissolved concentrations between the liquid
bulk and the close vicinity of the gas pocket surface in equili-
brium with the gaseous CO
2
in the gas pocket, and lis the
boundary layer thickness where a linear gradient of
CO
2
-dissolved concentration is assumed.
In a previous work, the transversal diffusion coefficient D
>
of CO
2
molecules through the fibre wall was approached and
properly bounded by D
>
/D
0
E0.1 and D
>
/D
0
E0.3.
21
For
modelling purposes, an intermediate value of about D
>
E
0.2D
0
was proposed and will be used hereafter.
21
The whole
cycle of bubble production being largely governed by the
growth of the gas pocket trapped inside the fibre’s lumen,
the period of bubble formation from a single cellulose fibre is
therefore equal to the total time Trequired by the tiny gas
pocket to grow from its initial length, denoted z
0
, to its final
length, denoted z
f
, as it reaches the fibre’s tip (see frame 5 in
Fig. 7). By retrieving eqn (17), it is therefore possible to access
the frequency of bubble formation ffrom a single fibre as
follows:
f1
T2<yD?Dc
rlðP0þ2g=rÞln½ðzfþ10rÞ=ðz0þ10rÞ ð18Þ
To go further on with the dependence of the bubbling
frequency on both liquid and fibre parameters, we can replace
in eqn (18) the diffusion coefficient D
0
by its theoretical
expression approached through the well-known Stokes–
Einstein equation (D
0
Ek
B
y/6pZd), k
B
being the Boltzmann
constant (1.38 10
23
JK
1
), and dbeing the charac-
teristic size of the CO
2
molecule’s hydrodynamic radius
(dE10
10
m). By replacing in eqn (18) each parameter by
its theoretical expression and each constant by its numerical
value, the variation of the bubbling frequency as a function of
the various pertinent parameters involved may be rewritten as
follows (in the MKSA system):
f2:41014 y2½cLkHðPþ2g=rÞ
ZrðPþ2g=rÞlln½ðzfþ10rÞ=ðz0þ10rÞ
ð19Þ
The boundary layer thickness lwas indirectly approached in a
recent paper and found to be in the order of 20 mm.
14
Finally,
let us apply eqn (19) to the standard textbook case fibre
displayed in Fig. 7 and modelled in Fig. 10 (i.e.,rE5mm,
z
0
E20 mm and z
f
E100 mm). Eqn (19) may therefore be
rewritten as follows, by replacing the fibre’s parameters r,z
0
,z
f
and lby their numerical values:
f5:2108y2½cLkHðPþ0:2Þ
ZðPþ0:2Þð20Þ
In the latter expression, c
L
is expressed in g L
1
,k
H
in
gL
1
atm
1
,Pin atm, and Zin kg m
1
s
1
, to fit the
standards used in enology.
We will discuss the relative influence of the following
parameters on the average bubbling frequency: (i) the
concentration c
L
of CO
2
-dissolved molecules, (ii) the liquid
temperature y, and (iii) the ambient pressure P.
(i) Following eqn (20), every other parameter being
constant, the dependence of the theoretical average bubbling
frequency fon the CO
2
-dissolved concentration c
L
is in the
form f=ac
L
b. By use of a high-speed video camera fitted
with a microscope objective, a few cellulose fibres acting as
bubble nucleation sites on the wall of a glass poured with
champagne were followed over time during the whole gas
discharging process (which may last up to several hours). This
method is developed in minute details in ref. 16. The depen-
dence of the experimental bubbling frequency f
exp
with c
L
was
found to follow a linear-like c
L
dependence, as expected from
the model developed above. Therefore, the frequency of
bubble formation from a given nucleation site is found to
progressively decrease with time, because the concentration c
L
Fig. 10 Real gas pocket trapped within the lumen of a cellulose fibre
acting as a bubble nucleation site in a glass poured with champagne
(A), modelled as a slug-bubble trapped inside an ideal cylindrical
micro channel and being fed with CO
2
-dissolved molecules diffusing,
(i) directly from the liquid bulk through both ends of the gas pocket,
and (ii) through the wall of the micro channel (B) (bar = 50 mm).
This journal is cThe Royal Society of Chemistry 2008 Chem.Soc.Rev., 2008, 37, 2490–2511 |2497
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of CO
2
-dissolved molecules progressively decreases as CO
2
continuously desorbs from the champagne matrix. Further-
more, it is worth noting that the bubbling frequency of a given
nucleation site vanishes (i.e., the bubble release ceases, f-0
bubble s
1
), although the CO
2
-dissolved concentration c
L
remains higher than a critical value, as shown in ref. 16.
Actually, following both Laplace’s and Henry’s laws, the
curvature rof the CO
2
pocket trapped inside the fibre’s lumen
induces in the close vicinity of the trapped CO
2
pocket a
concentration c
B
of CO
2
-dissolved molecules in the order of
k
H
(P
0
+2g/r). Consequently, as soon as the concentration of
CO
2
-dissolved in the liquid bulk reaches a critical value c*
L
=
c
B
Ek
H
(P
0
+2g/r), the diffusion toward the gas pocket ceases
and the given nucleation site stops releasing bubbles (simply
because Dc, the driving force of diffusion, vanishes as
c
L
Ec*
L
). Let us apply the latter condition to the charac-
teristic radius of a cellulose fibre (rE5mm). At 10 1C, the
critical concentration c*
L
below which bubble release becomes
impossible is therefore:
c*
L
Ek
H
(P
0
+2g/r)
E2.07 10
5
(10
5
+2510
2
/5 10
6
)
E2.5 g L
1
(21)
(ii) The dependence of the bubbling frequency on the liquid
temperature is much more difficult to test experimentally in
real consuming conditions. Actually, we needed time to
decrease or increase the liquid temperature, and we found no
satisfying possibility of modifying the liquid temperature
without significantly losing CO
2
-dissolved molecules which
continuously desorb from the supersaturated liquid matrix
due to diffusion through the liquid surface and due to
bubbling from the numerous nucleation sites found in the
flute. We will nevertheless discuss the theoretical influence of
the liquid temperature by retrieving eqn (20). In eqn (20), the
temperature directly appears as y
2
, but the Henry’s law
constant k
H
, as well as the champagne dynamic viscosity Z
are strongly temperature-dependent.
22
Increasing the liquid
temperature by 10 K (let us say from 278 to 288 K, which is
approximately the range of champagne tasting temperatures)
increases the theoretical bubbling frequency by about 50%.
For the fibre displayed in Fig. 7 (rE5mm, and z
0
E20 mm
and z
f
E100 mm) and with c
L
E12 g L
1
, the theoretical
temperature dependence of the bubbling frequency is
displayed in Fig. 11.
(iii) Increasing or decreasing the ambient pressure Palso
significantly modifies the corresponding average bubbling
frequency f. For the fibre displayed in Fig. 7 (rE5mm,
z
0
E20 mm and z
f
E100 mm) and with c
L
E12 g L
1
, the
theoretical pressure dependence of the bubbling frequency is
displayed in Fig. 12. Reducing the ambient pressure to only
0.3 atm (on the top of Mount Everest for example) would
increase the average bubbling frequency by a factor of almost
3. This is basically the same phenomenon which is responsible
for gas embolism in divers who have breathed high-pressure
air under water if they resurface too quickly. Inversely,
increasing the ambient pressure to 2 atm decreases the average
bubbling frequency by a factor of about 2 compared to that at
sea level.
3.5. Evidence for bubbling instabilities
The regular and clockwork release of bubbles from a cellulose
fibre is indeed the most common and usual way of blowing
bubbles, but cellulose fibres were recently found to experience
other various and sometimes very complex rhythmical
bubbling regimes.
23,24
After pouring champagne into a flute,
thorough examination (even by the naked eye) of the bubble
trains rising toward the liquid surface recently revealed a
curious and quite unexpected phenomenon. As time proceeds,
during the gas discharging process from the liquid matrix,
some of the bubble trains showed abrupt transitions during
Fig. 11 Theoretical dependence of the bubbling frequency fon
temperature y, as expected from the model displayed in eqn (20), in
the range of usual champagne-tasting temperatures (from 5 to 15 1C),
and for the textbook case fibre displayed in Fig. 7.
Fig. 12 Theoretical dependence of the bubbling frequency fon the
ambient pressure P(at 20 1C), as expected from the model displayed in
eqn (20) for the textbook case fibre displayed in Fig. 7.
2498 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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the repetitive and rhythmical production of bubbles. Visually
speaking, the macroscopic pertinent parameter which is
characteristic from the successive bubbling regimes is the
interbubble distance between the successive bubbles of a given
bubble train. In Fig. 13, micrographs of a bubble train in its
successive rhythmical bubbling regimes while degassing are
displayed. The duration of a given bubbling regime may vary
from a few seconds to several minutes. In frame (a), bubbles
are seen to be generated from a period-2 bubbling regime
which is characterized by the fact that two successive bubbles
rise in pairs. Then, the bubbling regime suddenly changes, and
a multiperiodic bubbling regime arises which is displayed in
frame (b). Later, in frame (c), clockwork bubbling in period-1
occurs where the distance between two successive bubbles
increases monotonically as they rise, and so on. This nuclea-
tion site experienced other various bubbling regimes during its
life, until it finally ended in a clockwork period-1 bubbling
regime presented in frame (g).
Such a curious and unexpected observation raises the
following question: what is/are the mechanism(s) responsible
for the transitions between the different bubbling regimes? To
better identify the fine mechanisms behind this rhythmical
production of bubbles from a few nucleation sites, some of
them experiencing bubbling transitions were filmed in situ by
use of a high-speed digital video camera. Two time sequences
are displayed in Fig. 14 and 15, where bubbles are blown in a
period-2 and in a very erratic way, respectively. The lumen of
the cellulose fibre displayed in Fig. 14 presents only one gas
pocket, whereas the fibre’s lumen displayed in Fig. 15 clearly
shows two gas pockets periodically touching and connecting
themselves through a tiny gas bridge (see frames 3 and 4 of
Fig. 15). The micrometric gas bridge connecting the two gas
pockets and disturbing the overall production of bubbles is
enlarged in Fig. 16. This tiny gas bridge is a likely source of
bubbling instabilities. Recently, a model was built which takes
into account the coupling between the bubbling frequency and
the frequency of the single gas pocket which oscillates while
trapped inside the fibre’s lumen (as in Fig. 14, for example).
The previously published data showed a general rule
concerning bubbling instabilities arising from some fibres
Fig. 13 Time sequence (from left to right) showing a bubble nuclea-
tion site at the bottom of a flute poured with champagne blowing
bubbles through different and well-established bubbling regimes
(bar = 1 mm). (Photographs by Ge
´rard Liger-Belair.)
Fig. 14 Close-up time sequence illustrating a tiny cellulose fibre
acting as a bubble nucleation site in its period-2 bubbling regime
(i.e., bubbles are blown by pairs); the time interval between two
successive frames is 40 ms (bar = 50 mm). (Photographs by Ge
´rard
Liger-Belair.)
Fig. 15 Two gas pockets are interacting in the lumen of this cellulose fibre, thus disturbing the periodicity of the bubbling regime; the black
arrows point to the various gas pockets interacting; the time interval between two successive frames is 10 ms (bar = 100 mm). (Photographs by
Ge
´rard Liger-Belair.)
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presenting just one trapped gas pocket. In this previous paper,
the successive rhythmical bubbling regimes followed the
so-called ‘‘period-adding scenario’’.
23
Nevertheless, this pre-
viously published scenario does not fit the various ways of
blowing bubbles from more complex cellulose fibres able to
entrap numerous gas pockets as shown in Fig. 15. Numerous
fibres, such as those shown in the present paper, presented a
sequence of various bubbling instabilities which is not
reproduced by our previous model. A huge collection of
successive rhythmical bubbling regimes has already been
observed, and the highest recorded periodicity was observed
for a fibre presenting a period-12 bubbling regime.
24
At the
moment, we cannot find any general rule with fibres presenting
numerous gas pockets interacting together, but the close up
observation and the discovery of the multiple gas pockets
interacting together is considered as a step toward a deeper
understanding of the successive rhythmical bubbling regimes
arising from complex fibres. The huge diversity in our
observations, in terms of the various successive bubbling
regimes seems to be directly linked with the ‘‘natural’’ varia-
bility of cellulose fibres (in terms of size, lumen diameter, inner
wall properties...).
3.6. A word about fliers
Some of the particles acting as bubble nucleation sites (most of
them including cellulose fibres) may detach from the glass wall
to finally get completely immersed in the champagne bulk.
Particles detached from the glass wall are nevertheless still
active (in terms of bubbling capacity) provided that a gas
pocket with a radius of curvature larger than the critical radius
has been trapped inside them. Those particles immersed in the
champagne bulk produce easily-recognizable bubble trains,
which seem to dance erratically inside the glass during
champagne tasting. Those particles in suspension in
champagne glasses are called fliers (due to their often complex
and circling trajectories in the champagne bulk). Fliers are
indeed a significant source of bubbles in glasses poured with
champagne. The photograph of a typical flute poured with
champagne displayed in Fig. 1a shows a detail in Fig. 1b,
where some fliers are recognizable. Fliers undoubtedly catch
the eyes of champagne-tasters, who also often are fine
observers. The dynamics of fliers was recently investigated
by use of long exposure time photography and laser
tomography techniques.
25
By use of long exposure time
photography, the trajectories of bubbles released by fliers were
found to leave very elegant and characteristic ‘‘prints’’ as they
crossed a section of champagne illuminated with a 1 mm-thick
laser sheet (see for example the tomography displayed in
Fig. 17). Because the flier immersed in the champagne bulk
is constantly moving, trajectories of bubbles released
during the 1 s exposure-time photography do not superimpose
on each other. Therefore, the print left by a flier which
crosses the laser sheet during the exposure time of the digital
camera is a typical multiple filaments structure, each filament
materializing the trajectory of a single rising bubble.
3.7. ‘‘Artificial’’ bubble nucleation
Artificial effervescence is related to bubbles nucleated from
glasses with imperfections done intentionally by the
glassmaker to promote or to eventually replace a deficit of
‘‘natural’’ nucleation sites. Actually, it has been known for
decades that bubbles may arise from microscratches on the
glass wall.
26,27
Those microscratches are geometrically able to
Fig. 17 Characteristic print left by the bubbles released from a flier
along its 1 s-path through a 2 mm-thick laser sheet which crosses a
flute poured with champagne; under laser illumination, the print left
by the flier during the 1 s-exposure time of a digital camera is a typical
multiple filaments structure, each filament materializing the trajectory
of a single bubble released from the flier (bar = 5 mm). (Photograph
by G. Liger-Belair, F. Beaumont and G. Polidori.)
Fig. 16 Detail of the cellulose fibre displayed in Fig. 15, which clearly
shows the establishment of a micrometric gas bridge between the two
gas pockets trapped inside the fibre’s lumen (bar = 10 mm). (Photo-
graph by Ge
´rard Liger-Belair.)
2500 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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trap tiny air pockets when champagne is poured into the glass
(as cellulose fibres do). Those microscratches on a glass can
be done by essentially two techniques: sandblast or laser
engraving. Nevertheless, effervescence produced from
scratches intentionally done by the glassmaker does not
resemble that arising from tiny individual cellulose fibres. A
rendering of such micro scratches releasing bubbles at the
bottom of a champagne flute is displayed in Fig. 18. It is worth
noting that the repetitive bubbling process arising from
artificial bubble nucleation is much more vigorous and chaotic
than the bubbling process from tiny cellulose fibres. Glasses
engraved at their bottom are thus indeed easily recognizable,
with a characteristic bubble column rising on their axis of
symmetry.
28
Effervescence promoted by engraved glasses is
indeed visually quite different than that naturally promoted by
cellulose fibres, but the difference is also suspected to go far
beyond the solely aesthetical (and rather subjective) point of
view. Differences are strongly suspected concerning the
kinetics of CO
2
and flavour release throughout champagne
tasting (see section 4.3).
4. Bubble growth, bubble rise, and mixing flow
patterns found in champagne glasses
4.1. Bubble growth and rise
After being born in micrometric gas pockets trapped inside
impurities of the glass wall, bubbles rise toward the liquid
surface due to their own buoyancy. While rising, they continue
to grow in size by continuously absorbing carbon dioxide
molecules dissolved in the liquid ‘‘matrix’’, as is clearly
illustrated in the photograph displayed in Fig. 19. Growing
bubbles thus continuously accelerate along their way through
the champagne. This continuous acceleration is also betrayed,
in high-speed photographs, by the continuously increasing
spacing ebetween the successive bubbles of a given bubble
train (see Fig. 19 for example).
The clockwork repetitive bubble production from
nucleation sites was used to develop a simple set-up which
consists of the association of a photo camera with a
stroboscopic light to follow the motion of bubbles.
12
It was
found that the bubble radius Rof bubbles increases at a
constant rate k=dR/dt, as they rise toward the liquid surface.
Thus,
R(t)=R
0
+kt (22)
where R
0
is the bubble radius as it detaches from the nuclea-
tion site. R
0
is of the same order of magnitude as the radius of
the mouth of the cellulose fibre which acts as the nucleation
site, i.e., around 5 to 10 mm.
11–13
Three minutes after pouring, experiments conducted with
champagne and sparkling wines led to growth rates kranging
between approximately 350 and 400 mms
1
,at201C.
11
Experiments were also performed with the growth rates of
bubbles rising in beer glasses. In beer, three minutes after
pouring, bubble growth rates were found to lay around
100–150 mms
1
,i.e., about three times less than those in
champagne and sparkling wines.
12
Fig. 18 At the bottom of this flute, on its axis of symmetry, the
glassmaker has engraved a small ring (done with adjoining laser beam
impacts) (a); single laser beam impact as viewed through a scanning
electron microscope (bar = 100 mm) (b); effervescence in this flute is
promoted from these ‘‘artificial’’ micro scratches in the form of a
characteristic and easily recognizable vertical bubbles column rising on
its axis of symmetry (bar = 1 mm) (Photographs by G. Polidori and F.
Beaumont) (c).
Fig. 19 A characteristic bubble train promoted by the repetitive
bubble formation process from a single cellulose fibre; bubbles are
clearly seen growing during their way up (bar = 1 mm). (Photograph
by Ge
´rard Liger-Belair.)
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The growth rate kof bubbles rising in champagne and beer
was also modelled and linked with some physicochemical
properties of liquids as follows (in the MKSA system):
12
k¼dR
dt0:63 <y
PB
D2=3
0
2arg
9Z

1=3
Dcð23Þ
where yis the liquid temperature, <is the ideal gas constant, P
B
is
the pressure inside the rising bubble, D
0
is the diffusion coefficient
of CO
2
molecules through the liquid bulk, rand Zare respectively
the liquid density and viscosity, gis the acceleration due to gravity,
ais a numerical pre-factor close to 0.7 for champagne and
sparkling wine bubbles,
11
his the distance travelled by the bubble
from its nucleation site, and Dc(the driving force responsible for
the diffusion of CO
2
into the rising bubble) is the difference in
dissolved-CO
2
concentrations between the liquid bulk and the
close vicinity of the bubble surface which is in equilibrium with the
gaseous CO
2
in the rising bubble (see Fig. 20).
Strictly speaking, the pressure P
B
inside the rising bubble is
the sum of three terms: (i) the atmospheric pressure P
0
, (ii) the
hydrostatic pressure rgH, and (iii) the Laplace pressure 2g/R,
originating from the bubble’s curvature. His the depth at
which the bubble rises, and gis the surface tension of the liquid
medium. However, with Hvarying from several millimetres to
several centimetres, the surface tension of champagne being in
the order of 50 mN m
1
,
5
and bubbles’ radii varying from
several tens to several hundreds of micrometres, the contribu-
tion of both hydrostatic and Laplace pressures are clearly
negligible in terms of the atmospheric pressure P
0
.
Let us test the applicability of eqn (23) in the case of rising and
expanding champagne bubbles at 20 1C. By using known values
of rand Zin champagne,
12
a=0.7,D
0
E1.4 10
9
m
2
s
1
(as
measured by nuclear magnetic resonance
29
), and the difference
in CO
2
concentrations between the liquid bulk and the close
vicinity of the bubble surface DcE10gL
1
E227 mol m
3
,
one finds,
k0:63 8:31 293
105ð1:4109Þ2=3
20:71039:8
91:5103

1=3
193
430 mms
1
which is in very good accordance with the order of magnitude of
observed growth rates.
11,12
These experimental observations about the growth and rise
of bubbles were first done by Shafer and Zare with bubbles
rising and growing in a glass of beer.
30
They were also very
recently confirmed by Zhang and Xu, who proposed a model
for the growth rate of rising bubbles in both champagne and
beer.
31
4.2. Average bubble size
Because champagne and sparkling wine tasters are often
concerned with the size of bubbles formed in the wine
(a proverb says that the smaller the bubbles, the better the
wine), much attention was paid recently to model the average
size of ascending bubbles. Actually, the final average size of
ascending bubbles is the result of a combination between their
growth rate and their ascending velocity. Recent calculations,
based on mass transfer equations, linked the final average
bubble size with various physicochemical and geometrical
parameters.
3,22
The following dependence of the ascending
bubble radius Ron some of the liquid parameters was derived
(in the MKSA system):
R1:24 9Z
2arg

2=9<y
PB

1=3
D2=9
0ðDcÞ1=3h1=3ð24Þ
Minute details about the exact determination of eqn (24) can
be found in ref. 22. To go further with the dependence of
bubbles’ radii on some few parameters, we can also replace in
eqn (24) the diffusion coefficient D
0
by its theoretical
expression approached through the well-known Stokes–
Einstein equation (D
0
Ek
B
y/6pZd). The following relation-
ship expressed in the MKSA system was thus obtained:
Rðh;y;...Þ2:53kB
4par

2=91
rg

2=91
P0

1=3
y5=9ðcLcBÞ1=3h1=3
ð25Þ
It is worth noting that the dependence of the bubble size on the
liquid viscosity vanishes. Finally, by replacing in eqn (25), k
B
,
a, and dby their known numerical values, and by developing
c
B
as k
H
P
0
, one obtains:
R2:7103y5=91
rg

2=9cLkHP0
P0

1=3
h1=3ð26Þ
Otherwise, because the liquid density rdoes not significantly
vary from one champagne to another (and even from one
carbonated beverage to another), we will discuss and put the
accent on the influence of the following parameters on the
bubble size: (i) the travelled distance h, (ii) the liquid tempera-
ture y, (iii) the gravity acceleration g, (iv) the ambient pressure
P
0
, and (v) the carbon dioxide content c
L
.
Fig. 20 Carbon dioxide concentrations in the close vicinity of the
CO
2
bubble surface.
2502 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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(i) The longer the travelled distance h, the larger the bubble
size. This dependence of the bubble size on its travelled
distance through the liquid means that, during champagne
tasting, the average bubble size at the champagne surface
varies from one glass to another. In a narrow flute, for
example, the level of champagne poured is about three times
higher than that in a typical coupe (with a shallower bowl and
a much wider aperture). Therefore, the average bubble
diameter in the flute will be larger than that in the coupe by
a factor of about R
flute
/R
coupe
E3
1/3
E1.45 (i.e., bubbles
about three times larger in volume!).
(ii) In eqn (26), the temperature appears directly as y
5/9
, but
we should not forget that the Henry’s law constant k
H
is also
strongly temperature-dependent (see Fig. 2) and conveniently
expressed by the Van’t Hoff eqn (3). The temperature being
expressed in K, the temperature dependence of the bubble size
is nevertheless quite weak. Increasing the liquid temperature
by 10 K (let’s say from 278 to 288 K, which is approximately
the range of champagne tasting temperature) makes bubbles
grow only about 5–6% in diameter.
(iii) The gravity acceleration which is the driving force
behind the bubble rise (through buoyancy) also plays a quite
important role in the final bubble size. This could indeed be
easily evidenced during a parabolic flight where the accelera-
tion changes from micro-gravity (close to zero g) to macro-
gravity (up to 1.8 g). On the Moon for example, where the
gravity is about 1/6 the gravity on Earth, the average bubble
size would increase by a factor of about g
Moon
/g
Earth
E
6
2/9
E1.49 (i.e., bubbles almost 50% larger in diameter and
therefore more than 3 times larger in volume).
(iv) The pressure inside the rising bubble is equivalent to the
ambient pressure P
0
(for the reasons detailed in the section
above). Usually, at sea level, this pressure is equivalent to
1 atm (or 10
5
Nm
2
). Reducing the atmospheric pressure to
only 0.3 atm (on the top of Mount Everest, for example)
would increase the average bubble diameter by about 55%
(and therefore by a factor of almost 4 in volume). This is
basically the same phenomenon which is responsible for gas
embolism in divers who have breathed high-pressure air under
water if they resurface too quickly.
(v) The carbon dioxide content of the liquid medium c
L
also
influences the final average bubble size. This is the main reason
why bubbles in beer are significantly smaller than bubbles in
champagne and sparkling wines. Actually, the carbon dioxide
content in beers may classically vary from about 4 g L
1
to
7gL
1
, whereas the carbon dioxide content in champagne and
sparkling wines may vary from 10 g L
1
up to 12 g L
1
(i.e.,
c
L
is approximately 2 times higher in champagne than in beer).
Reducing c
L
by a factor 2 in eqn (26) would decrease the
theoretical average bubble size by about 40% (thus leading to
bubbles almost 5 times smaller in volume). The two
photographs displayed in Fig. 21 illustrate the significant
difference in bubble size between a standard commercial
champagne and a standard commercial beer, both showing
very typical bubbling behaviour.
Moreover, after pouring champagne into a flute, due to
bubbling and diffusion through the surface of champagne,
CO
2
molecules progressively escape from the liquid medium.
Subsequently, the dissolved carbon dioxide content c
L
in the
liquid medium progressively decreases. Therefore, as time
proceeds during champagne tasting, the average bubble size
at the liquid surface progressively decreases, as can be clearly
seen in the sequence displayed in Fig. 22.
Fig. 21 Three minutes after pouring, bubbles rising in a glass of beer
(a) show diameters much lower than those of bubbles rising in a flute
poured with champagne (b) (bar = 1 mm); the very significant
difference between the bubble size in champagne and beer is mainly
due to amounts of dissolved-CO
2
about two times higher in
champagne than in beer. (Photographs by Ge
´rard Liger-Belair.)
Fig. 22 Time sequence showing successive top views of a flute poured
with champagne and followed as time proceeds; (a) immediately after
pouring, (b) 3 min after pouring, (c) 10 min after pouring, and (d)
25 min after pouring; it clearly appears that the average bubble size
decreases as time proceeds, as well as the average number of floating
bubbles. (Photographs by Ge
´rard Liger-Belair.)
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4.3. Evidence for flow patterns, and their likely impact on
champagne tasting
During champagne or sparkling wine tasting, consumers
certainly pay attention to the continuous flow of ascending
bubbles (often even before smelling and tasting the wine).
Ascending bubbles are indeed visually appealing, but in the
case of champagne tasting, their role is suspected to go far
beyond the solely aesthetical point of view. Actually, at the
bubble scale, the lower part of a rising bubble is a low pressure
area which literally attracts the fluid molecules around (see
Fig. 23). A rising bubble is thus able to drain some fluid along
its path toward the free surface. The huge number of bubbles
released from the numerous nucleation sites found in a typical
champagne glass (in the order of several hundreds of bubbles
released per second during the first minutes of champagne
tasting) is therefore able to set the whole liquid bulk in motion.
Very recently, it was demonstrated that ascending bubbles
act like many swirling motion generators in champagne
glasses.
28,32
Together with Professor Guillaume Polidori and
Fabien Beaumont from Reims University, laser tomography
techniques were used in order to visualize, as accurately as
possible, the flow patterns induced by the continuous flow of
ascending bubbles in flutes poured with champagne. The
principle of the experiment is to generate a 2 mm-thick laser
sheet, built from a multi-line argon laser source (INNOVA
70C–2W) centred on the 514 nm wavelength. The 2 mm-thick
laser sheet crosses the plane of symmetry of a champagne
glass. Before pouring champagne into the glass, the
champagne was seeded with tiny and roughly spherical
particles (called Rilsan
s
particles). Rilsan particles are poly-
meric materials which exhibit a high degree of reflectivity with
regard to the laser wavelength and are therefore able to diffuse
the laser light as they cross the 2 mm-thick laser sheet. Rilsan
particles are neutrally buoyant (75 mmodiameter o150 mm;
r= 1.06 g cm
3
). Moreover, Rilsan particles were found to be
completely neutral with regard to bubble formation (this was
definitely a crucial condition for the feasibility of the work).
Classical long exposure time photography of the laser sheet
was used in order to follow the motion of Rilsan particles, thus
freezing the flow patterns inside the fluid section crossed by the
laser sheet. Trajectories of convection currents in champagne
glasses were therefore made visible by numerous streaks of
light left by the Rilsan particles along their path through the
laser sheet. A photograph of the optical workbench used to
capture the champagne flow patterns is displayed in Fig. 24. In
Fig. 24, the laser sheet boundaries are made visible by solid
blue lines.
The stability of flow patterns was investigated in flutes
showing natural as well as artificial effervescence, throughout
the first fifteen minutes after pouring. Both engravement
Fig. 23 A rising bubble is able to drain some fluid along its path
through the champagne bulk.
Fig. 24 Photograph of the optical workbench used to capture the
champagne flow patterns; the laser sheet boundaries are made visible
by solid blue lines.
Fig. 25 Typical time sequence showing the flow patterns found in the
plane of symmetry of a flute showing natural effervescence; a detail of
the swirling motion (framed with white) is enlarged above the time
sequence. (Photographs by G. Liger-Belair, F. Beaumont and G.
Polidori.)
2504 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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conditions and glass-shape were found to strongly influence
the kinetics and the stability with time of the mixing flow
phenomena found in champagne glasses. In Fig. 25, three
successive frames of a typical time-sequence showing the flow
patterns found in the flute showing natural effervescence are
displayed. Throughout the first fifteen minutes which follow
the pouring process, champagne is found to be mechanically
mixed by various convection currents, made visible by the
movement of the neutrally buoyant Rilsan particles which
freeze the fluid motion during the 2 s exposure time of our
digital photo camera. It is worth noting that the various
convection cells and eddies found in the flute may change
randomly in size and location with time. Convection currents
induced by the flow of ascending bubbles are not at all stable
with time. Actually, in a flute showing natural effervescence,
bubbles arise from nucleation sites located randomly on the
flute’s wall. Furthermore, bubbles may also arise from nuclea-
tion sites directly found in the liquid bulk (called fliers and
presented in section 3.6).
25
The natural ‘‘bubbling environ-
ment’’ is therefore highly random. This is the reason why the
mixing flow mechanisms, directly induced by the random
distribution of bubble nucleation sites, are highly complex
and not at all stable with time in a flute showing natural
effervescence.
In Fig. 26, three successive frames of a typical time-sequence
showing the flow patterns found in a flute engraved at its
bottom are displayed. It is clear that strong differences appear
in the flow behaviour according to whether the glass has
sustained or not a specific surface treatment. Actually, due
to the high degree of reflectivity of bubbles with regard to the
laser wavelength, one clearly observes the formation of
the rising gas column along the vertical axis of symmetry of
the flute (from the treated bottom surface up to the free
surface of champagne). One can also clearly notice from
Fig. 26 that the rising bubble column generates two large
and well-established vortices which are very stable, and last
throughout the first fifteen minutes after pouring. Actually,
because the flute exhibits cylindrical symmetry around its
central axis, the real three dimensional structure of the flow
patterns in the bulk of the engraved flute is that of a deformed
torus. Therefore, and contrary to the case of the flute showing
natural effervescence, the convection currents found within the
engraved flute are very stable with time. The main reason is
that the ascending liquid flow generated by the rising central
bubbles column largely exceeds the other contributions to the
liquid flow generated by the likely presence of single bubble
trains randomly distributed within the glass. The main
convection currents are undoubtedly forced by this intense
and artificial effervescence. Moreover, it is worth noting that,
in the case of the engraved champagne flute, the whole domain
of the champagne bulk is homogeneously mixed, with high
values for the average fluid velocities, throughout the fifteen
minutes which follow the pouring process.
To complement the previous flow visualization method, to
better highlight the vortical structures and to access the
streak-line patterns of the champagne flow found inside an
engraved flute, another method based on dye dispersion was
used (see the laser tomography displayed in Fig. 27).
Fluorescent dyes of sulforhodamine and fluorescein have
carefully been injected in the champagne section crossed by
Fig. 26 Typical time sequence showing the flow patterns found in the
plane of symmetry of a flute engraved at its bottom (with a
ring-shaped engravement similar to that displayed in Fig. 18); a detail
of the swirling motion (framed with white) is enlarged above the
time sequence. (Photographs by G. Liger-Belair, F. Beaumont and
G. Polidori.)
Fig. 27 Flow patterns found inside an engraved champagne flute as
highlighted by use of fluorescent dyes injected in the flute
section crossed by the laser sheet: sulforhodamine (left), and fluores-
cein (right). (Photograph by G. Liger-Belair, F. Beaumont and
G. Polidori).
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the laser sheet after champagne was poured to highlight the
flow patterns without requiring the use of Rilsan particles.
Significant differences concerning the mixing flow patterns
within the champagne bulk were also found between an
engraved flute and an engraved coupe. In the case of an
engraved champagne coupe, only about half of the liquid
medium was found to be mixed by the flow of ascending
bubbles arising from the bottom of the coupe (see Fig. 28).
The external periphery of the coupe is characterized by a
‘‘dead-zone’’ where champagne is almost at rest.
28,32
There-
fore, it is clear that both glass-shape and engravement
conditions influence the overall characteristics of mixing flow
phenomena found in champagne glasses.
By vigorously and continuously mixing the liquid medium
throughout tasting, ascending bubbles are indeed suspected to
play a major role in flavour and gas release. Actually, the
flavour and gas release from the wine interface is a diffusion
process which is therefore ruled by the so-called Fick’s law,
expressed as follows:
J
!
i¼ciV
!Dir
!cið27Þ
where ~
J
i
,~
V,c
i
,r
!c
i
, and D
i
are the flux of a given compound i
through the gas/liquid interface, the velocity field of the liquid
flow near the wine interface, the bulk concentration of the
given compound, the concentration gradients of the given
compound close to the interface, and the diffusion coefficient
of the given compound in the champagne bulk, respectively. It
is clear from eqn (27) that both gas discharge and flavour
release are highly fluid velocity-dependent through the
parameter ~
V. Therefore, to better approach the kinetics of
flavour and gas release from glasses poured with champagne
and sparkling wines, the velocity field close to the wine
interface needs to be better known throughout the tasting
process.
In the near future, we plan to accurately investigate the
velocity field in various other models of champagne glasses
showing natural as well as artificial effervescence. We plan to
test various glass shapes (the inventive spirit of glassmakers is
fertile in this field) as well as various engravement conditions.
Actually, the modern techniques of glass engravement, done to
promote effervescence, enable various models of engravement
(in terms of shape and location in the glass), thus logically
modifying the overall convection currents conditions induced
by artificial effervescence. Moreover, since we strongly suggest
close links between the kinetics of convection currents and the
kinetics of flavour and CO
2
release, quantitative measure-
ments of the kinetics of CO
2
and volatile organic compounds
discharged from various champagne glasses under various
glass-shape and engravement conditions are also to be
conducted, together with sensory analysis experiments.
5. Close-up on bubbles bursting at the liquid
surface
5.1. The bursting process as frozen by high-speed photography
A champagne bubble reaches the liquid surface with a size that
depends on the distance htravelled from its nucleation site, as
expressed in eqn (26). Experimentally, it was observed that
bubble diameters rarely exceed about 1 mm. At the free
surface, the shape of a bubble results from a balance between
two opposing effects: the buoyancy F
B
, of the order of rgpR
3
,
which tends to make it emerge from the liquid surface and a
capillary force F
C
inside the hemispherical thin liquid film, of
the order of spR, which tends to maintain the bubble below
the liquid surface. In the case of champagne millimetric
bubbles, buoyancy will be neglected in front of capillary
effects. Consequently, like a tiny iceberg, a bubble only slightly
emerges from the liquid surface, with most of its volume
remaining below the free surface. The emerged part of the
bubble, the bubble-cap, is essentially a spherically shaped film
of liquid, which gets thinner and thinner as the liquid drains
back into the liquid bulk. A bubble-cap which has reached a
critical thickness of about 100 nm becomes so thin and
sensitive to such disturbances as vibrations and temperature
changes that it finally ruptures.
33
For bubbles of millimetre
size, the disintegration of the bubble-cap takes from 10 to
100 ms. During this extremely brief initial phase, the bulk
shape of the bubble is literally ‘‘frozen’’, and a nearly milli-
metric open cavity remains as a tiny indentation in the liquid
surface (see the high speed photograph displayed in Fig. 29).
Then, a complex hydrodynamic process ensues, causing the
collapse of the submerged part of the bubble and projecting
into the air a liquid jet which quickly breaks up into tiny
droplets of liquid (called jet drops). This process is indeed
characteristic of every carbonated beverage. Generally
speaking, the number, size, and velocity of jet drops produced
during bubble collapse depend on the size of the initial
bursting bubble.
34–37
In Fig. 30, the close-up high speed
photograph of a tiny liquid jet caused by the collapse of a
champagne bubble is displayed.
38
Fig. 28 Flow patterns found in the plane of symmetry of a coupe
engraved at its bottom (with a ring-shaped engravement similar to that
displayed in Fig. 18); it can be seen that, as for the flute engraved at its
bottom, the rising bubble column forces the flow patterns into the
form of two counter-rotative vortices close to the glass axis; never-
theless, in this case, the external periphery of the glass is characterized
by a dead-zone where the champagne is almost at rest; it means that,
for such a wide-brimmed glass, only about half of the liquid bulk
participates to the champagne mixing process. (Photograph by
G. Liger-Belair, F. Beaumont and G. Polidori.)
2506 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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It was also found that the ‘‘olfactive’’ role of bubbles does
not only concern the mixing mechanism of the liquid phase
presented in the above section. Actually, the myriad of bubbles
bursting at the liquid surface radiate hundreds of tiny liquid
jets which quickly break up into a multitude of tiny droplets
every second, thus forming a cloud of droplets above the
champagne surface, as shown in the photograph displayed in
Fig. 31. Those tiny droplets, ejected up to several centimetres
above the liquid surface, partly evaporate themselves, thus
accelerating the transfer of the numerous aromatic volatile
organic compounds above the liquid surface. This very
characteristic fizz considerably enhances the flavour release
in comparison with that from a flat wine for example. Laser
tomography techniques were applied to freeze the huge
number of bursting events and the myriad of droplets ejected
above champagne glasses in real consuming conditions (see the
tomography of the droplets’ cloud above the surface of a
coupe displayed in Fig. 32).
39
Fig. 30 The collapsing bubble cavity gives rise to a high-speed liquid
jet above the champagne surface (bar = 1 mm). (Photograph by
Ge
´rard Liger-Belair.)
Fig. 31 The collapse of hundreds of bubbles at the free surface
radiates a cloud of tiny droplets which is characteristic of champagne
and sparkling wines and which complements the sensual experience of
the taster (rAlain Cornu/Collection CIVC).
Fig. 32 The cloud constituted by myriads of tiny droplets ejected
from bubbles bursting above the surface of a coupe, as seen through
laser tomography technique; the droplets’ trajectories are materialised
by blue streaks of light during the 1 s exposure time of a digital
photo camera. (Photograph by G. Liger-Belair, F. Beaumont and
G. Polidori.)
Fig. 29 The bubble-cap of a bubble at the champagne surface has just
ruptured (on a time-scale of 10 to 100 ms); during this extremely brief
initial phase, the bulk shape of the bubble has been ‘‘frozen’’, and a
nearly millimetric open cavity remains as a tiny indentation in the
liquid surface (bar = 1 mm). (Photograph by Ge
´rard Liger-Belair.)
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5.2. When champagne bubbles dress up like flowers...
The close observation of bubbles collapsing at the free surface
of a glass poured with champagne also revealed another
unexpected and lovely phenomenon. A few seconds after
pouring, and after the collapse of the foamy head, the surface
of a champagne flute is covered with a layer of bubbles—
a kind of bubble raft, also called bi-dimensional foam, where
each bubble is generally surrounded by six neighbouring
bubbles (see Fig. 33).
40
Scientifically speaking, bubbles
arrange themselves in an approximately hexagonal pattern,
strikingly resembling those in beeswax. While snapping
pictures of the bubble raft after pouring, I also accidentally
took some pictures of bubbles collapsing close to one another
in the raft. When the bubble-cap of a bubble ruptures and
leaves an open cavity at the free surface, adjacent bubble-caps
are sucked towards this empty cavity and create unexpected
and short-lived flower-shaped structures, unfortunately
invisible to the naked-eye (see the high speed photograph
displayed in Fig. 34).
41,42
Shear stresses induced by bubbles
trapped in the close vicinity of a collapsing one are even better
visualized on the high-speed photograph displayed in Fig. 35,
where the bubble raft is not complete. Such behaviour first
appeared counter-intuitive to me. Paradoxically, adjacent
bubble-caps are sucked and not blown-up by bursting bubbles,
contrary to what could have been expected at first glance.
Actually, after the disintegration of a bubble-cap, the
hexagonal symmetry around adjoining bubbles is suddenly
locally broken. Therefore, the symmetry in the field of capil-
lary pressure around adjoining bubbles is also locally broken.
Capillary pressure gradients all around the now empty
cavity are detailed in Fig. 36. Signs +/indicate a pressure
Fig. 33 A few seconds after pouring, and after the collapse of the
foamy head, the surface of a champagne flute is covered with a layer of
quite monodisperse millimetric bubbles, where bubbles arrange them-
selves in an approximately hexagonal pattern, strikingly resembling
those in beeswax (bar = 1 mm). (Photograph by Ge
´rard Liger-Belair.)
Fig. 34 Flower-shaped structure found during the collapse of bubbles
in the bubble raft at the free surface of a flute poured with champagne
(bar = 1 mm). (Photograph by Ge
´rard Liger-Belair.)
Fig. 35 Shear stresses experienced by bubbles adjacent to a collapsing
one at the free surface of a flute poured with champagne (bar =
1 mm). (Photograph by Ge
´rard Liger-Belair.)
2508 |Chem. Soc. Rev., 2008, 37, 2490–2511 This journal is cThe Royal Society of Chemistry 2008
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above/below the atmospheric pressure P
0
. Finally, inertia and
gravity being neglected, the full Navier–Stokes equation ap-
plied to the fluid within the thin liquid film of adjoining
bubble-caps drawn by capillary pressure gradients, reduces
itself to a simple balance between the capillary pressure
gradients and the viscous dissipation as follows,
ZðDu
!ÞS¼ðr
!PÞSð28Þ
where uis the velocity in the thin liquid film of adjacent
bubble-caps, Zis the champagne viscosity, r
!Pare the
capillary pressure gradients, and sis the axial coordinate
which follows the bubble-cap’s curvature and along which
the fluid within the thin film is displaced.
The asymmetry in the capillary pressure gradients distribu-
tion around a bubble-cap adjacent to an empty cavity is
supposed to be the main driving force of the violent sucking
process experienced by a bubble-cap in touch with a bursting
bubble. Actually, due to higher capillary pressure gradients,
the liquid flows that develop in the half of the bubble-cap
closest to the open cavity are thus expected to be higher than
those which develop in the rest of the bubble-cap. It ensues a
violent stretching of adjoining bubble-caps toward the now
empty cavity, which is clearly visible in the photographs
displayed in Fig. 34 and 35.
More recently, those flower-shaped structures have been
observed during the coarsening of bi-dimensional aqueous
foams, obtained by mixing a surfactant, sodium dodecyl
sulfate (SDS), with pure water.
43
But it is worth noting that
this lovely and short-lived process was first done at the top of a
champagne flute.
41
Many fascinating processes in nature are
often hidden behind everyday phenomena such as those found
in a simple flute poured with champagne.
44
5.3. Avalanches of bursting events in the bubble raft?
Actually, avalanches of popping bubbles were put in evidence
during the coarsening of bi-dimensional and three dimensional
aqueous foams.
43,45,46
How does the bubble raft behave at the
surface of a flute poured with champagne? Does a bursting
bubble produce a perturbation which extends to the
neighbouring bubbles and induce avalanches of bursting
events which finally destroy the whole bubble raft? In the case
of champagne wines, a few time sequences of bubbles bursting
in the bubble raft have been captured with a high-speed video
camera. One of them is displayed in Fig. 37. Between frame 1
and frame 2, the bubble pointed with the black arrow has
disappeared. In frame 2, neighbouring bubbles are literally
sucked toward this now bubble-free area. Then, neighbouring
bubbles oscillate for a few milliseconds and progressively
recover their initial hemispherical shape. In conclusion, in
the case of bubbles adjacent to collapsing ones, despite high
shear stresses produced by a violent sucking process, bubbles
adjacent to collapsing ones were never found to rupture and
collapse in turn, thus causing a chain reaction. At the free
surface of a flute poured with champagne, bursting events
appear to be spatially and temporally non-correlated. The
absence of avalanches of bursting events seems to be linked to
the champagne viscosity (which is about 50% higher than that
of pure water).
43
It can also be noted that a tiny daughter
bubble, approximately ten times smaller than the initial central
bubble, has been entrapped during the collapsing process of
the central cavity (as clearly seen in frames 4 and 5 of Fig. 37).
Fig. 36 Schematic transversal representation of the situation, as
frozen after the disintegration of the central bubble-cap.
Fig. 37 Time sequence illustrating the dynamics of adjoining bubbles
in touch with a collapsing one at the free surface of a flute poured with
champagne; the whole process was filmed at 1500 frames s
1
; from
frame 4, in the centre of the empty cavity left by the collapsing bubble,
a tiny air-bubble entrapment is observed (bar = 1 mm). (Photographs
by Ge
´rard Liger-Belair.)
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Bubble entrapment during the collapsing process was
already experimentally and numerically observed with single
millimetric collapsing bubbles,
47,48
including champagne
bubbles.
38
5.4. A particular situation: as the jet deviates from vertical
The photograph displayed in Fig. 38 finally illustrates the
alluring of the liquid jet in a quite particular situation. On the
right side of this picture, the collapsing bubble is bordered by
three neighbouring bubbles, whereas on the left side, there are
no adjoining bubbles. The hexagonal symmetry is broken. In
this case, the tiny liquid jet (previously perfectly vertically
oriented, as in Fig. 30) deviates from vertical.
49
The jet is
deviated toward the ‘‘bubble-free’’ area. There are certainly no
enological consequences of such a situation, but experts in the
science of bubbles and foams ask themselves why such a
deviation from vertical is observed...
To end this critical review about the latest advances in the
science of champagne bubbles, Ge
´rard Liger-Belair would like
to pay homage to two scientists who inspired him so much
when he was a student: the recently deceased Professor
Pierre-Gilles de Gennes (1932–2007), Nobel Prize in Physics
in 1991, and Doctor Harold Edgerton, the twentieth century
master of stop-action photography. Prof. de Gennes was a
pioneering scientist who invented and developed a new area of
science devoted to what we call today ‘‘soft matter’’. His
contribution to the science of thin films, bubbles and foams
is huge. He recently wrote, together with two renowned
colleagues, a wonderful book, which provides numerous
answers to common questions about everyday phenomena.
50
Dr Harold Edgerton (1903–1990) revealed to the general
public the beauty of ‘‘high-speed events’’ and inspired genera-
tions of young scientists. Dr Edgerton devoted his entire career
to recording what the unaided eye cannot see, in order to
reveal the laws of nature.
51
His most famous snapshot, the
coronet made by a drop of milk, is familiar to millions of
people throughout the world, and has become an icon and
hallmark of the juncture between pure science and modern art.
‘‘The experience of seeing the unseen has provided me with
insights and questions my entire life’’, told Harold Edgerton.
This sentiment exactly captures the heart of the matter. Who
could have thought at first glance that a flute poured with
champagne could turn into such a fantastic playground for a
physicist in love with high-speed microphotography, and for
any champagne lover with the knowledge and time to reflect.
Acknowledgements
This research was partially supported by the Europol’Agro
institute and by the Conseil Ge
´ne
´ral de la Marne. The authors
warmly thank Fabien Beaumont, from Reims University,
for valuable discussions and for his precious help concerning
the recent and exciting experiments conducted with laser
tomography techniques. The authors are grateful to the team
of the Laboratoire d’Oenologie et Chimie Applique
´e, for their
constant help and valuable discussions. Thanks are also due to
Champagne Moe
¨t & Chandon and Champagne Pommery
for regularly supplying us with wine samples, to ARC-
International for supplying us with various and up-to-date
glasses, and to Jean-Claude Colson and AROCU for
encouragements and for supporting our research. The authors
are finally also grateful to the CIVC for providing the
photograph displayed in Fig. 1, and to Jacques Honvault for
providing the high-speed photograph displayed in Fig. 5.
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... Go ahead and pour yourself some nice sparkling wine into a glass, and observe the beautiful sight of rising bubbles and their effervescence [ Fig. 10(a)]. Champagne and sparkling wines are supersaturated with dissolved CO 2 gas, which, along with ethanol, is a product of the wine fermentation process [265]. When the bottle is uncorked, there is a continuous release of this dissolved CO 2 gas in the form of bubbles. ...
... When the bottle is uncorked, there is a continuous release of this dissolved CO 2 gas in the form of bubbles. Hence, this physicochemical system provides a great opportunity to study several fundamental fluid mechanics phenomena involving bubbles: their nucleation, rise, and bursting dynamics, which in turn affect the taste of carbonated drinks [265][266][267][268][269][270][271]. ...
... The pleasing effervescence (bubbling) that we observe in champagne can arise from either natural or artificial sources [265,278], as shown in Fig. 10(a,b). Natural effervescence refers to bubbling from a glass which has not received any specific surface treatment. ...
Preprint
Full-text available
Innovations in fluid mechanics have refined food since ancient history, while creativity in cooking inspires science in return. Here, we review how recent advances in hydrodynamics are changing food science, and we highlight how the surprising phenomena that arise in the kitchen lead to discoveries and technologies across the disciplines, including rheology, soft matter, biophysics and molecular gastronomy. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, we first provide an introduction accessible to food professionals and scientists in neighbouring fields. We then assess the state-of-the-art knowledge, the open problems, and likely directions for future research. New gastronomic ideas grow rapidly as the scientific recipes keep improving too.
... Each case is identified by the terms oversaturation, saturation, and undersaturation respectively. As an example, rapid decompression of liquids-as experienced when celebrating with a Champagne bottle (c i /c s ≈ 5)-forces gases to flow from the liquid bulk to pre-existent gas nuclei in the serving glass [2]. An analogous situation, albeit in a more complex rheological system, is experienced by humans when scuba diving. ...
... Yet, these beverages yield bubbles despite being oversaturated only by about c i /c s ≈ 5. From these two facts, it is logically concluded that homogeneous nucleation is not at hand. Indeed, Liger-Belair [2] has shown that the bubbling of Champagne is triggered heterogeneously. In some cases, fibers present in the serving flute trap gases whence bubbles may continuously escape and grow. ...
Thesis
In this work, we investigate the dissolution or growth of bubbles in polymeric systems driven by means of temperature variations. In this regard, laminated safety glass serves as an inspiration. The latter is a multi-layered assembly reminiscent of a sandwich and includes a thin, hygroscopic, polymeric film (typically, polyvinyl butyral-PVB) positioned in between two layers of float glass. The assembly, guarantees that, if broken, glass shards remain bonded to the polymeric interlayer. As a result, it improves resistance to breaking and entering, but also protects individuals from life-threatening projectiles during a car collision and is thus widely used in the façade of buildings or in the windshields of cars However, it is common to observe bubbles in laminated glass. These bubbles, which are anathema to the beautiful appearance of glas, can occur during production, quality testing at high temperatures or during normal operation and are typically associated with air oversaturation. During the thesis, an experimental transparent setup was developed to reproduce one of the main steps involved in the production of safety glass at the laboratory scale, i.e., autoclaving at high temperatures (140°C) and pressures. The setup allows tracking the dissolution or growth of interfacial gases (gas pockets) or bubbles in glass/PVB/glass samples (or in otherwise transparent samples) when subjected to variations in temperature or pressure. We identify that air and water vapour follow distinct thermodynamic paths in terms of solubility with increasing temperature. As a result, water vapor leads to bubble growth while air favours dissolution. For the specific case of water, we dive deeper into the polymer chemistry and its relationship to mass transport properties. Contrary to the simple thermodynamic picture, the observed kinetic behaviour of gas pockets/bubbles is highly non-monotonous and is strongly influenced by the rheology of the interlayer. For the latter part, a high-temperature mechanical characterization is provided that identifies this polymer as a Maxwell fluid at long timescales, contrary to the widely held assumption of a Maxwell solid. Time-temperature superposition constants, as well polymer characteristic times that delineate the glassy, rubbery, and melt states are further provided. Additional blends of the base PVB polymer were investigated in terms of rheology and bubbling behaviour. A non-isothermal kinetic bubble model is then proposed for standard PVB addressing the nature of the two gases, the finiteness of the system, as well as the complex viscoelastic behaviour of the polymeric interlayer. The comparison between the model and experiments highlights the following points.. First, bubble growth is impacted by initial bubble size, maximum temperature, as well as initial bubble composition, and amount of dissolved gas in the polymer. Then, the gases, by virtue of their shared flexible enclosing volume, can potentially affect each other’s chemical equilibrium, thereby forcing mass flows in opposition to their solubility preference. Moreover, in finished glass assemblies, either gas, depending on initial nuclei size, presence of pollutions (fibres or dust), or initial oversaturation, can lead to bubble formation at high temperatures.
... En oenologie, les expérimentateurs mesurent généralement la viscosité cinématique ν et la masse volumique ρ d'une boisson pour obtenir sa viscosité dynamique η = νρ. Ils peuvent alors estimer le coefficient de diffusion d'une espèce au sein du liquide en appliquant la formule de Stokes-Einstein ( 3.22) [34,102,110,111]. ...
... .3.1 Diffusion moléculaireLes vins de Champagne sont des liquides complexes composés d'une multitude d'espèces allant des ions mono-atomiques aux protéines et acides aminés[102]. La diffusion de molécules dans ces mélanges devrait donc vraisemblablement être décrite par les équations de Fick généralisées[103], les théories proposées par Maxwell-Stefan[104] ou Onsager[105]. ...
Thesis
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... Bubble bursting processes abound in nature and technology and have been studied for long in fluid mechanics [338]. For example, they play a vital role in transporting aromatics from champagne [85,[104][105][106], and pathogens from contaminated water [263,339]. ...
Thesis
Full-text available
This thesis investigates several free-surface phenomena to illustrate the role of viscous stresses. In part I (chapters 1-4), we study the impact of spherical liquid drops on non-wetting substrates. After impact on a rigid substrate, a falling liquid drop deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show in chapter 1, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. Throughout this drop impact process, viscous dissipation enervates internal momentum. Subsequently, gravity and viscosity conspire to inhibit bouncing, which we delineate in chapter 2. Furthermore, chapter 3 investigates drops bouncing off viscous liquid films that mimic atomically smooth substrates. Then, in chapter 4, we examine the drop-on-drop impact process whereby an impacting liquid drop lifts off a lazy sessile one from a non-wetting substrate. In part II (chapters 5-6), we focus on capillary-driven retraction of films and the bursting of free-surface bubbles. In chapter 5, we show that even when the surrounding medium interacts with the Taylor-Culick retraction of a film, the film still retracts with a constant velocity, provided that it is long enough to avoid finite film size and internal viscous effects. Lastly, in chapter 6, we reveal that the influence of viscoplasticity on the capillary-driven bursting of a bubble at a liquid-gas free-surface is twofold: (i) it manifests as an increase in effective viscosity to attenuate the capillary waves that control the bursting process, and (ii) the plasticity of the medium resists any attempts to deform its free-surface.
... S11 and see Materials and Methods for details). We obtained a lowest CO 2 (aq) concentration of ~0.4 g/liter in grape wine, highest of ~10 g/liter in champagne, and similar concentrations of ~6 g/liter in sparkling water and coke (Fig. 2D), matching well with reported CO 2 levels (58,59) in these beverages. ...
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... In support of the findings of Study 1 on visual appeal, participants in other studies have been observed paying attention to the continuous flow of ascending bubbles during champagne and sparkling wine tasting and noting their visual appeal [37]. Similarly, a medium level of beer "head" foam has been judged the most visually appealing by both males and females [10]. ...
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... We performed micro-IR measurements of CO2(aq) in sparkling water, coke, grape wine, and brut champagne applying the above calibration curve, and the various solutes in these drinks (including ethanol, sugar, minerals and flavoring agents) did not interfere with acquiring clear and quantifiable CO2(aq) peaks in micro-IR spectra (Fig. S9, see Materials and Methods for details). We obtained a lowest CO2(aq) concentration of ~ 0.4 g/L in grape wine, highest of ~ 10 g/L in champagne, and similar concentrations of ~ 6 g/L in sparkling water and coke ( Fig. 2D), matching well with reported CO2 levels 55,56 in these beverages. ...
Preprint
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Chapter
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Chapter
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Chapter
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Capillarity: Unconstrained Interfaces / Capillarity and Gravity / Hysteresis and Elasticity of Triple Lines / Wetting and Long-Range Forces b/ Hydrodynamics of Interfaces -- Thin Films, Waves, and Ripples / Dynamics of the Triple Line / Dewetting / Surfactants / Special Interfaces / Transport Phenomena
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The size distributions of the jet drops produced by individual air bubbles bursting on a fresh water surface are presented. The bubbles studied ranged in size from 349 to 1479 mum radius. The probability that a bubble of radius rb produces at least n drops, p(rb,n), is given for n up to 7. The underwater sound made by collapsing bubbles is discussed briefly.
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The parameters describing the birth of film droplets originating from bubbles bursting on seawater surfaces are presented. Results are given for bubble sizes Db from 2 to 14.6 mm equivalent volume diameter. It is shown, contrary to earlier reports, that the films of all bubbles with Db up to at least 14.6 mm burst in an orderly manner in which a hole appears at a well-defined location, usually the film's edge, and propagates from there gathering up the film's mass into a toroidal ring as it progresses. This process is enabled because surface tension provides the force required to sustain the centripetal accelerations. Film drops are created when beads, of sufficient size, form along the length of the toroidal ring and surface tension is insufficient to maintain the centripetal accelerations at these accumulation points. Pieces of the ring break loose and leave the toroidal ring along paths tangential to the bubble's cap. It is shown that only bubbles larger than 2.4 mm diameter can launch film droplets by this means and that this begins when the film has rolled up through an angle of about 31° independent of both bubble size and (theoretically) surface tension. Film drop spray patterns recorded on MgO-coated cylindrical shells surrounding the burst bubbles yield film drop numbers and trajectories. In addition, film drop size distributions, their speed of launch, and the speed at which the film opens have been determined as a function of bubble size. The droplet sizes cited here are substantially larger than most previous estimates, and with a high probability, these droplets follow downward trajectories which lead them to impact the surface. A strong inference may be drawn that these impacts give birth to secondary droplets that are smaller than their parents and which have upward velocity components.
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Although beer and champagne are mostly enjoyed at leisure, the myriad physical and chemical processes in them are challenging. Furthermore, studying these processes sheds light on explosive volcanic and lake eruptions because bubble growth is a process common to all of them. We model the growth rate of rising bubbles in beer and champagne. Due to different initial gas concentrations, the eruption velocity of champagne is two orders of magnitude higher than that of CO2-based beer. In N2-based Guinness beer, bubble growth is slow, leading to smaller bubbles that can be entrained by downward flow; these are often seen as sinking bubbles.
Article
The parameters of the births of jet drops originating from bubbles bursting on seawater surfaces are presented. This report supplements an earlier one by providing the birth times and heights of all the jet drops, not just the top. Results are given for bubble sizes from 350- to 1500-μm equivalent volume radius. The ejection speeds of the jet droplets generated by a collapsing bubble and the height above the surface, as well as the time, at which all the drops break off the ascending jet have been measured. For the bubble sizes used in this study, the first drop emitted, the top drop, is closest to the surface at birth, the second is the highest, and all subsequent drops are at intermediate heights. Furthermore, each drop after the second is born at a height that is lower than the drop that preceded it. Size distributions of the jet drops from each of 10 bubble sizes are reported. They differ from size distributions published earlier in that the sizes of the lower drops are not bimodally distributed. This difference is attributed to a difference in water temperature.