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Yield Stress Dependent Foaming of Edible
Crystal-Melt Suspensions
Kim Mishra,∗,†Damien Dufour,‡,¶and Erich J. Windhab¶
†Institute of Food, Nutrition and Health, Swiss Federal Institute of Technology,
Schmelzbergstrasse 9, 8092 Zürich
‡Current address: Ubertone, Rue du Brochet 14, 67300 Schiltigheim
¶Institute of Nutrition and Health, Swiss Federal Institute of Technology,
Schmelzbergstrasse 9, 8092 Zürich
E-mail: kim.mishra@hest.ethz.ch
Phone: + 41 44 632 97 10
Abstract
Crystal-melt suspensions (CMS) are yield stress shear thinning fluids in which crys-
tal network formation is responsible for the appearance of a yield stress. This study
investigates the influence of crystal concentration and morphology on the yield stress of
CMS made from palm kernel oil (PKO), and aims to understand gas bubble stabiliza-
tion in such systems. Crystallization in laminar flow depends on shear, thus different
shear rates were applied to produce PKO CMS. With increasing shear rate, higher yield
stress at constant crystal content was found. This behavior is expected to originate from
the increased aspect ratio and/or smaller size of crystals or crystal agglomerates formed
at higher shear rates. The related influence of crystal network formation on gas bubble
stabilization was investigated. Normalized bubble diameters of PKO CMS foams were
shown to decrease for increasing Bingham number approaching a value of 1. We demon-
strate hereby that gas bubbles are best stabilized within fat melts by crystal network
1
formation resulting in stable fat micro-foams with adjustable structure-rheology rela-
tionship through tailored crystallization and low dissipation membrane micro-foaming.
Introduction
The flow behavior and material characterization of yield stress fluids containing crystals
plays a major role in lipid (fat/oil), polymer, metal or magma melts as well as in concen-
trated solution/dispersion systems. They have in common that a liquid (melt or solution)
and solid (crystal) may coexist under given temperature conditions.1–4 From a rheological
perspective, cooling a melt below its crystallization temperature or a solution below a tem-
perature at which supersaturation reaches a critical value, crystal formation transforms the
fluid system from a Newtonian fluid to a non-Newtonian suspension or even a semi-solid
body. Rheology-structure relationships of crystallizing fluid systems are mostly quite com-
plex, since the crystal structure and formation kinetics can be altered by shear stress and
related viscous friction based energy dissipation acting in shear flow fields. Accordingly,
thixotropy or rheopexy can be superimposed with related characteristic time scales depend-
ing on shear stress and energy dissipation rates as well as on the generated crystal shape and
morphology. Such complex relationships are often poorly understood despite their relevance
in applications of lipid, polymer, metal or magma melt flow. Theoretical and experimental
studies investigating lipid and magma melt rheology were found to reassemble each other.4–6
Models proposed to describe lipid melts and magma systems do not contradict but rather
complement each other in their different rheological description approaches. Lipid melts
are characterized as weakly aggregated particle networks in the non-Newtonian shear flow
regime, whereas magmas are treated as crystal-melt suspensions (CMS), with crystals in-
terpenetrating each other (soft-core continuum percolation).4,6 The main difference between
the two models is the derivation of a scaling factor αfor the yield stress as a function of
solids volume fraction and the presence/absence of a percolation threshold denoted as critical
2
crystal fraction. For lipids, the fractal nature of the crystals is used to calculate such scaling
factor αwhereas for magmas the excluded volume of a given shape is used as calculation
basis for α.4,6 The critical crystal fraction is calculated as function of crystal shape and
defines the onset of a yield stress.6
Whereas few have witnessed magmatic flow in their lives, lipids are a major component
in our daily food experience. From all macronutrients, lipids contain the highest dietary
energy density. Hence, recent nutritional studies focus on low-fat diets to treat the prevail-
ing problem of global obesity.7,8 The main effort to replace lipids in the human diet has
been done by substitution with carbohydrates or by emulsification of a water phase into
the lipid (fat melt/oil).9–11 More recently, efforts have been made to introduce gas bubbles
into lipid systems, thereby largely reducing their dietary energy density.12–15 Such systems
are denoted lipid foams. First discoveries of lipid foams date back to the 1970s and more
recently, studies on edible or skin applicable lipid foams have been published.16–26 Most of
these studies relate foam formation of lipid systems to the presence of crystals. Several stabi-
lization mechanisms are proposed such as Pickering stabilization, viscoelastic gel formation
of the continuous phase and jamming of crystal particles between bubbles.13,14,17–26 Edible
lipid foams usually contain (1) higher melting and lipid soluble components such as mono- or
diglycerides, fatty acids, fatty alcohols or high melting fats and (2) lower melting lipid such
as triglyceride oils.13,14,21–26 These binary mixtures are cooled down from the molten state
to induce crystal formation thereby converting into a CMS. The CMS is subsequently aer-
ated.13,14,21,22,24–26 Another way to produce lipid foams is the use of confectionery fats which
are natural mixtures of high melting and low melting triglycerides.23 Little is so far known
about the influence of crystal concentration, morphology and polymorphic form on the lipid
foam formation. However, crystal concentration, morphology and polymorph form affect the
rheological properties of the CMS and are therefore expected to play a major role in foam
formation and stabilization processes. Attempts to link the elastic modulus with the foam
formation and stabilization process have not been conclusive.25 Regarding crystal size and
3
polymorphic form, it has been shown that small βpolymorph crystals favor foam formation,
whereas αpolymorph crystals show poor foam formation properties.14 Understanding the
foam formation process requires the knowledge of both, the material and the process. Dy-
namic membrane foaming allows to create well defined bubbles in size and size distribution
width at low volumetric energy input.27 Superimposing a radial velocity gradient onto the
axial flow of the continuous phase between a rotating solid cylinder and a concentric mem-
brane cylinder has been introduced in our previous work as dynamically enhanced membrane
foaming.28 This is a prerequisite to estimate the acting shear stresses on a bubble during
foam formation. Another prerequisite to calculate such are the rheological properties of the
continuous fluid phase. CMS of lipids show highly dynamic crystallization processes which
practically disqualifies off-line rheological measurements.29,30 Consequently, in-line measur-
ing techniques are required to acquire reliable rheological data. One such technique applied
in pipe flow is the ultrasound velocity profiling in combination with a pressure difference
measurement (UVP-PD).31–35 This technique has been successfully applied to crystalliza-
tion processes with CMS.29,36,37 From non-invasive in-line velocity profile measurements by
UVP-PD we extracted the yield stress , the consistency factor and the flow exponent by
fitting the velocity profiles with the Herschel-Bulkley model:29,33,38
τ=τ0+K˙γn(1)
This allows to calculate the shear stress at any given shear rate.39 The viscosity can be
derived from Newton’s shear stress law according to η=τ/˙γ
In this paper, we investigated the rheological properties of CMS in order to draw conclusions
on gas bubble stabilization in such systems. Therefore, palm kernel oil (PKO) was used
as CMS model system. PKO was transformed into a CMS with a scraped surface heat
exchanger. Ultrasound velocity profiling - pressure difference, polarized light microscopy,
pulsed nuclear magnetic resonance spectroscopy, differential scanning calorimetry and X-ray
4
diffraction spectrometry were employed to analyze and relate crystal volume fraction, crystal
shape and crystal polymorphic form to the yield stress of CMS. Dynamic membrane aeration
served as a process to adjust bubble size distribution, characterized by the 90th percentile
number weighed bubble size, and investigate its dependency from the applied wall shear
stress under given CMS rheology during foam formation. From this we got a mechanistic
insight into gas bubble stabilization in yield stress fluids.
Experimental Procedures
Palm Kernel Oil: PKO (RSPO-SG) was purchased from Florin AG (Muttenz, Switzer-
land). The PKO was fully molten overnight at 40 ◦C using a blade stirrer (RW 28W, IKA
Werke GmbH, Staufen, Germany) before being used for trials.
Crystallization: Crystallization was performed with a scraped surface heat exchanger
(SSHE) (Schröder GmbH &Co KG, Lübeck, Germany) as depicted in Figure 1. The stator
diameter 2Rowas 60 mm with a length of 400 mm. Using a MS25-HT/P water bath (Julabo
Labortechnik GmbH, Seelbach, Germany) with 3.2 kW cooling capacity the double mantled
stator was tempered within a temperature range of 5 – 18 ◦C. The rotor with two blades
had a diameter 2Riof 57 mm and was tempered at 27 ◦C with a Julabo F32 water bath
(Julabo Labortechnik GmbH, Seelbach, Germany). The rotational speed of the rotor was
adjusted by using a V-belt transmission. Since Reynolds numbers according to Stranzinger
et al.40 were calculated to be larger than 10 during crystallization, the shear rate ˙γSSH E
was calculated by solely considering the velocity field between rotor and stator as described
previously:40–42
˙γSSHE =πnS SHE
15
R2
o
R2
o−R2
i
(2)
where nSSHE is the rotational speed, Rothe stator radiuus and Rithe rotor radius. An ec-
centric worm-drive pump (Allweiler GmbH, Radolfzell, Germany) pumped the liquid PKO
at 40 ◦C from the double mantled stainless steel vessel through double mantled and tempered
5
25 mm pipes into the gap between stator and rotor.
Ri
nSSHE h
Ro
blades with
angle
and
height h
stator with
radius Ro
rotor with radius Ri
and rotational
speed nSSHE
Figure 1: Cross-sectional view of the scraped surface heat exchanger used to crystallize liquid
palm kernel oil with Ro= 30 mm, Ri= 28.5 mm, h = 2 mm and δ= 5 ◦C.
Solid Fat Content determination: Solid fat content was measured by pulsed nuclear
magnetic resonance spectroscopy using a 20 MHz (0.47 T) minispec mq20 (Bruker Biospin,
Fällanden, Switzerland) in the direct mode. The device was calibrated using paraffin–acrylic
standards. Tempered glass tubes with an inner diameter of 1 cm, a wall thickness of 0.06
cm and a height of 18 cm were filled with 3-4 cm of sample and immediately analysed as
described previously.43 For highly viscous samples a tempered syringe with a plastic tube
was used to fill the glass tubes. Analyses were performed in triplicate.
Melting Curve Determination: A differential scanning calorimeter (dsc822e, Mettler
Toledo GmbH, Greifensee, Switzerland) was used to investigate the melting behavior of
PKO. For each sample, triplicates were measured. Sample weight was 5 ±0.2 mg for every
triplicate. Samples were put in precooled 40 µl aluminum crucibles (Mettler Toledo GmbH,
Switzerland) that weighted 50.49 ±0.2 mg. Measurements were performed from -30 to +60
◦C with a heating rate of +5 ◦C/min. Heat flow at a given temperature was evaluated us-
ing the STARe-Software (SW 8.1, Mettler Toledo GmbH, Greifensee, Switzerland). Sample
preparation was done with precooled instruments. Scraped surface heat exchanger crystal-
lized samples: In order to avoid further polymorphic changes during sampling and sample
storage, a liquid nitrogen (LN2) bath was used to quench crystallization. Small amounts
6
of the product stream were dropped directly into the LN2bath to ensure rapid and uni-
form cooling. Subsequently, samples were transferred to a dry ice box prior to analysis. All
samples were continuously produced at 10 ◦C stator wall temperature with 20 kg/h flow
rate corresponding to a mean residence time tRof 84 s. Statically crystallized samples: Two
different cooling rates were applied to statically crystallize samples. Such were either poured
in their molten state into a LN2bath (fast cooling) or left to crystallize at room tempera-
ture (23 ◦C) for two hours (slow cooling). After crystallization treatment, the samples were
transferred to a dry ice box.
Polymorphic Crystal Form Determination: An X-ray diffractometer (D8 advanced,
Bruker GmbH, Karlsruhe, Germany) was used to characterize the samples in this study.
The diffractometer radiation source was Cu-Kα1 with a wavelength of λ= 0.15406 nm and
Ebeam = 40 keV. The diffraction angle 2θwas between 18◦and 25◦with a step size of 0.02◦.
Samples were rotated but not tempered during analysis. The total measurement time was
350 s. Scraped surface heat exchanger crystallized samples and statically crystallized samples
were prepared identically to the differential scanning calorimetry protocol except that
small amounts of product stream were filled into LN2precooled sample holders (fast cooling)
or left to crystallize in the sample holders at room temperature for two hours (slow cooling).
Yield Stress Determination: The UVP-PD measurements were done directly after crys-
tallization. Double mantled 15 mm pipes held at 27 ◦C were used to convey the crystal-melt
suspension. The pressure difference was measured in a 3.29 m pipe section. A diaphragm
pressure sensor (CC1020, Labom GmbH, Hude, Germany) with a measurement range of 1.0
– 1.4 bar absolute pressure was used at the beginning of the pipe segment in order to cal-
culate the pressure difference against atmospheric pressure at the pipe exit. In between the
pressure sensor and the end of the pipe segment a custom built polyvinyl chloride cell with
inserted ultrasonic transducers was used to record the flow profile. Two 4 MHz transducers
(Imasonic SAS, Voray-sur-L’Ognon, France) with an active diameter of 5 mm were placed at
60°and 90°angle with respect to the flow axis in order to determine the velocity profile across
7
the pipe diameter and the speed of sound consecutively. The transducers were preferably
operated at 3.75 MHz with a pulse repetition frequency of 750 Hz and 128 repetitions. The
signals of the transducers were recorded with the UB-Lab device (Ubertone, Schiltigheim,
France). During approximately 60 s a total of six averaged profiles were recorded for one pro-
cess setting. This procedure was repeated three times for each process setting. Subsequently
the profiles were deconvoluted44–46 and fitted with the Herschel-Bulkley model. Fitting the
Herschel-Bulkley model onto the measured velocity profile requires the plug radius Rp, Flow
index nand Consistency factor Kas fitting parameters:
νHB (r) =
n
n+1
∆P
2LpK
1
n"(R−Rp)1+ 1
n−(r−Rp)1+ 1
n#,if r≤Rp
νHB (Rp),if r < Rp
(3)
The fitted plug radius Rpis related to the yield stress of the CMS as follows:
Rp=2τ0Lp
∆P(4)
Consequently, the larger Rpand ∆Pthe higher the yield stress τ0of the CMS as depicted
in Figure 2. Examples of measured flow profiles are presented in Figure S1. The piping and
instrumentation diagram as well as the geometry of the measurement cell can be seen in
Figures S2 and S3.
Foam Formation: A membrane foaming apparatus (Kinematica Megatron MT-MM 1-52,
Kinematica AG, Luzern, Switzerland) was used for the foaming of the CMS. The dynami-
cally enhanced membrane foaming apparatus consists of two concentric cylinders. The static
outer cylinder with a radius of 54.5 mm and an axial length of 60 mm acts as a membrane
with nominal pore size of 3.5 µm. The inner rotating cylinder with a radius of 44.5 mm
generates a defined rheometric shear flow or a homogeneously turbulent flow field depending
on the fluid viscosity and the related Reynolds number (Re) in the 5 mm gap between the
outer and inner cylinder thereby detaching the gas bubbles from the membrane surface and
8
-R
Pipe radius r
0
x
Rp
0
HB(r)
x
x(r)
(r)
w
(1)
(2)
+R
Figure 2: (1) Schematic velocity profile in xdirection νxand shear stress distribution τ(r)as
function of the pipe radius r.(2) Schematic yield stress estimation by fitting the Herschel-
Bulkley velocity profile νHB (r, Rp, n, K)as function of the pipe radius r, plug radius Rp,
Flow index nand Consistency factor K. Measurement accuracy of the fluid velocity is
schematically indicated by the length of the standard deviation lines emerging from the data
point.
9
dispersing these into the continuous CMS phase. The CMS was axially pumped at 20 kg/h
through the 5 mm gap of 60 mm length. Nitrogen gas was injected through the membrane
into the gap at 7 bar with a flow rate of 20 l/h. A schematic radial cross-section of the
foaming cell is depicted in Figure S4.
Crystal Shape and Bubble Size Determination: Polarized light microscopy (Leica
DM6, Leica Microsystems AG, Heerbrugg, Switzerland) was used to investigate crystal mor-
phology as well as bubble size distributions. Samples were slightly cooled during imaging by
placing an ice container on the stage of the microscope. Gas bubble size and size distribution
was calculated by using a custom-built image analysis software. The software uses a man-
ually set threshold to detect the edges of the bubbles. Subsequently, the bubble edges are
approximated manually with a circle of radius rc. A minimum of 300 bubbles was counted
to calculate a single bubble size distribution. SPAN values correspond to width divided by
median of the distribution (x90,0−x10,0)/x50,0.
Non-linear data fitting: The OriginPro 2019 Software was used for the fitting procedure.
Yield stress as function of solid fat content: Equation 5 was used for the fitting procedure.
τ0=6γ
aΦ1
3−D(5)
The Levenberg-Marquardt iteration algorithm was used. No weighing was applied. Fits
converged. ξ2-tolerance value of 10−9was reached.
Results and discussion
Rheology of Crystal-Melt Suspensions: Yield stress determination was performed with
the in-line ultrasound velocity profiling – pressure difference method. The yield stress τ0as
function of solid fat content ΦSF C for Palm Kernel Oil (PKO) crystallized at various scraped
surface heat exchanger shear rates ˙γS SHE is shown in Figure 3. The ˙γSSHE was calculated
in the gap between rotor and stator Ro−Riaccording to Equation 2. For each ˙γS SH E a
10
yield stress model fit as proposed by Marangoni and Rogers 4was performed. The fits were
done by changing solely the primary particle diameter a, but keeping the fractal dimension
Dand the interfacial tension γconstant at 2.7 and 0.01 Nm−1, respectively. Similar fractal
dimensions of D≈2.5 have been proposed for diffusion controlled particle aggregation in
the 3 dimensional space.47 The fits were performed with the assumption that the solid fat
content ΦSF C as determined by nuclear magnetic resonance spectroscopy can be used as the
crystal volume fraction ΦSF C ≈Φv,crysal. For increased ˙γSSH E , the τ0=f(ΦS F C )curves
become steeper due to the decreased fitted primary particle diameter a. PKO crystallized
at 430 s−1has a fitted aof 848 nm, whereas at 2150 s−1the fitted value for adropped to 28
nm. This decrease in particle size increased the attenuation of the ultrasound waves required
to record the velocity profile. Consequently, the measurement window was narrowing with
increased ˙γSSHE . At ˙γSSHE = 430 s−1, velocity profiles up to a ΦSF C value of 13.7 ±1.1
%were obtained, whereas at ˙γSSH E = 2150 s−1profiles only up to a ΦS F C of 3.7 ±0.47
%were manageable. The primary particle diameter gives qualitative information about
the microstructure of crystal networks. Crystal aggregate diameter ξand primary particle
diameter ascale by:48
aN
1
D
a≈ξ(6)
where Nais the number of primary particles. From Equation 6 one cannot distinguish
whether aggregates may be broken up or the primary particle diameter gets smaller. The
conclusion one can draw from the decreased fitted primary particle size ais, that smaller
microstructural elements are present. Such could originate from smaller initial crystal size
or shear-induced breakup of crystal aggregates.
Using a primary particle/crystal diameter to describe crystal size is a simplification, which
does not take into account the morphology of the particle/crystal. Therefore, not only size
but also the aspect ratio rpof primary particles/crystals has to be considered. Even though
the aspect ratio rpis not accounted for in the indicated fits, we can calculate it from the crit-
ical crystal concentration. Reading off the ΦSF C values of the fitted curves at a given yield
11
0.000 0.025 0.050 0.075 0.100 0.125 0.150
0
20
40
60
80
100
120
g
SSHE
=
2150 s
-1
g
SSHE
=
1075 s
-1
g
SSHE
=
430 s
-1
Yield stress
t
0
[Pa]
Solid fat content
F
SFC
[-]
2150 s
-1
F
c
= 0.015
a
= 28 nm
R
2
= 0.96
1075 s
-1
F
c
= 0.022
a
= 170 nm
R
2
= 0.87
430 s
-1
F
c
= 0.035
a
= 848 nm
R
2
= 0.99
Figure S1(a)
Figure S1(b)
Figure S1(c)
Figure 3: The yield stress τ0as function of solid fat content ΦSF C for PKO CMS crystallized
at ˙γSSHE = 430, 1075 and 2150 s−1. The dashed lines indicate the fitted curves according to
τ0=6γ
aΦ1
3−Dwhere γ= 0.01 Nm−1and D= 2.7. The corresponding value of the primary
particle diameter a, the critical crystal concentration Φc, and the adjusted R2are displayed
in the boxes. Velocity profiles of selected points are depicted in Figure S1.
12
stress of τ0= 1 Pa an approximated Φcwas obtained. Assuming prolate particles/crystals
the aspect ratio can be determined according to the simulations presented by Saar et al.6.
Table 1 shows the ΦSF C for PKO crystallized at various ˙γSSH E . It was found that the higher
the ˙γSSHE during crystallization the lower the ΦSF C ranging from 0.035 at ˙γSSH E = 430 s−1
to 0.015 at ˙γSSH E = 2150 s−1. The lower the ΦSF C the higher the rpof the crystals ranging
from 18 at ˙γS SH E = 430 s−1to 30 at ˙γSS HE 2150 s−1. The calculated aspect ratios indicate
that the formed primary particle/crystals are needle like rather than spherical. Furthermore,
with increasing ˙γSS HE the needles elongate instead of breaking. In order to verify the calcu-
lated aspect ratios, polarized light microscopy was performed.
Table 1: The fitted primary particle size a, the critical crystal fraction Φcand the aspect
ratio rpfor PKO CMS crystallized at different scraped surface heat exchanger shear rates
˙γSSHE . Aspect ratios were graphically determined from the results of Saar et al.6.
˙γSSHE [s−1]a[nm] Φc[-] rp[-]
430 848 0.035 18
1075 170 0.022 23
2150 28 0.015 30
Figure 4 shows polarized light microscopy images of PKO crystallized at 10 ◦C stator wall
temperature and for ˙γSSH E of 430, 1075 and 2150 s−1. The mass flow rate was kept constant
at 20 kg/h. At 430 s−1large, spherulic crystal aggregates composed from single needle like
crystals are visible. At the spherulite surface, needle like crystals form smaller, brush like
aggregates. Increasing ˙γSSHE to 1075 s−1, those large crystal aggregates are partially broken
up but still aggregated. Finally at 2150 s−1small, single, needle like crystals are visible in
a less aggregated arrangement. The calculated rpof 30 for PKO crystallized at 2150 s−1
seems plausible judging from the images. However, for PKO crystallized at 430 and 1075
s−1the calculated rpseems too high at first. At a second look the images seem to teach
that the primary particle/crystal dimension is not strongly changing, however the packing
of these in aggregates and the aggregate size are differing more significantly. Hence, it is
13
not clear which length scale reflects the aspect ratio and an average/mixed aspect ratio of
larger crystal aggregates and smaller crystal aggregates should be considered to relate the
derived aspect ratios with the microscopy images as shown in Figure 4. As a result we can
interpret the rpof 18 and 23 for PKO crystallized at 430 and 1075 s−1as superposition of
spherical and needle like aggregates. Another possible reason for the high derived aspect
ratios at ˙γSSH E of 430 and 1075 s−1is the fluid immobilization which occurs between the
crystal aggregates. As a consequence, effective crystal concentration is higher than the total
crystal concentration ΦSF C . The ΦSF C as determined by nuclear magnetic resonance spec-
troscopy measures the total crystal concentration and not the effective crystal concentration,
which leads to an overestimation of rp. The polarized light microscopy images correlate with
the rheological measurements since the average/mixed aspect ratio increases with increased
˙γSSHE as a result of deagglomeration. Crystal aggregates with increased average/mixed as-
pect ratio show steeper τ0=f(ΦS F C )curves as predicted by the increased excluded volume
as proposed by the model of Saar et al. 6. The decreased crystal agglomerate size indirectly
decreases the primary particle size via Equation 6 by assuming constant particle number per
agglomerate. As a consequence, steeper τ0=f(ΦSF C )are expected for smaller aggregate
size as proposed by the model of Marangoni and Rogers 4.
So far, only crystal size and shape was addressed but not the crystal polymorphic form. The
effect of shear and cooling rate on the polymorphic form of PKO crystals was investigated
by X-ray diffraction analysis. Figure 5a shows the X-ray diffraction spectrogram of PKO
crystallized under static conditions with (a) fast LN2or (b) slow cooling as well as PKO
crystallized at 10 ◦C stator wall temperature with ˙γSSHE of (c) 430, (d) 1075 and (e) 2150
s−1. The spectrum of the statically and fast LN2cooled PKO shows two distinct and strong
peaks at 0.382 and 0.423 nm with two less pronounced/weak peaks at 0.404 and 0.433 nm.
In contrast, the spectrum of the statically and slow cooled PKO shows four distinct peaks
at 0.377, 0.402, 0.423 and 0.439 nm, with the peak at 0.423 nm being the strongest. Less
pronounced and smaller peaks were found in (a) compared to (b) as well as two peak shifts
14
ሶ
𝜸𝑺𝑺𝑯𝑬 = 1075 s-1
large aggregate small aggregate
large aggregate small aggregate
large aggregate single crystal
ሶ
𝜸𝑺𝑺𝑯𝑬 = 430 s-1
ሶ
𝜸𝑺𝑺𝑯𝑬 = 1075 s-1
ሶ
𝜸𝑺𝑺𝑯𝑬 = 2150 s-1
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 4: Polarized light microscopy images of PKO CMS crystallized at 10 ◦C stator wall
temperature and at scraped surface heat exchanger shear rates ˙γS SH E of 430, 1075 and
2150 s−1. Flow rate was held constant at 20 kg/h. (a-c): 20-fold magnification with bar
representing 100 microns. (d-f): 60-fold magnification with bar representing 25 microns.
(g-i): Schematic illustration of the average/mixed aspect ratio concept.
15
from (a) 0.377 nm to (b) 0.382 nm and from (a) 0.433 nm to (b) 0.439 nm. PKO samples
crystallized in the scraped surface heat exchanger (c, d, e) show very similar spectrograms
with four distinct peaks at 0.378-0.379, 0.399-0.401, 0.419-0.421 and 0.432-0.436 nm. Curves
(c, d) show a slight peak shift from 0.435-0.436 nm to 0.432 nm compared to curve (e).
Comparing the spectra (a, b, c, d, e) with previous studies, the β0-polymorphic form is
prevalent in all samples.49–51 The characteristic d-spacing for α-polymorphic form crystals
lies between 0.41 and 0.415 nm.49–51 Due to the broad peaks around 0.42 nm in curve (a)
and (d), a small fraction of α-polymorphic form crystals could be present in those samples.
The less pronounced peaks in (a) compared to (b) occur due to the signal contribution of
an amorphous fraction, which decreases the signal/baseline ratio. Regarding the peak shifts
between (a) and (b) as well as between (e) and (c,d), minor fractions of α-polymorphic forms
in (a) and (e) are the most probable cause. To unambiguously determine the polymorphic
form of the PKO samples further, melting profiles in the form of thermograms were recorded.
Figure 5b shows thermograms, measured by differential scanning calorimetry, of PKO crys-
tallized under static conditions with (a) fast LN2or (b) slow cooling rate as well as PKO
crystallized at 10 ◦C stator wall temperature with varying shear rates of (c) 430, (d) 1075
and (e) 2150 s−1. The thermogram of statically and fast LN2cooled PKO shows a distinct
peak at 28.8 ◦C with a ridge between 18 and 26 ◦C. The thermogram of statically and slow
cooled PKO shows a broad peak with three small peaks at 27.9, 28.8 and 29.8 ◦C. Consid-
ering the curves of PKO crystallized in the scraped surface heat exchanger, melting peaks
lie between 28.8 and 29.3 ◦C. Curves (d) and (e) show a slight hump between 10 and 20 ◦C,
which is almost inexistent in curve (c). The thermograms confirm the previous findings since
main melting peaks were detected at similar temperatures of 27.9 to 29.3 ◦C for all curves in
Figure 5. Furthermore, the ridge detected in curve (a) explains the peak shift determined in
the X-ray diffraction measurements. The fast cooling rate led to a broadening of the melting
peak towards lower temperatures, which indicates the formation of a low melting tempera-
ture crystal fraction belonging to the α-polymorphic form. The slight hump between 10 and
16
20 ◦C in curves (c, d, e) decreases with increasing crystallization shear rate. Considering the
viscous dissipated energy EV
diss =tRη˙γ2, the disappearance of the hump is most likely due
to local heating effects during crystallization. The disappearance of the hump falls together
with the peak shift in the X-ray diffraction spectrogram from 0.432 nm (c) to 0.436 nm (d)
and 0.435 nm (e). This confirms that the peak shift is related to a lower melting crystal frac-
tion belonging to the α-polymorphic form. Similar results were found in previous studies on
cocoa butter.30 Accelerated formation of higher melting polymorphic forms with increasing
shear rate during crystallization was explained by the orientation of crystals under shear or
the melting of less stable polymorphic forms as consequence of dissipated energy.30,52
Summarizing the crystallographic results, it is evident that fast cooling rates promote crystal
compositions with lower melting points and broader melting ranges, whereas slow cooling
rates promote crystal compositions with higher melting points and narrower melting ranges.
The differences in melting ranges and slight peak shifts could indicate small fraction of α
polymorphic form crystals.
In conclusion, crystal morphology was identified as the most important parameter affecting
the yield stress of PKO CMS. With increasing shear rate, spherulic crystal aggregates are
broken down into needle like crystal aggregates and single needle like crystals, thereby in-
creasing the mixed aspect ratio of the system. The increased mixed aspect ratio of large
aggregates, small aggregates and single crystals decreases the critical crystal concentration
and increases the slope of the τ0=f(ΦSF C )curve. PKO crystallized dominantly into
the β0-polymorphic form, irrespective of shear or cooling rate in the applied ranges, which
rules out morphological changes due to polymorphic transitions. Small peak shifts and low
temperature melting peaks were attributed to lower temperature melting fractions of the
α-polymorphic form.
PKO CMS Foams: Relating rheological properties of crystal-melt suspensions (CMS) to
foam formation processes has so far not been conclusive. Previous studies formulated the hy-
pothesis that lipid crystals are able to form a hull of jammed crystals around gas bubbles.14,25
17
5 10 15 20 25 30 35 40
0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46
Heatflow [mW/g]
Temperature [°C]
Exo
(e) 430 s
-1
(d) 1075 s
-1
(c) 2150 s
-1
(b) static, slow
(a) static, fast
5 °C/min
28.9
27.9
28.8
29.8
29.3
28.8
28.8
hump
hump
ridge
hump
(b)
(a)
Intensity [a.u]
d-spacing [nm]
(c) 2150 s
-1
(d) 1075 s
-1
(e) 430 s
-1
(b) static, slow
(a) static, fast
0.379
0.399
0.419
0.432
0.379
0.401
0.421
0.436
0.378
0.399
0.420
0.435
0.377
0.402
0.423
0.439
0.382
0.404
0.423
0.433
Figure 5: (a) X-ray diffraction spectrograms of PKO CMS crystallized statically with fast
LN2or slow cooling at 23 ◦C, or crystallized at 10 ◦C stator wall temperature and scraped
surface heat exchanger shear rates ˙γSS HE of 430, 1075 and 2150 s−1. (b) Differential scanning
calorimetry thermograms of PKO CMS crystallized statically with fast LN2or slow cooling
at 23 ◦C, or crystallized at 10 ◦C stator wall temperature and scraped surface heat exchanger
shear rates ˙γS SH E of 430, 1075 and 2150 s−1.
18
The studies focused on the adsorption of the crystals to the lipid/air interface. However,
no study was able to show why the position at the lipid/air interface is thermodynamically
favorable for a lipid crystal compared to the fully immersed position in the lipid. Therefore,
the possibility that the stabilization of gas bubbles in CMS occurs preferably as result of gas
bubble immobilization due to a continuous crystal network formation cannot be ruled out.
Foam formation of CMS was investigated with a continuously operated membrane foaming
apparatus previously described.28 A schematic view of the apparatus is depicted in Figure
S4. Previous work on membrane emulsification showed that the drop diameter is determined
by the wall shear stress τwacting at the membrane surface and the pore diameter of the
membrane.53 For the boundary condition τw> τ0, the wall shear stress τwin the membrane
foaming apparatus was calculated via the wall shear rate γwaccording to the DIN 53019-1
for rotational rheometers with a rotating inner cylinder and a static outer cylinder, the latter
representing the membrane:54
˙γw=2Ω
n((α)2/n −1) (7)
τw=τ0+K˙γn
w=τ0+τvs (8)
where Ωis the angluar velocity of the rotor and αthe quotient of Ro/Ri,Kthe Consistency
factor and nthe Flow index derived from the Herschel-Bulkley fit at a given crystal concen-
tration ΦSF C as described previously. The dependencies of nand Kwith increasing ΦSF C
for a PKO CMS produced at ˙γS SHE = 430 s−1are depicted in Figure S5. The use of a yield
stress fluid as continuous phase is a major difference between this study and previous studies
on gas bubble dispersion in membrane devices.55,56 Consequently, the yield stress should
be accounted for in the dimensionless dispersion characteristics. The Bingham number Bm
allows to separate the yield stress τ0and the viscous stress τvs component during gas bubble
dispersion into a CMS. Hence, material property (τ0) and material dependent flow conditions
(τvs) are represented in one dimensionless number. The Bingham number for a CMS in a
19
shear flow can be expressed as:
Bm =τ0
η( ˙γn
w) ˙γn
w
=
6γ
aΦ1
3−D
K˙γn
w
(9)
Figure 6 shows the x90,0/xpore as function of the reciprocal Bingham number for PKO
10
0
10
1
10
2
10
3
10
4
10
0
10
1
10
2
10
3
t
0
g
SSHE
= 430 s
-1
Normalized bubble diameter x
90,0
/ x
pore
[-]
Bm
-1
= t
vs
/
t
0
[-]
SFC = 12.7
±
0.65
SFC = 7.2
±
0.96
SFC = 4.9
±
0.42
SFC = 2.3
±
0.47
SFC = 1.3
±
0.18
Fig. 7b
Fig. 7c
2
t
vs
t
vs
-1
-1
-1
2
x
90,0
µ
(hg
w
)
-1
E
v
diss
µ
g
2
w
m
12.7
m
7.2
Fig. 7d
Fig. 7a
m
4.9
m
2.3
m
1.3
2
t
0
Figure 6: The normalized bubble diameter x90,0/xpore as function of the reciprocal Bingham
number Bm−1for foamed PKO CMS crystallized at ˙γS SHE of 430 s−1. Direction of increasing
viscous stress τvs for a given ΦSF C is indicated (solid lines) as well as direction of increasing
yield stress τ0(dashed line).
CMS crystallized at ˙γSSHE = 430 s−1. It is evident that x90,0/xpore becomes smaller as the
Bingham number increases thereby approaching a value of 1. The higher the ΦSF C the higher
the Bingham number due to the increase in τ0. At constant ΦSF C and hence constant τ0, the
x90,0/xpore decreases with increasing reciprocal Bingham number Bm−1for all ΦSF C point
clouds. For ΦSF C = 12.7, 7.2, 4.9 and 2.3%a minimal x90,0/xpore is reached (m12.7, m7.2, m4.9,
m2.3) after which x90,0/xpore increases with Bm−1. As indicated in Figure 6, the normalized
bubble size x90,0/xpore scales with the viscous stress τvs to the power of minus one for every
ΦSF C point cloud. This finding deviates from the scaling factor proposed in a previous work
on membrane dispersion which proposes x90,0/xpore ≈τ−1/2assuming dripping mode of oil
20
drop dispersion in water systems.53 For gas bubbles detaching from the membrane pore, the
high radial velocities of the continuous CMS, the low interfacial tension between gas phase
and CMS and the high volumetric flow of the disperse phase favor the jetting mode.57 Hence,
the scaling factor x90,0/xpore ≈τ−1/2is no longer valid, since it cannot be assumed that the
bubble diameter equals the membrane pore diameter at the moment of detachment. In order
to determine the equilibrium bubble diameter during a filamentous break up, the Laplace
pressure inside the created bubble and the shear stress acting on the bubble can be related
by the Capillary number:
Ca =xbτw
4γ(10)
where xbis a chosen statistically representative value for the bubble diameter. A critical
Capillary number Cacrelates to the maximum bubble diameter for a given viscosity ratio
λbetween disperse and continuous phase in a quasi-equilibrium steady shear flow state.55
Hence, such maximum bubble diameter as function of the acting shear stress can be written
as follows:
xb=x90,0=4γC acrit(λ)
τw
=k1(λ)τ−1
w(11)
where k1is a system specific constant depending on the viscosity ratio of disperse and
continuous phase and hence the ΦSF C of the CMS. From Equation 11, the bubble diameter
scales with the wall shear stress to the power of -1. This is in accordance with the ΦSF C
–specific measured point clouds which show a slope of -1 in good approximation (see Figure
6). Since CMS are temperature sensitive, the increase in x90,0/xpore for ΦS F C = 12.7, 7.2,
4.9 and 2.3%with further increasing wall shear stress is hypothesized to be related to partial
fat crystal remelting due to viscous energy dissipation. Such can be expressed as:
EV
diss =tRη˙γ2
w(12)
where EV
diss is the volume specific dissipated energy by viscous friction and tRdenotes the res-
idence time in the membrane gap during foam formation. From Equation 12, EV
diss scales with
21
γwto the power of 2. This scaling factor matches approximately the slope of the x90,0/xpore
increase after passing the local minimum mxwhen increasing the wall shear stress in the
membrane gap. The viscous energy dissipation is expected to induce some melting of fat
crystals contained in the CMS leading to an increase in x90,0/xpore. Elevated viscous power
dissipation at low ΦSF C leads to almost complete melting of the CMS contained fat crys-
tals. As a consequence, the resulting foams are no longer stable enough to determine bubble
size/size distribution. For the ΦSF C = 1.3%point cloud the increase in x90,0/xpore at higher
shear stresses was therefore not detectable.
Figure 7 shows polarized light microscopy images of PKO CMS foamed at increasing recip-
rocal Bingham numbers from (a) to (d). Figure 7a shows small bubbles with narrow size
distribution surrounded by a continuous dense crystal network. Figure 7b shows small bub-
bles with narrow size distribution surrounded by a discontinuous matrix of small crystalline
patches. Figure 7c shows large and small bubbles with broad size distribution surrounded
by a continuous network of large crystalline patches. Figure 7d shows small bubbles with
narrow size distribution surrounded by a continuous dense crystal network. Figures 7a to
7c demonstrate that for constant ΦSF C an unsteady x90,0/xpore trend with increasing Bm−1
is observed. From Figure 7a to 7b, a decrease in x90,0/xpore at constant SPAN takes place.
From Figure 7b to 7c, an increase in both x90,0/xpore and SPAN occurs. The overlapping
of dispersion stresses and dissipated viscous energy with increasing ˙γwand consequently
increasing Bm−1are the reason for the reversing x90,0/xpore trend. At low ˙γw, dispersion
stresses dominate leading to smaller bubbles. After passing the local minimum mx, dissi-
pated viscous energy is expected to cause partial remelting of the crystal matrix thereby
inducing instability effects such as Ostwald ripening and coalescence leading to increased
x90,0/xpore and SPAN values. Figures 7b and 7d illustrate that for increasing ΦSF C , bubble
diameter at the local minimum mxdecrease while approaching Bingham numbers closer to
1. A Bingham number of 1 is practically impossible to reach during dispersion as this defines
the boundary between flow and no flow. If the Bingham number exceeded a value of 1, the
22
membrane would be covered by a non-flowing CMS layer inducing clogging of the membrane
pores. Therefore, gas dispersion into a yield stress fluid can only occur if the Bingham num-
ber is smaller than 1.
Concluding, the normalized bubble diameter x90,0/xpore of PKO CMS foams depends on the
ratio between shear stress and yield stress as expressed by the Bingham number. For every
ΦSF C there exists a local minimum mxwhere dispersing stresses and dissipated energy are
at balance. At the local minimum, x90,0/xpore and SPAN values are lowest. For varying
ΦSF C ,x90,0/xpore at the local minimum becomes smaller for Bingham numbers approaching
the value 1. Consequently, a hypothetical global minimum at Bm = 1 exists, where smallest
possible normalized bubble diameters x90,0/xpore are formed. This finding gives evidence
that gas bubble stabilization is most efficient if the CMS is subjected to a membrane wall
shear stress equal or slightly greater than the related yield stress.
Conclusion
Predicting the rheological properties of crystal-melt suspensions (CMS) assists in under-
standing the flow and structure formation characteristics of liquid to semi solid polymer,
metal, magma and lipid systems under crystallization conditions. For the specific case of
palm kernel oil (PKO) CMS, we observed that the increase in shear rate during crystalliza-
tion lead to the break-up of spherulic crystal aggregates into smaller aggregates and single
needle-like crystals. The overall increased aspect ratio of the crystal aggregates and crystals
resulted in a steeper increase of the yield value with increasing solids fraction and a lower
critical crystal concentration Φcfor the onset of a yield stress τ0. By introducing gas bub-
bles into CMS, complex foams were generated. In the present study, we demonstrate that
the dispersion of gas bubbles into yield stress fluids, such as CMS, can be related to the
Bingham number Bm. The dimensionless gas bubble diameter x90,0/xpore is further shown
to decrease for increasing Bingham number approaching the value of Bm = 1, given that the
gas dispersion is performed at quasi-equilibrium where viscous shear stress τvs and dissipated
23
Figure 7: Polarized light microscopy images of foamed PKO CMS produced at increasing
reciprocal Bingham numbers from (a) to (d). (a): Bm−1= 2.5, x90,0/xpore = 6.6, SPAN =
1.2, γn
w= 418 s−1,τ0= 73 Pa (b): Bm−1= 4.4, x90,0/xpore = 4.4, SPAN = 1.3, γn
w= 1255
s−1,τ0= 73 Pa (c): Bm−1= 6.0, x90,0/xpore = 11, SPAN = 2.8, γn
w= 2092 s−1,τ0= 73 Pa
(d): Bm−1= 18, x90,0/xpore = 8.6, SPAN = 1.2, γn
w= 856 s−1,τ0= 11 Pa. The PKO CMS
was crystallized at ˙γSSH E = 430 s−1. (a-c: initial ΦSF C = 12.7%; d: initial ΦS F C = 7.2%).
Bar represents 100 microns.
24
viscous energy EV
diss enable adjustment of a steady state crystal-stabilized microfoam struc-
ture. With the insights gained from this work, one can derive a mechanistic understanding
of gas bubble dispersing and related foam stabilization in CMS. The applied dimensionless
approach is expected to derive foam processing solutions in a wider range of gas dispersing
processes and materials from lipids to metals and polymers and even further to volcanic
(magma) systems.
Acknowledgement
The Swiss Innovation Agency is gratefully acknowledged for funding support. The authors
thank Daniel Kiechl, Bruno Pfister, Bernhard Koller, Lydia Zehnder, Johannes Burkard and
Peter Bigler for their technical support. Furthermore Peter Fischer, Pascal Bertsch and
Jotam Bergfreund are acknowledged for the fruitful discussions.
Supporting Information Available
The following files are available free of charge.
•Figure S1: Velocity profile as measured by the UVP-PD method of PKO CMS (S2)
•Figure S2: Process and Instrumentation scheme for the PKO CMS foam production
(S2)
•Figure S3: Schematic drawing of the UVP-PD measurement set up (S3)
•Figure S4: Schematic radial cross-section of the dynamically enhanced membrane foam-
ing cell (S3)
•Figure S5: Linear regressions of the Flow index nand Consistency factor Kas function
of solid fat content ΦSF C (S3)
25
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31
"For Table of Contents Use Only"
Yield Stress Dependent Foaming of Edible
Crystal-Melt Suspensions
Kim Mishra,∗,†Damien Dufour,‡,†and Erich J. Windhab†
†Institute of Nutrition and Health, Swiss Federal Institute of Technology,
Schmelzbergstrasse 9, 8092 Zürich
‡Current address: Ubertone, Rue du Brochet 14, 67300 Schiltigheim
E-mail: kim.mishra@hest.ethz.ch
Phone: + 41 44 632 97 10
Here, the influence of crystal volume fraction and crystal morphology on the rheology of palm
kernel oil crystal-melt suspensions (PKO CMS) is reported. In addition, PKO CMS were
foamed with a dynamically enhanced membrane foaming apparatus. A new dimensionless
gas bubble dispersion characteristics for temperature sensitive yield stress fluids is proposed.
