Evaporation of Droplets on Superhydrophobic Surfaces:
Surface Roughness and Small Droplet Size Effects
Xuemei Chen,1Ruiyuan Ma,2Jintao Li,1Chonglei Hao,1Wei Guo,1B.L. Luk,1Shuai Cheng Li,3
Shuhuai Yao,2and Zuankai Wang1,*
1Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong 999077, China
2Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Hong Kong 999077, China
3Department of Computer Science, City University of Hong Kong, Hong Kong 999077, China
(Received 10 January 2012; revised manuscript received 20 July 2012; published 10 September 2012; publisher error corrected
12 September 2012)
contact line (CCL), a constant contact angle (CCA), or both, our fundamental understanding of the effects of
surface roughness on the wetting transition remains elusive. We show that the onset time for the CCL-CCA
transition and the critical base size at the Cassie-Wenzel transition exhibit remarkable dependence on the
droplet becomes comparable to the surface roughness, the line tension at the triple line becomes important in
the prediction of the critical base size. Last, we show that both the CCL evaporation mode and the Cassie-
Wenzel transition can be effectively inhibited by engineering a surface with hierarchical roughness.
DOI: 10.1103/PhysRevLett.109.116101 PACS numbers: 68.08.Bc, 68.03.Fg
Understanding and controlling the droplet contact line
dynamics on textured surfaces, especially superhydropho-
bic surfaces, is of critical importance for a wide range of
applications including self-cleaning, drag reduction, water
harvest, anticorrosion, thermal management, and biosens-
ing [1–11]. Although the contact line dynamics of a droplet
on hydrophobic or superhydrophobic surfaces in the equi-
librium conditionhas beenextensivelystudied [12–15], the
contact line dynamics during the phase change processes
such as evaporation and condensation remains relatively
less exploited. In the case of droplet evaporation, most
studies to date focus either on the investigation of the
evaporation patterns [16–18] or on the evaporation modes
including a constant contact line (CCL), a constant contact
angle (CCA), and a mixed mode on various surfaces or on
the Cassie-Wenzel transition occurring at the late stage of
evaporation [19–21]. Despite extensive progress, our fun-
damental understanding of how the surface roughness
affects the wetting transition remains elusive. In this
work, we systematically investigated the full spectrum of
evaporation dynamics of droplets on rough surfaces based
on microscopic and macroscopic observations and found
that the wetting transition exhibited remarkable depen-
dence on the geometric arrangement of the substrate. In
particular, when the droplet shrinks to a size that is com-
parable to the substrate roughness, the line tension be-
comes more important. We developed general models to
accurately predict the CCL-CCA transition onset time and
critical base size at the Cassie-Wenzel transition,
We first studied the evaporation dynamics on the micro-
textured silicon surfaces with pillar-to-pillar spacings (L)
of 10, 20, and 40 ?m, respectively. For simplicity, these
surfaces are denoted as m10, m20, and m40, respectively.
The diameter (D) and height (H) of pillars of all three
surfaces are set as 20 and 80 ?m, respectively. All these
surfaces were fabricated by using standard microfabrica-
tion processes including photolithography and deep
reactive-ion etching [22,23]. To render them superhydro-
phobic, the samples were treated with ?1 mM hexane
solution of perfluorooctyl trichlorosilane for ?30 min,
followed by heat treatment at ?150?C in air for 1 h.
Figure 1(a) shows the scanning electron microscopy image
of the as-fabricated m40 surface. The evaporation process
was carried out at ?17?C, and the relative humidity was
?65%. The water droplets on the microstructured surface
(m10, m20, and m40) exhibited three distinctive evapora-
tion stages: a CCL mode with a decreasing contact angle at
the early stage, a CCA mode with a shrinking contact line,
and a mixed mode with a Cassie-Wenzel transition. The
evaporating droplet in the CCL and CCA modes stayed in
a Cassie state, as can be clearly seen from Fig. 1(b).
Although all the microstructured surfaces exhibit three
evaporation stages, we found that the CCL-CCA transition
exhibited remarkable sensitivity to the geometry arrange-
ment: The CCL-CCA transition onset time on m40 surface
is the lowest (2558 s), which is ?26% lower than the m10
surface (3230 s) [see Figs. 1(c) and 1(d)].
The existence of a CCL stage on the microtextured
surface might be explained by considering the local
forces at the triple contact line [10,24]. The depinning
force FD can be expressed as 2Rb?lgðcos? ? cos?cÞ,
where Rbis the base radius of droplet, ?lgis the surface
tension of water, ?is the dynamic contact angle during the
evaporation, and ?cis the apparent contact angle on the
PRL 109, 116101 (2012)
14 SEPTEMBER 2012
? 2012 American Physical Society
rough surface. The pinning force FPcan be expressed as
2Rb?lg½ðcos?ro? cos?aoÞ; þ Hr?, where ?roand ?aoare
receding and advancing contact angles on the flat surface
(? 80?and 120?in our case), respectively, and ; is the
solid fraction. Hrdenotes the adhesive force due to sur-
face roughness and heterogeneity (Hr? cD2=L2). The
constant c is obtained by fitting the measured contact
angle hysteresis with the theoretical data. In our case,
c ¼ 0:02 [see Fig. 2(a)]. Assuming the ratio of depinning
force to the pinning force as the driving ratio (?),we have
? ¼ FD=FP
¼ ðcos? ? cos?cÞ=½ðcos?ro? cos?aoÞ; þ Hr?:
Thus, based on the dynamic contact angle obtained in the
experiments, the progression of driving ratio (?) with
time is plotted in Fig. 2(b). We can see that, at the
beginning of evaporation, ? is less than 1, indicating
that the droplet stays in the sticky CCL mode. When ?
reaches the maximum (? 1:1, 1.3, and 1.5 for three sur-
faces, respectively), the droplet transits to CCA mode.
To theoretically predict the CCL-CCA transition onset
time, we referred to the spherical cap model derived by
Rowan et al., which describes the evaporation time (t) of
a droplet in the CCL stage [25,26]. Briefly, t is governed
by the following equations:
where ?criis the critical receding angle, ?0is the apparent
contact angle, Rbois the initial base radius of the droplet,
Dfis the diffusion coefficient of water (1:83?10?5m2=s),
C1and Coare the concentration of saturated water vapor
at infinity (9:425 g=m3) and immediately surrounding the
droplet (14:5 g=m3) , respectively, and ? is the liquid
density (1 g=cm3). By assuming ? equivalent to 1.0 in
Eq. (1), the critical receding angle on m10, m20, and
m40 surfaces at the CCL-CCA transition are calculated
to be 119?, 137?, and 152?, respectively, which are in good
agreement with our experimental data on the transition
points [Fig. 2(c)]. As shown in Fig. 2(d), the time predic-
tion obtained from our model is in reasonable agreement
with our experimental observation: The larger the spacing,
the more favorable for CCL-CCA transition.
The surface that is more prone to CCL-CCA transition
also corresponds to a larger critical base size at the Cassie-
Wenzel transition. The critical drop base radius R?
m40 surface at the Cassie-Wenzel transition is ?130 ?m,
which is much larger than those on m10 (? 80 ?m) and
m20 (? 100 ?m) surfaces [Fig. 3(c)]. In order to elucidate
the effect of surface roughness on the Cassie-Wenzel
FIG. 2 (color online).
cos?a) as a function of pillar-to-pillar spacing (L). The theoreti-
cal predictions are obtained through the equation cos?r?
cos?a¼ ;ðcos?ro? cos?aoÞ þ cD2=L2, where c is a constant.
When c ¼ 0, the theoretical value is underestimated, whereas
when c is equal to 0.02, there is a good fit between our
experimental (squares) and theoretical data (solid line).
(b) Time evolutions of the driving ratio (?) on microtextured
surfaces (m10, m20, and m40). ? is less than 1.0 in the CCL
stage and fluctuates around 1 after transiting to the CCA mode.
(c) The effect of pillar-to-pillar spacing (L) on the critical
receding angle based on theoretical analysis (solid line) and
experimental measurements (square). The theoretical receding
angles are obtained when the driving ratio ? ¼ 1. (d) The effect
of pillar-to-pillar spacing (L) on the onset time corresponding to
the CCL-CCA transition based on both experimental (squares)
and theoretical prediction (solid line).
(a) Contact angle hysteresis (cos?r?
FIG. 1 (color online).
of a microstructured surface with pillar-to-pillar spacing L ¼
40 ?m (m40). (b) Time-dependent images of an evaporating
droplet on the m40 surface. (c),(d) Time evolutions of normal-
ized contact base radius and contact angle on microstructured
surfaces (m10, m20, and m40).
(a) Scanning electron microscopy image
PRL 109, 116101 (2012)
14 SEPTEMBER 2012
transition, we first considered a number of models includ-
ing the touchdown model, pinning instability model, etc.
[28–31]. However, these models could not accurately pre-
dict the accurate droplet base radius, partially due to the
fact that the droplet size at the late stage of evaporation is
very comparable to our substrate roughness. For example,
in the touchdown model , the critical radius R?
Cassie-Wenzel transition is ?L2=H ¼ 20 ?m, which is
much smaller than the observed droplet base radius R?
(? 130 ?m).
To enable a more accurate prediction of the critical base
size, we compared the interfacial energy of a droplet at
both Cassie and Wenzel states [32–34]. Note that at the late
b=sin?) of the droplet on the m40 surface at the
stage of evaporation previous to the Cassie-Wenzel tran-
sition, the droplet size is comparable to the pillar diameter.
Underthis condition,thelinetension (?),theexcess offree
energy per unit length of the three-phase contact line, is not
negligible in the energy analysis because of the increasing
line-to-surface and line-to-volume ratios in the small drop-
let [35–40] [Fig. 3(a)]. Thus, the total energy in the system
includes the interfacial energy associated with the solid-
gas (?sg), liquid-gas (?lg), and solid-liquid (?sl) as well as
the line energy. Moreover, since the pillars underneath the
evaporating droplet exhibit different contact lines and the
total number of pillars is limited, it is important to separate
the inside pillars, which are completely covered by the
droplet, from external ones, which are partially covered by
the droplet, in the calculation of the interfacial energy of
the system. Thus, we first calculated the number of internal
pillars (N1) as well as external pillars (N2). Based on the
study of the Gaussian circle problem and the parameter
settings of the linear regression method [41–44], we ob-
Material ). Accordingly, to calculate the total interfa-
cial energy, the solid-liquid surface area (Asl), the solid-gas
surface area (Asg), and the total contact line (LT) were
divided into two parts, respectively. Briefly, Aslconsists
of the liquid surface area contacting with the external
pillars (Asl-ex) and the inside pillars (Asl-in), Asgconsists
of the gas surface area contacting with the external pillars
(Asg-ex) and the inside pillars (Asg-in), and LTincludes the
contactline contributed bytheexternal pillars(Lex)and the
inside pillars (Lin) [see Fig. 3(b)].
Thus, the energy associated with the Cassie state ECcan
be expressed as
EC¼ Acap?lgþ Alg?lgþ ðAsl-inþ Asl-exÞ?sl
þ ðAsg-inþ Asg-exÞ?sgþ ðLinþ LexÞ?;
where Acapis the surface area of the water cap in contact
with the gas, which can be expressed as
the base liquid area contacting with the gas and is equiva-
lent to ?R2
Asl-ex¼0:119N2?D2. Asg-in¼ N1?DH þ ?R2
and Asg-ex¼ N2LABCH ¼ 0:546N2?DH. Lin¼
N1?D and Lex¼ N2ðLABCþ LADCÞ ¼ 0:834N2?D (see
Supplemental Material ), where N2LABCand N2LADC
are the total inside and outside arc length of water contact
with the external pillars, respectively.
Similarly, the energy in the Wenzel state is governed by
b? Asl-in? Asl-ex, where Asl-in¼ N1?D2
where Acap1is the surface area of the water cap in contact
with thegas, which can be expressed as
contact angle of the cap after droplet transiting to the
1þcos?1and ?1is the
FIG. 3 (color online).
microscope images of a Cassie- and Wenzel-state droplet with
surface tension and line tension labeled. (b) Schematic drawing
of a Cassie drop sitting on the microstructured surface. The
enlarged image shows the contact line of single internal and
external pillars. (c) Comparison of the critical drop base radius
bat the Cassie-Wenzel transition on various surfaces between
experimental data (square) and theoretical prediction using the
global interfacial energy analysis (solid line). (d) The variation
of the critical drop base radius R?
values. When the line tension is larger than 3 ? 10?5J=m, the
bremains almost unchanged, whereas below this
critical line tension value, there is a sharp increase in R?
corresponding to a large discrepancy between theoretical and
(a) Environmental scanning electron
bunder different line tension
PRL 109, 116101 (2012)
14 SEPTEMBER 2012
Wenzel state. Assuming EC¼ EW, and Rband droplet
volume remain unchanged during the transient transition,
we can get the critical droplet base radius R?
calculation, ? is set to be 3 ? 10?5J=m, and this value
falls within the wide range (10?12–10?4J=m) found in the
literature [36–38]. Figure 3(c) shows both the experimental
critical base radius R?
band theoretical values obtained from
the model for surfaces of different pillar-to-pillar spacing
(L). We can see a reasonable agreement between the
theoretical and experimental results for m10 and m20
surfaces. Note that the theoretical R?
is ?188 ?m, which is relatively larger than our experi-
mental data. In order to illustrate the influence of line
tension on the critical droplet base radius R?
Cassie-Wenzel transition, we compared data under differ-
ent line tension values (from the order of 10?6to
10?3J=m). As shown in Fig. 3(d), the theoretical R?
almost unchanged when the line tension is larger than
3 ? 10?5J=m, while the R?
smaller than 3 ? 10?5J=m. For example, when line ten-
sion is 3 ? 10?6J=m, R?
which is 150% and 73% larger than our experimental data
and the theoretical R?
respectively, indicating the significance of line tension in
the energy analysis. Note that, among the three surfaces,
the m10 surface has the largest line energy percentage
(? 83:8% for the Cassie state and ?78:1% for the
Wenzel state) due to its largest pillar density or the smallest
pillar-to-pillar spacing (L).
The contact line pinning at the early stage of evaporation
and Cassie-Wenzel transition as well as the small droplet
size effect at microstructured surfaces could be suppressed
by engineering hierarchical surfaces. In order to verify this
hypothesis, we deposited uniform nanopillar arrays on the
top and valley of our microstructured surfaces (m10,
m20, and m40). The nanopillars are ?400 nm in diameter,
?5 ?minheight,and?200–400 nminpitch.Accordingly,
we term three hierarchical surfaces as mn10, mn20, and
mn40. Figure 4(a) shows the snapshots of an evaporating
droplet on the mn40 surface over time. Distinct from that on
microstructured surfaces, the evaporating droplets on hier-
archical surfaces exhibit only two distinct stages: the CCA
mode and the mixed mode [see Figs. 4(a)–4(c)]. The dis-
appearance of the sticky CCL mode is ascribed to the large
ness. The force analysis at the triple contact line indicates
that the depinning force at the micro- or nanopatterned
surface is more than 2–5 times larger than the pinning force
enhanced dynamic wetting properties, the hierarchical sur-
faces exhibit superior global depinning at the macroscopic
level during the evaporation of droplets in the air; i.e., the
sticky CCL evaporation mode is inhibited. Similarly, the
presence of nanoscale roughness on the microscale rough-
ness significantly lowers the solid surface energy, and
b. In our
bof the m40 surface
bincreases sharply when ? is
bof the m40 surface is ?326 ?m,
bin the case of ? ¼ 3 ? 10?5J=m,
therefore the Cassie-Wenzel transition is prevented .
For example, assuming a droplet with a base radius of
130 ?m, a size that a droplet will transit to the Wenzel state
upon the m40 surface, the Cassie energy on the hierarchical
mn40 surface is ?9:5 ? 10?7J, which is much lower than
the Wenzel energy calculated for the Wenzel state (? 1:0 ?
10?6J), indicating that the droplet might stay in a meta-
stable Cassie state. Note that, although we did observe an
obvious contact angle change at the late stage of evapora-
tion, the drop remained in a composite state. In order to
accurately monitor the wetting state transition with high
spatial resolution, we investigated the evaporation dynamics
of microdroplets on hierarchical surfaces using an environ-
mental scanning electron microscope (Philips XL-30). We
used condensation to produce droplets whose sizes were
?100 ?m. We found that, during the evaporation, the
droplet preferentially wetted the micropillars instead of
nanoscale pillars [see the dashed circles in Fig. 4(d)], sug-
gesting the effect of nanoscale roughness in preventing
contact line pinning. Moreover, we did not observe the
Cassie-Wenzel transition during the evaporation. Similarly,
L (mn40), we can clearly see that there exists a vapor layer
between the droplet and substrate during the evaporation,
inhibiting the complete Cassie-Wenzel transition.
The unique evaporation phenomenon on a hierarchical
surface offers several advantages for biosensing. First, the
FIG. 4 (color online).
orating droplet on the mn40 surface. (b),(c) Time evolutions of
normalized contact base radius and contact angle on hierarchical
surfaces (mn10, mn20, and mn40). Droplet evaporation on all
the surfaces exhibits two evaporation modes: a CCA mode and a
mixed mode. (d) Snapshots of microdroplet evaporation on the
mn10 surface. During the evaporation, the droplet preferentially
wets the micropillars rather than the nanopillars, as shown in the
inset. (e) Snapshots of microdroplet evaporation on the mn40
surface. The presence of nanoscale roughness in the cavities and
at the tops of micropillars (inset) prevents the Cassie-Wenzel
transition during the evaporation.
(a) Time-dependent images of an evap-
PRL 109, 116101 (2012)
14 SEPTEMBER 2012
absence of a sticky CCL evaporation mode enabled by the
presence of nanoscale roughness on hierarchical surfaces
significantly decreases the solid-molecule interaction, lead-
ing to minimal molecule loss during the transport and
enrichment process. Moreover, since the transduction struc-
tures for biosensing are usually located on the top of a
surface, the formation of a composite state on the hierarch-
ical surfaces at the late stage of evaporation might signifi-
cantly promote the interaction between molecules diluted in
novel detection strategy eliminates the need for extra filtra-
tion steps, allowing for the detection of molecules at a very
low concentration level.
In summary, we systematically investigated the full
spectrum of contact line dynamics during the droplet
evaporation based on microscopic and macroscopic obser-
vations and found that the contact line dynamics exhibited
remarkable dependence on the geometric arrangement of
the substrate. We developed general models to accurately
predict the CCL-CCA transition onset time and critical
base size at the Cassie-Wenzel transition. Interestingly,
we demonstrated the significance of incorporating line
tension in the analysis of energy states of droplets, espe-
cially when the evaporating droplet shrinks to a size com-
parable to the feature size of the solid roughness. We
further show that the presence of nanoscale roughness on
hierarchical surfaces not only prevents the onset of contact
line pinning at the early stage of evaporation but also leads
to the formation of a composite droplet without transiting
to the sticky Wenzel state. The unique evaporation phe-
nomena on hierarchical surfaces, coupled with the ability
to control the contact line and wetting transition dynamics,
might provide important insights for the design of robust
superhydrophobic surfaces for various applications.
This work was supported by the Early Career Scheme
Grant (No. 9041809),National
Foundation of China (No. 51276152) and National
Program on Key Research Project (No. 2012CB933301),
Centre for Functional Photonics at CityU, HKUST Direct
Allocation Grant (No. DAG08/09.EG03), and RGC
General Research Fund (621110). The authors also thank
Professor Howard Stone for many useful discussions.
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