J. Phys. Chem. B 2008, 112, 11317–11323
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Wetting and Evaporation of Binary Mixture Drops Khellil Sefiane,*,† Samuel David,† and Martin E. R. Shanahan‡ UniVersity of Edinburgh, School of Engineering and Electronics, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JL, U.K., and UniVersite´ Bordeaux 1, Laboratoire de Me´canique Physique, CNRS UMR 5469, 351 Cours de la Libe´ration, 33405 Talence Cedex, France ReceiVed: April 8, 2008; ReVised Manuscript ReceiVed: May 15, 2008
Experimental results on the wetting behavior of water, methanol, and binary mixture sessile drops on a smooth, polymer-coated substrate are reported. The wetting behavior of evaporating water/methanol drops was also studied in a water-saturated environment. Drop parameters (contact angle, shape, and volume) were monitored in time. The effects of the initial relative concentrations on subsequent evaporation and wetting dynamics were investigated. Physical mechanisms responsible for the various types of wetting behavior during different stages are proposed and discussed. Competition between evaporation and hydrodynamic flow are evoked. Using an environment saturated with water vapor allowed further exploration of the controlling mechanisms and underlying processes. Wetting stages attributed to differential evaporation of methanol were identified. Methanol, the more volatile component, evaporates predominantly in the initial stage. The data, however, suggest that a small proportion of methanol remained in the drop after the first stage of evaporation. This residual methanol within the drop seems to influence subsequent wetting behavior strongly. Introduction Wetting of solid surfaces by liquids accompanied by evaporation is a phenomenon encountered in a wide range of areas and impinges on many fields ranging from biological systems to industrial applications. Ring formation from evaporating drops and its use for thin films coating1 and DNA chain elongation using drying sessile droplets are examples of existing new developments stressing the need for a better understanding of the process of evaporating droplets. Several references can be found in the literature of work dedicated to understanding the fundamentals of this process, e.g., Picknett & Bexon,2 de Gennes,3 and Shanahan.4,5 It is worth noting that the majority of research on the subject has considered pure liquids. Although wetting and evaporation of binary mixtures is important in many applications, little work has been done to investigate the fundamentals of the problem. In a study by Rowan et al.,6 the wetting behavior of a 1-propanol and water mixture was studied. Contact angle and base diameter measurements of the droplet were made for a variety of compositions. The results of this investigation show two distinct trends of wetting behavior: one for mixtures with 1-propanol mole fractions of less than 0.39 and one for mixtures with higher mole fractions. For mixtures containing mole fractions of 1-propanol greater than 0.39, it was found that the contact angle decreased at a steady rate during the droplet lifetime, whereas the base diameter was steady for about 60 s before decreasing at a fast rate. For mixtures containing less than 0.39 mol fraction of 1-propanol, the behavior observed was markedly different. Initially, for a short period of time, the contact angle decreased. Following this phase, contact angle measurements were found to be unobtainable due to instabilities around the droplet periphery. An explanation suggested for this behavior is concerned with the azeotropic nature of the * To whom correspondence should be addressed. E-mail: ksefiane@ ed.ac.uk. Phone: +441316504873. Fax: +441316506551. † University of Edinburgh. ‡ Universite ´ Bordeaux 1.
1-propanol/water mixture. When the mixture contains a water fraction in excess of the azeotropic composition, evaporation will result in a residual liquid that tends toward pure water as the 1-propanol is preferentially adsorbed at the interface. The combined effects of the preferential adsorption of 1-propanol and cooling caused by evaporation induce local surface tension variations and extrema, leading to the observed instabilities. When most of the 1-propanol has evaporated, the dynamic surface tension will tend to that of pure water, which is indicated by the higher contact angles detected in the latter stages of the experiment. Sefiane et al.7 studied the evaporation of water/ethanol binary drops resting on a rough PTFE substrate. Drops were left to evaporate in a semiopen chamber at atmospheric pressure. The authors recorded the drop volume in time and deduced the evaporation rate. They also measured the evolution of the contact angle and the drop base diameter. Different from the behavior of pure components (water and ethanol), where the drop profile evolved monotonically, the evaporation of binary mixtures could be divided in three stages. From the evaporation rate measurements, it was shown that the more volatile component evaporated principally in the first stage. During this first stage, the contact angle was similar to that of pure ethanol. Toward the end of the drop lifetime, the behavior resembled that of pure water. Recently, Cheng et al.8 investigated the evaporation of microdroplets of ethanol/water mixtures on gold surfaces. The substrate used in the investigation (gold coated on a microscope slide) was very smooth. Identical volumes (2 µL) from various compositions (25, 50, and 75% in volume) were deposited and left to evaporate in air under ambient conditions. By plotting initial contact angle against composition, a near linear relationship was found. The evaporation process of pure water or ethanol drops could be divided into two stages: pinning and shrinking. At the beginning, water/ethanol mixtures showed an increase in contact angle and a reduction in the contact area. Various stages corresponding to different wetting behavior were identified in this investigation.
10.1021/jp8030418 CCC: $40.75 2008 American Chemical Society Published on Web 08/16/2008
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It is clear that, besides the limited number of investigations of the evaporation and wetting behavior of binary drops, the reported results remain essentially descriptive of firsthand observations of the phenomenon. More work on the subject is needed to fully elucidate various aspects of this important problem. The aim of this paper is to present the findings of an experimental investigation of the evaporation and wetting behavior of methanol/water droplets. The physical mechanisms behind the experimental observations will be discussed. Experimental Section Methanol/water mixtures were chosen on the basis of their relatively different surface tensions and volatilities yet good mutual mixing properties. Water has a surface tension of ca. 72 mN m-1 and methanol ca. 22.5 mN m-1. Methanol is the more volatile of the two components. It is worth noting that surface tension variation of the mixture is more pronounced at lower methanol concentrations. For instance, the drop in γ from 0 to 20% methanol is ca. 24 mN m-1, whereas, from 80 to 100%, it is ca. 3 mN m-1. Ultrapure deionized water (MilliQ) was used together with (almost) absolute methanol (99.8%) purchased from Fisher Scientific. The mixtures were prepared before running each experiment in order to maintain constant mixture composition. A microbalance (Mettler Toledo XS205) was used for the preparation of the binary mixtures. Three concentrations were prepared: water/methanol mixtures with mass-to-mass concentrations of 10, 50, and 80%. Because of its very smooth surface, a silicon wafer was chosen as a substrate to conduct experiments. The wafer was cut in 10 mm × 10 mm squares (1 mm thick) to produce identical samples for the experiment. Since silicon has a relatively high surface free energy, it is completely wet by most liquids. The substrates were coated with a very thin PDMS (polydimethylsiloxane) hydrophobic layer to obtain measurable wetting angles. This operation did not modify the surface roughness of the silicon. Surface profile analysis, performed by profilometry (ZYGO) and atomic force microscopy (AFM), showed that the coated silicon substrates were very smooth (RA < 0.5 nm). Before running each experiment, the samples were cleaned following a standardized procedure: cleaning in an ultrasound bath, rinsing, and drying with nitrogen gas. For all experiments, drops were placed inside an “environmental chamber”. This allows a better control of the experimental conditions (ambient temperature and pressure) as well as the possibility of saturation of the atmosphere by one of the two components. To eliminate the influence of humidity, the chamber was filled with nitrogen. The ambient temperature was maintained at 23 °C and the pressure at 1000 mbar. A DSA100 goniometer was used to measure the contact angle and drop base diameter, allowing drop volume to be calculated (assuming the form of a spherical cap). Uncertainties in measurements of the drop base radius and the contact angle were estimated at within (1%. The environmental chamber is a cell, cylindrical in shape, connected to a vacuum pump and a gas supply line. It was designed to be used with the DSA100 apparatus. Two optical windows are positioned on two opposite sides to allow simultaneous lighting and video recording. On the top of the chamber, a valve is connected to the injection system. Droplets of controlled volume can be dispensed at a controlled rate. The laboratory is equipped with an air conditioning unit to maintain constant ambient temperature. Temperature, pressure, and humidity in the room were monitored. To minimize perturbations, the DSA100 apparatus was placed on an antivibration table. In contrast to Cheng et al.8 and Rowan
Figure 1. Evolution of drop volume, V, vs time, t, for various initial, relative concentrations of water and methanol.
et al.,6 in which they compared drops with identical initial volumes, it was decided in the present investigation to study drops with identical initial base radii. The reason for this choice is that overall evaporation rate is (assumed) proportional to the drop base radius (Deegan et al. (2000)).9 Droplets of similar base should exhibit similar evaporation rates, with all other conditions being equal. Results 1. Comparison of Drops of Different Composition. The initial contact angle, θi, of water/methanol sessile drops was found, not surprisingly, to depend on the initial relative concentrations of the liquid components. Clearly, the surface tension of binary mixtures is expected to change with composition, hence, the initial contact angle, θi. Water and methanol were chosen for their relative difference in surface tension: this leads to a large range of values of initial angles, θi, over the range of investigated concentrations. The initial contact angle values for the three fractions of methanol were (θi ) 95°, 10% methanol), (θi ) 72°, 50%), and (θi ) 60°, 80%). These all fall within the extremes given by the values of the two pure components, namely, 105° for pure water and 35° for pure methanol drops. Cheng et al.8 claim that the plot of the initial contact angle against the drop mixture concentration may serve as a chart to estimate the concentration from contact angle measurements. Figures 1, 2, and 3 show the evolution with time, t, of the volume, V, base radius, R, and contact angle, θ, for the three mixtures and the two pure components. The data show the large differences in drop lifetime for the various concentrations. A drop of pure water takes around 40 min to evaporate, while a drop of pure methanol takes ca. 100 s. The graph of volume, V, against time, t, shows rapid evaporation at the beginning, with a slow decrease in the final stage of droplet lifetime. This indicates that the evaporation rate is greater for higher initial fractions of methanol, as may be expected. If we look at the evolution of the base radius, R, in Figure 2, it can be seen that it is only constant over the first ca. 10 s. The contact line is clearly pinned at the very beginning and recedes continuously thereafter. This suggests that the silicon substrates used were very smooth indeed. From the three variables presented above, namely, V, R, and θ, the behavior
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Figure 2. Evolution of drop base radius, R, vs time, t, for various initial, relative concentrations of water and methanol.
Figure 4. Evolution of the drop parameters (a) contact angle, θ, and height, h, and (b) base radius, R, and height, h, vs time, t, for an initial, relative concentration of 80% methanol.
Figure 3. Evolution of drop contact angle, θ, vs time, t, for various initial, relative concentrations of water and methanol.
of the contact angle, θ, is the most remarkable. Pure water shows monotonic decreasing θ, or else it remains constant (in fact, θ remains constant for most of the droplet lifetime), whereas methanol exhibits a maximum. For the mixtures and throughout the whole evaporation process, the general trends are similar and can be divided into four stages. The first stage corresponds to an increase in contact angle. This stage however differs in duration from one concentration to another. For 80% concentration in methanol, the contact angle, θ, increases during the first 40 s and then decreases slightly to reach a minimum after ca. 100 s. The last two stages are similar for all mixtures. In the third stage, the contact angle, θ, tends to a maximal value before the drop shrinks and then θ tends to zero during the last stage. The maximum contact angle reached at the end of the third stage is worthy of closer scrutiny. The maximum contact angle, θmax, decreases with increasing initial methanol concentration. It also shifts to later times for lower initial concentrations. For the lowest concentration, the maximum corresponds to a reduction by evaporation of almost half of the drop volume, 70% in the case of the intermediate concentration and 85% for the highest concentration. This result is plausible if one associates θmax with a stage where most of the methanol has evaporated and mainly water remains. This
means that, for a lower initial concentration of methanol, θmax corresponds to a higher fraction of the initial drop volume. The argument suggests that θmax should be the same, since the drop in its last stage is composed mainly of pure water. However, this is in fact not the case, as shown in Figure 3. The behavior shown suggests a tendency as a function of decreasing methanol concentration: the initial decrease in θ and the following “hump” corresponding to increasing contact angle become less accentuated. The result is also in disagreement with previous studies by Cheng et al.8 and Rowan et al.6 In order to investigate these trends, further experiments were undertaken with an atmosphere saturated in water vapor. In this situation, only methanol can evaporate appreciably. Although data have been obtained for all three mixtures, for the sake of brevity, only results for the 80% methanol mixture are presented in the following section. Figure 4 shows the variation of the contact angle, θ, and droplet base radius, R, as well as droplet height, h, as a function of time, t. The stages discussed above should be considered together with the evolution of drop height. Droplet heights show clear differences in evolution from stage 1 to stage 3. Notwithstanding, the overall, average value of dh/dt seems to be relatively constant, particularly over the last two stages. It is of interest to note that the strange effects observed, concerning contact angle, are much more clearly defined for the higher methanol concentrations (50% and greater). This could be connected to the (relatively) faster initial kinetics involved when the liquid in majority, at least at the beginning of the experiment, is of higher volatility.
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Figure 5. Evolution of drop volume, V, vs time, t. Comparison between saturated and unsaturated atmospheres for an initial, relative drop concentration of 80% methanol, 20% water.
Sefiane et al.
Figure 7. Evolution of contact angle, θ, vs time, t. Comparison between saturated and unsaturated atmospheres for an initial, relative drop concentration of 80% methanol.
Figure 8. Schematic representation of the region near the triple line. A corresponds to the expected, virtually flat, liquid/vapor interface in the absence of evaporation. B shows the increase in curvature due to evaporation, but without local flow correction, which alleviates the Laplace pressure excess, ∆p.
Figure 6. Evolution of drop base radius, R, vs time, t. Comparison between saturated and unsaturated atmospheres for an initial, relative drop concentration of 80% methanol.
2. Binary Drops in Water-Saturated Atmosphere. Saturation in water vapor of the local atmosphere surrounding the drops was achieved by placing a reservoir of water inside the environmental chamber. Experiments were run until drop equilibrium was clearly established, i.e., there was no further noticeable evaporation, implying total disappearance of the methanol (but see below). Volume, V, base radius, R, and angle, θ (referred to as θeq) remained at constant values. These three variables (θ, R, and V) were plotted against time, and the results are represented in Figure 5 (V(t)), Figure 6 (R(t)), and Figure 7 (θ(t)). Figures 5 and 6 show that the behavior of the volume, V(t), and the base radius, R(t), is similar: they decrease toward asymptotic values, which confirms that the evaporation process stops. In Figure 7, it can be seen that the contact angle, θ, increases to a maximum before reaching its equilibrium value, θeq, a few degrees below the saturated case. Figure 7 shows that the equilibrium contact angle, θeq, differs from the maximum contact angle in the nonsaturated case. It is also important to notice that the equilibrium contact angles, θeq, also differ for each composition. They vary from 101° at the lowest
methanol concentration, 10%, to 86-87° at 50% and 78° at the highest concentration, 80%. The values of the initial contact angles, θi, are similar for the two cases (saturated and unsaturated). This suggests that the presence of a saturated atmosphere does not affect the wettability of the drops and that the saturation only plays a role in the evaporation process, i.e., in the evolution of the drop profile. The values of the equilibrium contact angles, θeq, in the case of a saturated atmosphere are greater than the values of the maximum contact angles, θmax, obtained in the absence of saturation. These results indicate that despite the preferential evaporation during earlier stages, methanol does not entirely evaporate when in an unsaturated atmosphere. The physical mechanisms controlling the transport of the two components (water and methanol) within the phase and across interfaces must be discussed to shed some light on the observed phenomenon. Discussion and Tentative Interpretation Clearly, the behavior of binary mixture drops is complex. Although by no means claiming to explain all aspects of observed phenomena adequately, in the following, we propose a tentative explanation for at least some tendencies. The behavior of pure water drops is “conventional”, with monotonically decreasing contact angle and radius, but that of pure methanol and the binary mixtures is less expected. We may attempt to describe the behavior of binary drops presented
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in the previous sections by consideration of the mechanisms intervening during evaporation. Motion of the contact line will be the result of (at least) two competing mechanisms: evaporation (mass loss) and flow. Since the contact line is not pinned in the present case, in contrast to other scenarios,9 any evaporation will lead to its receding. Triple line recession speed should, a priori, increase with increasing evaporation rate. Flow is induced by a difference between actual and equilibrium contact angles, and an unbalanced Young relation supplying a surface-tension-based “spreading (or recession) motor”.3 We shall first attempt to understand the behavior of single component liquids, i.e., pure methanol and pure water. 1. Drops of Pure Liquid. Mass loss by evaporation, of single component liquids (ignoring suspended particles, which acted as tracers), was assessed by Deegan et al.,9 using an analogy with electrostatics, to give the expression
( )
J(r) ) J0 1 -
r2 R2
-λ
(1)
in which for present purposes J(r) and J0 are taken as liquid/ vapor interface speeds (ms-1) resulting from liquid loss, and obtained from the (more commonly cited) fluxes on division by liquid density, F. These speeds, perpendicular to the local liquid surface, represent, respectively, that at radial distance, r, measured along the liquid/solid interface from the drop center at r ) 0 to the triple line at r ) R, and a reference value, corresponding effectively to that at r ) 0 (an essentially planar, unperturbed surface). The form of the exponent, λ, was improved upon by Hu and Larson,10 who suggested λ ) 0.5 - θ/π. It has been previously pointed out that the rate-limiting step in evaporation is the diffusive relaxation of the vapor immediately above the free liquid surface, and not the transfer rate of molecules across the liquid/vapor interface.11-15 It is, however, instructive to demonstrate this from another viewpoint. It is possible to estimate the molecularly-kinetically controlled evaporation rate, in the absence of marked liquid surface curvature, from5
J0 )
V∆P (2πMRT)1⁄2
The local average value of J, taken over length ε and termed jJ(R), may be estimated from eq 1. Since we anticipate the local evaporation/flow compensation to occur close to the triple line, we linearize and integrate eq 1 over (R - ε) to R to give
jJ(R) ∼
J0 (1 - λ)
λ
( 2εR )
(3)
where ε is a cutoff distance (see Figure 8). We assume ε to be of the order of 10-9 m for the following reasons. This cutoff is likely to be comparable in magnitude with the value adopted for the divergent flow field in the hydrodynamic theory of wetting3 which can, at least in some cases, be attributed to the presence of long-range van der Waals forces near the triple line.5,16,17 In both cases, a physical mechanism is required to remove an apparent singularity. The bulk liquid behavior is seriously perturbed near the triple phase line. It has also been suggested elsewhere that evaporation is negligible for film thicknesses of ca. 1 nm or less in the context of very flat drops.18 It is quite reasonable to suppose that the same basic phenomenon may occur near the triple line of a drop of non-negligible contact angle. The local speed of triple line recession due to evaporation, dR-/dt, is given by
-J0 R dR- -Jj(R) ∼ ∼ ( dt sin θ 1 - λ)θ 2ε
λ
( )
(4)
Taking typical values of J0, R, and θ, and therefore λ, as above, we obtain the order of magnitude of |dR-/dt| as 1 mm s-1. Compared to experimental values, this is too great by 2 orders of magnitude! It is for this reason that we invoke the possible role of hydrodynamics. As evaporation continues, the contact angle, θ(t), will increase, with all other things being equal, and at a high rate, as suggested by eq 4. However, increased contact angle will also induce hydrodynamic spreading, dR+/dt. We adopt a simple model for spreading rate:3
(2)
where V is (liquid) molar volume (m3/mol), ∆P is vapor pressure deficit (Pa), M is molar mass (kg/mol), and RT has its usual meaning of the product of the gas constant and absolute temperature. For pure methanol, we have V ∼ 4 × 10-5 m3/ mol, ∆P ∼ 1.3 × 104 Pa, and M ∼ 32 × 10-3 kg/mol, and thus, at room temperature, we obtain J0 ∼ 2 × 10-2 ms-1. Our experimental values of J0 are typically in the range of 10-6-10-5 ms-1! Therefore, clearly, this mechanism is not predominant during drop evaporation, although, at a fundamental level, it must represent the transfer process. Clearly, eq 1 predicts infinite evaporation rate at the triple line, r ) R, for θ < π/2. However, if evaporation continues following eq 1, a very high local meniscus curvature will be produced near the triple line, unless some local flow occurs (which need not be long-range). See Figure 8. This implies that we may not take, per se, dR/dt as being equal to -J(R). The high curvature, C, resulting from evaporation alone, will lead to an excess Laplace pressure, ∆p, of γC. This induced Laplace pressure excess will lead to local flow near the triple line, such that, under quasi-equilibrium conditions of evaporation, the flow just compensates liquid loss to reduce the curvature. As a result, the interface will maintain its virtually flat form (at the scale anticipated: ,1 µm).
2 2 2 dR+ γθ(t)(θ (t) - θ0 ) γθ0 ∆θ(t) ∼ ∼ dt 6ηl 3ηl
(5)
where θ0 is the Young, equilibrium contact angle and l the logarithm of the ratio of a macroscopic distance (ca. drop contact radius) and a microscopic cutoff length to avoid divergence of the flow field near the contact line (possibly related to the evaporation cutoff discussed above). The latter is usually accepted to have a value of ca. 12. Overall spreading (or recession) rate of the triple line will be given approximately by the following expression: 2 2 J0 dR dR+ dR- γθ(t)(θ (t) - θ0 ) R ∼ + ∼ (1 - λ)θ 2ε dt dt dt 6ηl
λ
( )
(6) We shall not attempt to solve eq 6 here but simply consider its implications. For θ sufficiently small, we eliminate R from eq 6, by using the expression θ/2 ≈ h/R for a spherical drop. Drop height, h(t) (see Figure 9), decreases approximately linearly with time, t, such that h(t) ≈ h0 - J0t, leading after rearrangement to
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[
Sefiane et al.
) ]
(
h0 - J0t λ J0θ 1 dθ -1 ∼ dt (h0 - J0t) 2(1 - λ) θε γθ3(t)(θ2(t) - θ02) (7) 12ηl(h0 - J0t) From eq 7, we may estimate the sign of dθ/dt from the ratio, j: R
j) R
12ηlJ0 γθ2(t)(θ2(t) - θ02)
[
) ]
(
h0 - J0t λ 1 -1 2(1 - λ) θε
(8)
For values of θ(t) removed from π/2, the (-1) in square brackets is negligible, giving
j≈ R
6ηlJ0 (2+λ)
γθ
(θ
(t)
(t) - θ02 (1 - λ)
2
)
(
h0 - J0t ε
)
λ
(9)
j > 1 or R j < 1, dθ/dt is, respectively, Depending on whether R either positive or negative. For small angles, the term in brackets, to the power λ, is significantly greater than unity (e.g., for methanol in the middle of the range in question, at t ) ca. 30 s, h(t) ) ca. 0.3 mm, ) ca. 0.8 rad, giving this term as ca. 20). In the case of methanol, J0 in the numerator is relatively large, since the liquid is volatile (of the order 10-6-10-5 ms-1), whereas θ(t), and therefore the functions thereof appearing in the denominator, are small (θ(t) e 0.9 rad). Of less importance, γ is relatively small for methanol (ca. 20 mN m-1). η plays an insignificant role, being of the same order of magnitude for the liquids considered here (ca. 0.5 mPa · s for methanol and 1 mPa · s for water). Let us now consider the case of water. Ignoring the minor effect of the reduced ratio η/γ in eq 9, we observe that J0, typically of the order (3-4) × 10-7 ms-1 (see Figure 10), is much smaller. Also, contact angles for water are of the order 100°, or 1.7 rad, in the range of interest. Since the evaporation theory presented above is really inadequate to treat contact angles greater than π/2, we assume that the case of water is close to θ ) π/2. The contact angle terms in the denominator j with respect to the case of methanol, of eq 9 then decrease R but more importantly, λ is near zero, thus reducing the bracketed j is less than unity and dθ/ term to unity. As a consequence, R dtis negative at the outset, in contrast to the case of methanol. This tentative analysis can thus point toward an explanation of the different initial trends of increasing θ(t) for methanol and monotonically decreasing θ(t) for water. More intricate behavior, such as the higher value of |dθ/dt| for water during the first 80 s or so, remains unexplained, as does the change in trend of dθ/dt for methanol toward 60 s. It is clear that subtle changes in the conditions of the drop may bring about a reversal in the sign of dθ(t)/dt. 2. Binary Mixtures. We attempt to use the above schematic analysis developed for drops of pure liquids to consider qualitatively the behavior of binary drops described in the previous sections. Contact line motion is assumed to be the result of the two competing mechanisms of evaporation and hydrodynamics, or what we may term “neutralizing flow”. Figure 7 shows the evolution of the contact angle for evaporating methanol (80%)/water (20%) drops. The four stages for an unsaturated environment in Figure 7 correspond to (a) an initial increase of contact angle, followed by (b) a decrease, and then another increase/decrease cycle (c) and (d), and will be discussed in the light of the mechanisms described. During this stage (a), the majority of the evaporating liquid is methanol. With a relatively high evaporation rate and smaller hydrody-
Figure 9. Droplet height and contact angle vs time for pure methanol.
Figure 10. Droplet height and contact angle vs time for pure water.
namic term (smaller contact angle(s)), the contact line recedes rapidly as the contact angle increases. This contraction of the drop is similar to the behavior described above for pure methanol. Toward the end of stage (a), the contact angle reaches higher values, leading to an increase in the hydrodynamic spreading term (θ > θe . 0). This is combined with a relative reduction in the evaporation rate so that the overall outcome is a decrease in the contact angle, as seen in stage (b). Stage (b) corresponds to a decrease in contact angle, which proceeds until most of the methanol has evaporated. At the end of this stage, the equilibrium contact angle is higher (corresponding to a drop mostly consisting of water). The contact angle will tend to this equilibrium value, resulting in an increase of the contact angle, as observed in stage (c). After reaching their maximum value, all parameters (θ, R, and h) decrease as the drop approaches total disappearance and tend to zero. This corresponds to stage (d). One important observation can be made when comparing the evolution of the contact angle with time for methanol/water drops in both the saturated and unsaturated cases: the maximum contact angle at the end of stage (c) is higher for the saturated case at all concentrations investigated (see Figure 11). This observation suggests that, at the end of stage (c), in the unsaturated situation, there remains some methanol in the drop. Some attention is required to establish what mechanism(s) could be responsible for such interesting behavior. We suggest two plausible mechanisms.
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J. Phys. Chem. B, Vol. 112, No. 36, 2008 11323 to be observed, and at 10% methanol, stage (a) has disappeared and stage (b) is scarcely visible. Finally, for pure water, we return to a fundamentally more classic situation in which contact angle decreases monotonically. Conclusion
Figure 11. Maximum contact angle vs initial concentration, comparison between saturated and unsaturated cases.
Preferential evaporation of methanol leads to depletion of the latter near the interface. This results in a diffusive flux of methanol from the bulk to the interface, in order to sustain evaporation. A comparison of the diffusion time scale of methanol in water shows that it is of the same order of magnitude as the drop lifetime. The diffusion coefficient of methanol molecules in water at 20 °C is of the order19of 2 × 10-9 m2 s-1; hence, the characteristic time for diffusion is
j 2/D ∼ (2 × 10-3)2/2 × 10-9 ) 2000 s t∼L
(10)
j is the characteristic length, which corresponds to drop where L size (2 mm). The value of the characteristic time suggests that diffusion of methanol molecules is much slower than evaporation. This, in turn, suggests that residual methanol will not have time to diffuse to the interface before total evaporation of the drop. As a result, a very small amount of methanol remains in the drop, evaporating at an asymptotically low rate. However, this low concentration is apparently enough to affect the wetting behavior of the binary drop. In an unsaturated atmosphere, the maximum value reached by the contact angle at the end of stage (c) corresponds to the contact angle of a drop containing residual methanol which has not had time to diffuse to the interface to evaporate. A second plausible mechanism for the difference in the maximum contact angles between the saturated and unsaturated cases could be that of “adsorption” of some methanol molecules onto the solid/liquid interface, i.e., preferential adsorption of methanol in the presence of a binary methanol/water mixture. This is plausible, since the solid surface was coated with a hydrophobic layer (PDMS). The methanol/PDMS interface has a lower interfacial free energy than that of water/PDMS. Since the system tends to minimize its free energy, a scenario is plausible in which methanol molecules adsorb “between” the PDMS and the water drop. This should lead to a smaller contact angle, even after most of the “free” methanol has evaporated. We have discussed the case of the binary mixture methanol (80%)/water (20%), since the phenomenological aspects are clear. Considering Figure 3, we may see the evolution of behavior as the initial methanol concentration decreases, with 50 and 10% methanol. The behavior tends toward that of pure water. At 50% concentration, stage (a) is presumably too rapid
The evaporation and wetting behavior of water, methanol, and methanol/water (binary mixture) drops has been investigated experimentally. In the case of pure water, fairly “conventional” behavior was observed, showing monotonically decreasing contact angle and contact radius with increasing time, as evaporation occurred. More surprising was the initial, relatively slow, increase of contact angle of drops of pure methanol, followed by a decrease (while contact radius continually decreased). Binary mixtures showed behavior between the two, with a definite trend toward the two extremes of pure liquids as initial relative liquid fractions were changed. The overall behavior has been tentatively explained by the antagonistic effects of evaporation tending to increase contact angle, due to increased evaporative flux near the triple line, and hydrodynamic flow causing spreading because of increased contact angle. In the case of binary mixtures, wetting behavior shows distinct, successive stages. Preferential evaporation of methanol probably dictates the various observed stages, essentially due to its changing the intrinsic, equilibrium contact angle, Via modification of liquid surface tension. An atmosphere saturated with water vapor has been investigated in an attempt to elucidate the behavior of contact angle. We conclude that methanol does not entirely evaporate in an unsaturated atmosphere. Instead, residual amounts seem to influence the wetting behavior of the binary drops. Acknowledgment. This work was supported by the United Kingdom Engineering and Physical Sciences Research Council via joint grants GR/S59444. References and Notes (1) Bigioni, T. P.; Lin, X.; Nguyen, T.; Corwin, E.; Witten, T. A.; Jaeger, H. M. Nature 2006, 5, 265. (2) Picknett, R.; Bexon, R. J. Colloid Interface Sci. 1977, 61, 336. (3) de Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827. (4) Bourges-Monnier, C.; Shanahan, M. E. R. Langmuir 1995, 11, 2820. (5) Shanahan, M. E. R. Langmuir 2001, 17, 3997. (6) Rowan, S. M.; Newton, M. I.; Driewer, F. W.; McHale, G. J. Phys. Chem. B 2000, 104, 8217. (7) Sefiane, K.; Tadrist, L.; Douglas, M. Int. J. Heat Mass Transfer 2003, 23, 4527. (8) Cheng, A. K. H.; Soolaman, D. M.; Yu, H. J. Phys. Chem. B 2006. (9) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. ReV. E 2000, E62, 756. (10) Hu, H.; Larson, R. G. J. Phys.Chem. B 2002, 106, 1334. (11) Poulard, C.; Guena, G.; Cazabat, A. M. J. Phys.: Condens. Matter 2005, 17, 4213. (12) Fuchs, N. A. In EVaporation and Droplet Growth in Gaseous Media; Bradley, R. S., Ed. Pergamon: New York, 1959. (13) Frohn, A.; Roth, N. Dynamics of Droplets; Springer: 2000. (14) Sultan, E.; Boudaoud, A.; Ben Amar, M. J. Fluid Mech. 2005, 543, 183. (15) Popov, Y. O.; Witten, T. A. Eur. Phys. J. 2001, E 6, 211. (16) de Gennes, P. G.; Hua, X.; Levinson, P. J. Fluid Mech. 1990, 212, 55. (17) Brochard-Wyart, F.; di Meglio, J. M.; Que´re´, D.; de Gennes, P. G. Langmuir 1991, 7, 335. (18) Cachile, M.; Benichou, O.; Poulard, C.; Cazabat, A. M. Langmuir 2002, 18, 8070–8078. (19) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids, 4th ed.; McGraw-Hill: 1987.
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