Stick–Slip of Evaporating Droplets: Substrate Hydrophobicity and

ARTICLE pubs.acs.org/Langmuir

Stick
Slip of Evaporating Droplets: Substrate Hydrophobicity and Nanoparticle Concentration Daniel Orejon,† Khellil Sefiane,*,† and Martin E. R. Shanahan‡ †

Institute for Materials and Processes, School of Engineering, The University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom ‡ Universit
e de Bordeaux, Institut de M
ecanique et d’Ing
enierie-Bordeaux (I2M) UMR 5295, B^atiment A4, 351 Cours de la Lib
eration, 33405 Talence Cedex, France ABSTRACT: The dynamics of the three-phase contact line for water and ethanol is experimentally investigated using substrates of various hydrophobicities. Different evolutions of the droplet profile (contact line, R, and contact angle, θ) are found to be dependent on the hydrophobicity of the substrate. A simple theoretical approach based on the unbalanced Young force is used to explain the depinning of the contact line on hydrophilic surfaces or the monotonic slip on hydrophobic substrates. The second part of the article involves the addition of different quantities of titanium oxide nanoparticles to water, and a comparison of the evaporative behavior of these novel fluids with the base liquid (water) on substrates varying in hydrophobicity (i.e., silicon, Cytop, and PTFE) is presented. The observed stick
slip behavior is found to be dependent on the nanoparticle concentration. The evaporation rate is closely related to the dynamics of the contact line. These findings may have an important impact when considering the evaporation of droplets on different substrates and/or those containing nanoparticles.

’ INTRODUCTION The interaction between liquids and solid substrates, as encountered in wetting situations, is relevant to a very wide range of industrial and biological applications.1 From crop dusting to pharmaceuticals, a full understanding of this interaction is crucial. Recent applications such as DNA stretching2 and nanopatterning3 have sparked a new interest in wetting phenomena and phase change. Despite more than two centuries of scientific work on this topic, since Thomas Young,4 many important questions remain to be elucidated. More recently, a number of studies have been carried out that aim to ascertain the different mechanisms associated with spreading, pinning, depinning, evaporation, and contact line dynamics.5
9 When a droplet is gently deposited on a substrate, different profiles can be observed depending on the surface tension of the fluid, the nature of the substrate, and the surrounding environment. For small droplets (radius smaller than the capillary length, ca. 2.7 mm for water), the effect of gravity is negligible and a water droplet of a few microliters tends to form a spherical shape, thus minimizing the energy of the system. The equilibrium contact angle, θ0, of such a droplet on an ideal, flat, rigid solid surface is given by Young’s equation, which was postulated at the beginning of the 19th century.4 This equation (eq 1) takes into account the respective surface tensions: solid
gas, γSG, solid
liquid, γSL, and liquid
gas, γ: γSG
γSL ¼ γ cos θ0

ð1Þ r 2011 American Chemical Society

Depending on the nature of the substrate, the droplet can exhibit either complete or partial wetting. The complete wetting (or spreading) regime applies when the equilibrium contact angle tends to 0° and the liquid spreads over the surface. The partial wetting regime is defined by a measurable contact angle. In the partial wetting regime, we can distinguish between the wetting and nonwetting cases. This gives us an idea of the hydrophobicity of the substrate. For the same liquid, hydrophobic substrates lead to larger contact angles whereas hydrophilic ones lead to smaller contact angles. On real surfaces, as opposed to ideal ones, the equilibrium contact angle can assume different values. These range between the advancing and receding contact angles because of the presence of chemical heterogeneities or surface defects such as cavities, bumps, dust, or scratches.10 The equilibrium contact angle is achieved at thermodynamic equilibrium (i.e., no further mass transfer between phases). This rules out any evaporation or condensation. However, if the ambient atmosphere is not saturated, then the droplet will experience some evaporation. The phase change process will modify the droplet profile. This may be observed as a variation in the contact angle, the contact line position, or a combination of both. Many studies have tried to link the wetting behavior to the evaporation process. Some authors pointed out that if the contact angle is smaller than 90° for a Received: July 13, 2011 Revised: August 12, 2011 Published: August 26, 2011 12834

dx.doi.org/10.1021/la2026736 | Langmuir 2011, 27, 12834–12843

Langmuir water droplet then the evaporation behavior of the droplet (profile evolution) is different than if the contact angle is greater than 90°.5 For example, Bourges-Monnier and Shanahan observed that when the contact angle is smaller than 90° (e.g., water on glass) the contact line is anchored and the weight loss, induced by evaporation, is linear with time during almost the whole process of evaporation.6 However, different behavior was found for the nonwetting case, where the contact line recedes, leading to a nonlinear evolution in time of the mass or volume.11,12 This clearly demonstrates the effect of substrate hydrophobicity on the evolution of the droplet profile when induced by evaporation. Shanahan et al., in a more recent publication, related the droplet lifetime to the hydrophobicity of the surface depending on the evaporative mode at constant contact angle or at constant contact radius.13 In essence, the constant contact radius leads to a linear volume evolution and a constant mode of evaporation, and the constant contact angle follows a power law. By looking more closely at the contact line, one can conclude that the dynamics of the latter is dictated by a competition between pinning forces on one hand and depinning forces on the other hand. The pinning forces are usually due to the contact line being anchored to the substrate because of chemical and surface heterogeneities. The depinning forces on the other hand are the result of the deviation of the droplet profile from equilibrium; this deviation is induced by loss mass (evaporation). In the case of evaporation, if the contact line is pinned, the contact angle decreases until depinning occurs and the triple contact line recedes. The deviation from equilibrium during evaporation (unbalanced Young’s force) is what governs the dynamics of the contact line for pure fluids.14 This is, of course, the case when no surface tension gradients are present. Besides the wide interest in wetting and phase change phenomena for more than a decade now, a new area of research has been dedicated to the study of the behavior of colloidal nanosuspensions, or nanofluids.15 This is driven by recent technological advances that have led to different methods for the production of easier, cheaper, and better-quality nanoscale particulates.16 Moreover, the addition of these nanoparticles to base fluids can drastically change their properties, for instance, by enhancing their thermal conductivity. Applications of these nanofluids are found in many areas, such as patterning, drug delivery, film coating, detergency, and cooling.15 It is well known that during the evaporation of these colloidal suspensions, nanoparticles are drawn to the droplet periphery to replace the evaporated liquid, leading to what is commonly known as the coffee ring effect studied by Deegan et al.17 The presence of particles is shown to promote the self-pinning of the contact line. Understanding how these particles interact among themselves, with the base fluid and the substrate, is of great importance to the comprehension and characterization of these novel fluids. Recent studies have been dedicated to elucidating the mechanisms involved during the free evaporation of wetting droplets of these fluids. Moffat et al. found that the addition of TiO2 nanoparticles to ethanol promoted stick
slip behavior, where the contact line pins not due to irregularities on the surface but to the accumulation of nanoparticles at the contact line.18 Reproducible stick
slip behavior is associated with an energy barrier that the droplet has to overcome for each slip to ensue. The theoretical description of this has been presented in other work.14,19 In the work of Moffat et al.,18 photographs of nanoparticle residues were presented, forming approximately circular rings. These rings were recently analyzed using atomic force microscopy (AFM) by Askounis et al.20 The authors used the high resolution of AFM to detect the structure and shape of the deposits of the outer ring after

ARTICLE

the free evaporation of 0.1% TiO2
ethanol and presented a plausible theory that suggests how the nanoparticles accumulate at the contact line. Other authors such as Li et al. focused their research on the nanoparticle flow inside 0.1 μL droplets during evaporation, pointing out a circulatory fluid flow that is 200-fold greater than diffusion.21 This flow is found to be induced by pinning and depinning of the contact line. The authors used silica nanoparticles and found that the flow can be controlled by varying the nanoparticle concentration or changing the surface tension by adding surfactants. Anderson et al. proposed that on ideal surfaces the base diameter recedes while the contact angle remains constant.22 On the other hand, Sefiane and Tadrist found that for rough surfaces, there is a first stage where the droplet radius remains constant and the contact angle decreases linearly with time, until it reaches a limiting value and then the contact line recedes.23 In the literature, some authors have related the depinning force to the initial contact angle, the angle just before the jump, and the surface tension of the liquid.13,24 Some cases show that if the initial contact angle is fairly small, the pinning of the droplet during the whole evaporation process occurs even for very smooth surfaces. On the contrary, for high initial contact angles, the contact line tends to recede as the droplet evaporates. Shin et al.25 carried out some experiments on different surfaces with varying substrate hydrophobicity, and various evaporation behaviors were reported. The authors used an octadecyltricholorosilane substrate (OTS) with an initial contact angle of 120° for water, reporting the pinning of the contact line that is probably due to imperfections on the surface. The roughness of the surface is not reported in this article, but Ramos et al. stated that the observed pinning of the drop via OTS grafting was due to topographical modifications, with 19 ( 2 and 3 ( 1 nm being the diameter and the height of the irregularities, respectively.26 Grandas et al. observed the pinning of water droplets on PTFE, which was explained by heterogeneities on the substrate.27 From the above brief review, it is clear that the dynamics of the contact line of wetting systems accompanied by evaporation is a complex problem. The interplay between the phase change and the dynamics of the contact line still needs to be further investigated. Moreover, in the presence of nanoparticles, the situation is even more complex. Indeed, various interactions between the phases involved in the process are worth the attention of the scientific community. In this work, we investigate experimentally the dynamics of the contact line of pure liquids and nanofluid droplets on substrates with variable hydrophobicity. The aim is to elucidate the mechanisms controlling the dynamics of the contact line and their dependence on the substrate hydrophobicity as well as the nanoparticle concentration.

’ EXPERIMENTAL SECTION Different liquids were used to produce sessile drops: deionized water, ethanol (from Sigma-Aldrich), and TiO2
water nanofluids of different concentrations. For the preparation of the nanofluids, a two-step method was adopted. Polydisperse TiO2 particles manufactured by Sigma-Aldrich with a typical size smaller than 25 nm (characterized using transmission electronic microscopy, TEM) were dispersed in water at different concentrations on a weight basis and then ultrasonicated for several hours to minimize the agglomeration of the particles. All samples were ultrasonicated for another hour prior to the droplet deposition on the substrate to ensure good dispersion. The concentrations 12835

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Table 1. Values of the Equilibrium Contact Angle, θ0 (in Degrees), Measured Immediately after the Deposition of the Drop on the Substrate (t = 0) for Water and Ethanol on the Different Surfaces Tested (Ethanol/Parylene from ref 28) hydrophobicity initial contact angle glass silicon glass* parylene C4F8 Cytop PTFE water ethanol

28°

57°

71° 10°

89° 10°

104° 108° 26° 41°

114° 45°

prepared were as follows: 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, and 0.1% by weight. The following substrates were used: glass, bare silicon, glass with a special finish (thickness of 0.1 mm from TAAB) henceforth described as glass*, and silicon coated with various materials: parylene (poly(p-xylylene) polymer), C4F8 (octafluorocyclobutene), Cytop (perfluorinated polymer consisting of C
C, C
F, and C
O bonds), and PTFE (Teflon). The coated substrates were prepared by spin coating to deposit a layer of less than 1 μm thickness of C4F8, parylene, Cytop, or PTFE on a silicon wafer by the SMC (Scottish Microelectronic Centre). After the spin coating, annealing was performed at 330 °C in a semiconductor industry standard furnace filled with flowing nitrogen at all times, ensuring that the solvent that is evaporated is removed from the atmosphere. The different substrates were cleaned for around 15 min by immersing them in an ultrasonic bath with isopropanol. Prior to the deposition of the droplet, a stream of nitrogen was blown onto the substrate to avoid any dust and to remove any contaminants. PTFE and Cytop are well known as hydrophobic surfaces, and glass, silicon, and glass with the special finish are hydrophilic. Parylene could be considered to be in between hydrophilic and hydrophobic with a contact angle of water of ca. 89°. The use of these substrates permits the coverage of a wide range of hydrophobicities. To illustrate the degree of hydrophobicity, the equilibrium contact angles of water and ethanol, as measured using the experimental setup described below, are given in Table 1 for the different substrates. Small droplets of known volumes, ca. 3 μL, of the various liquids were gently deposited on surfaces with varying hydrophobicity. All experiments were performed in air at atmospheric pressure and an ambient humidity of 30%. After being deposited on the substrate, the droplets were left to evaporate until they completely disappeared. A typical evaporation time for a 3 μL water droplet was between 15 and 40 min (1000 to 2400 s), depending on the hydrophobicity. The evaporation time for ethanol droplets was between 1.5 and 5 min (90 to 300 s) for hydrophilic and hydrophobic substrates, respectively. Droplet profiles were recorded during the complete evaporation under an ambient atmosphere with the help of a DSA100 droplet shape analyzer from Kr€uss (Kr€uss GmbH, Hamburgh, Germany). The analyzer is equipped with a CCD camera capable of recording up to 25 frames per second and connected to a video-digitizer board (frame grabber). The equipment comprises a computer-controlled dosing system enabling the deposition of droplets of controlled volume, a moveable sample table, and a back light to illuminate the droplet. Subsequently, the contact angle, θ, the base radius, R, the volume, V, and the height, h, of the droplet were extracted as a function of time, t, with the help of DSA1 v1.9 software. The AFM analysis of silicon and PTFE showed the very smooth nature of the surfaces, with an Rrms equal to 0.1231 nm in the case of silicon and 0.8804 nm in the case of PTFE (Figure 1). The imaging of these substrates was performed by a Veeco Multimode/Nanoscope IIIa AFM (Veeco, Santa Barbara, CA) in tapping mode. Images were processed by a scanning probe imaging processor (SPIP).

’ EXPERIMENTAL RESULTS The aim of the experiments is twofold. In the first step, we explore the effect of the hydrophobicity of the substrates on the kinetics of the

Figure 1. Height profiles of (smooth) silicon and (rough) PTFE surfaces showing the roughness in nanometers. three-phase contact line of pure evaporating droplets. In the second step, we aim to investigate the effect of nanoparticle concentration on the pinning
depinning phenomenon of evaporating nanofluid droplets. Experimental Data of Pure Fluids. In what follows, we present experimental results concerning the evaporation of pure ethanol and pure water droplets on substrates with different degrees of hydrophobicity. The main results show the evolution in time of both the contact radius and the contact angle of these droplets during evaporation.29 Ethanol. The evolution of the contact radius, R, versus time, t, for pure ethanol on glass*, C4F8, Cytop, and PTFE, as substrates, is presented in Figure 2 (left). Two different types of behavior of the contact line can be distinguished, depending on the hydrophobicity of the surface. In the case of Cytop and PTFE, which are both hydrophobic, there is virtually a monotonic receding of the base radius, at constant rate, for at least half of the droplet lifetime, followed by more rapid receding until evaporation is complete. This evolution is similar to the behavior expected on ideal surfaces, apart from the change in the gradient.22 However, for glass* and C4F8, pinning of the contact line is observed during most of the droplet lifetime. We note that the contact line of ethanol droplets on glass* and C4F8 exhibits a slight decrease in the contact radius during the pinning stage. This indicates that the pinning during this first stage is not complete: there is a slight drift.18 It may be noted that the propensity for pinning increases with the contact radius. If we now turn our attention to the contact angle, θ, presented in Figure 2 (right), we note that it remains fairly constant during half of the droplet lifetime, followed by a gentle decrease and then an increase toward the end of the droplet lifetime for the hydrophobic substrates (PTFE and Cytop). The sharp increase in the contact angle toward the end of the droplet lifetime observed for Cytop and PTFE is due to droplet contraction and results from the sharp decline in the base radius (Figure 2, left). For glass* and C4F8, the contact angle decreases steadily for most of the droplet lifetime, which is due to the pinning of the contact line. It is clear from this that the higher the contact angle, the less the contact line remains pinned. The results obtained for the hydrophilic surfaces (glass* and C4F8) show that the contact line remains pinned during almost the whole process of evaporation. In agreement with additional experiments carried out and previous studies,17 this pinning regime leads to a linear evolution of volume or mass in time, hence a constant evaporation rate. This trend is similar to the evaporative behavior on very rough surfaces. However, on the hydrophobic substrates (PTFE and Cytop), the contact line recedes steadily. The results for PTFE and Cytop resemble the expected evaporative behavior of droplets on ideal surfaces where 12836

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Figure 2. (Left) Evolution of the contact radius, R (mm), vs time, t (seconds) and (right) evolution of the contact angle, θ (degrees), vs time, t (seconds), on glass* (diamonds), C4F8 (triangles), Cytop (circles), and PTFE (squares) for ethanol.

Figure 3. (Left) Evolution of the contact radius, R (mm), and (right) evolution of the contact angle, θ (deg), on glass (crosses), silicon (stars), glass* (diamonds), parylene (triangles), Cytop (circles), and PTFE (squares) plotted with time, t (s), for water. hysteresis effects are negligible for ca. 100 s, whereafter θ decreases.18 It is worth noting that the evaporation time for hydrophilic surfaces is less than for hydrophobic surfaces for the same initial volume. This is consistent with the findings of previous investigations.13 Lowering the contact angle and increasing the contact radius both tend to increase the evaporation rate. It is worth emphasizing that the types of behavior described above are reproducible and consistent as shown from experiments repeated several times (at least six times). Water. In Figure 3 (left), the experimental results of the contact radius, R, versus time, t, obtained during the evaporation of pure water on glass, silicon, glass*, parylene, Cytop, and PTFE substrates, listed from hydrophilic to hydrophobic, are presented. For the case of water, two types of evaporation behavior were observed, depending on the hydrophobicity of the surface. For both hydrophobic substrates (Cytop and PTFE), the base radius receded monotonically during most of the droplet lifetime with a sharper decrease toward the end. However, for hydrophilic surfaces (i.e. silicon, glass*, and parylene) an initial pinning of the contact line is observed for at least the first 40% (in the case of silicon) of the droplet lifetime, followed by a continuous and sometimes interrupted decrease. For the case of glass, the pinning of the contact line is observed throughout the evaporation. The evolution of the contact angle, θ, versus time, t, for the six surfaces mentioned above is shown in Figure 3 (right). For the

hydrophilic substrates, a steady decrease in the contact angle is noticed for at least the same initial 40% of the droplet lifetime (in the case of silicon) or more, corresponding to the pinning of the contact line. For glass, the contact angle decreases monotonically during evaporation. In contrast, for hydrophobic substrates, there is a slight decrease in the contact angle during the short first stage of the evaporation, followed by a plateau behavior for about 80% of the remaining droplet lifetime. At the very end, a rapid decrease in the contact angle is observed. The results presented in Figure 3 indicate a pattern in the contact line dynamics and wetting behavior based on the hydrophobicity of the substrate. In the case of hydrophobic surfaces, the contact radius decreases until complete evaporation while the contact angle remains roughly constant, leading to a decrease in the overall evaporative flux. On the contrary, for hydrophilic surfaces, the initial pinning of the contact line is observed for at least the initial 40% of the droplet lifetime while the contact angle decreases. We may compare this to ethanol either on glass* or C4F8, where a constant evaporative rate is observed because of the pinning of the contact line during the whole droplet lifetime. It is worth mentioning that pinning of the contact line on hydrophilic substrates such as silicon occurs, even if it is about 10 times smoother (Rrms = 0.1231 nm) than that for PTFE (Rrms = 0.8804 nm), 12837

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Figure 4. (Left) Evolution of the contact radius, R (mm), with time, t (s), and (right) contact angle, θ (deg), with time, t (s), for different TiO2 concentrations in water on silicon. as shown in Figure 1. Pinning is clearly not uniquely dependent on the substrate roughness.

TiO2
Water-Based Nanofluids and the Effect of Hydrophobicity. Following the experiments with ethanol and water (pure

fluids), the evaporative behavior of droplets with nanoparticles suspended in water was investigated. It is widely known that the presence of particles can promote the pinning of the contact line.17 The question that we attempt to address in the following section is how the concentration of nanoparticles and the hydrophobicity of the substrate affect the pinning
depinning of the contact line. The nanoparticles investigated were TiO2, with the motivation being the growing interest in a wide range of applications such as photocatalysts,30 solar cells, biomaterials, and patterning.31 A series of experiments using a range of concentrations were undertaken on silicon, Cytop, and PTFE substrates. For the hydrophilic silicon surface, the concentrations chosen were 0.01, 0.005, 0.001, and 0.0005%. In Figure 4 (left), the evolution of the contact radius, R, and (right) the evolution of the contact angle, θ, versus time, t, are presented. As we reported in the previous section, for the case of pure water on silicon, there is a noticeable pinning of the contact line at least during the first 40% of the droplet lifetime as a result of a low equilibrium contact angle corresponding to a hydrophilic substrate, θ0 (θ0 ≈ 60°). The pinning gives the nanoparticles more time to deposit at the contact line (where evaporation takes place), acting as defect barrier preventing the receding of the droplet base. Moreover, a small addition of nanoparticles, such as 0.001% TiO2 to water by weight, on silicon promotes the pinning of the contact line during almost the whole process of evaporation. Reducing the concentration to 0.0005% leads to the pinning of the contact line for at least the 70% of the droplet lifetime; thereafter, the contact line recedes and no stick
slip is reported. To compare the effect of the initial contact angle on the nanofluid evaporation, a more hydrophobic substrate than silicon (θ0 > 90°) was chosen. On Cytop, pure water exhibits a constant contact angle mode,

with the contact line receding through the droplet lifetime. The addition of TiO2 nanoparticles is found to induce noticeable stick
slip behavior as shown in Figure 5. The evolution of the contact radius, R, and the contact angle, θ, versus time, t, for 0.1, 0.05, 0.025, and 0.01% by weight is shown in Figure 5. Stick
slip behavior is observed for all of the concentrations tested. It is noticeable that the jumps of the contact line and the changes in the contact angle are dependent on the nanoparticle concentration. The case of pure water is included to permit the comparison with these novel fluids. Similar findings were obtained for the most hydrophobic of the substrates tested (i.e., PTFE (θ0 ≈ 115°)). The evolution of the contact radius, R, and the contact angle, θ, vs time, t, for 0.1, 0.05, 0.025, 0.01, and 0.001% is shown in Figure 6. It is possible to identify a clear trend depending on the nanoparticle concentration. At the bottom of both columns of the graphs, the pure case (water) is shown to allow an easier comparison of the evaporative behavior with the different nanofluids tested. It is observed that for all concentrations investigated the evolution of the base radius shows stick
slip behavior with regular steps and terraces. These steps are found in the behavior of the contact angle as discrete jumps. As the concentration of nanoparticles is increased, more pronounced steps of the base radius, δR, and jumps in the contact angle, δθ, are observed. Jumps in the contact angle are clearly correlated with the stick
slip of the contact radius, which is due to the contraction of the droplet following each step. The transition from ideal dewetting at a constant contact angle, for the case of pure water, to a gradual increase in the stick
slip steps with the addition of nanoparticles is clearly noticeable. Figures 7 and 8 compare the magnitudes of the steps in the contact line, δR, and the jumps in the contact angle, δθ, for the different concentrations. With the exception of the third jump, which apparently has strange (unexplained) behavior in some cases, a trend with jump number can be seen for the various concentrations. Linear regression lines have been added 12838

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Figure 5. (Left) Evolution of the contact radius, R (mm), with time, t (s), and (right) contact angle, θ (deg), with time, t (s), for different TiO2 concentrations in water on Cytop (θ0 ≈ 110°).

Figure 6. (Left) Evolution of the contact radius, R (mm), with time, t (s), and (right) contact angle, θ (deg), with time, t (s), for different TiO2 concentrations in water on PTFE (θ0 ≈ 115°). simply to show the trend in evolution. At present, no theoretical explanation is available. Although ref 14 suggested δR scaling with R1/2, this was for a

constant energy barrier. In the present case, because of the gradually increasing particulate concentration, the energy barriers may well evolve. 12839

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Figure 9. Schematic representation of the triple line region with the liquid surface at the equilibrium contact angle, θ, and at a slightly smaller angle, (θ0
δθ).

Figure 7. Jump distance, δR, of the contact line (in millimeters) for the different TiO2
water concentrations: 0.1% (squares), 0.05% (circles), 0.025% (triangles), 0.01% (diamonds), and 0.001% (hexagons) on PTFE. (Lines are present only to show the trends for each concentration.)

expected.20 These deposits act as irregularities or defects inducing the pinning of the contact line and leading to a decrease in the contact angle, which drives the droplet out of its thermodynamic equilibrium. The depinning phenomenon of the contact line appears to be dictated by an energy barrier to be overcome for the droplet to depin. Seemingly, this energy barrier for depinning is higher for larger concentrations.

’ INTERPRETATION AND DISCUSSION The aim of this section is to elucidate the mechanisms of triple-line behavior during the evaporation of a droplet using the results described in the previous section. For the case of pure liquids, the dynamics of the three-phase contact line can be studied using a force balance or an energy-minimization approach. The purpose is to elucidate the effect of hydrophobicity, corresponding to the initial contact angle, on the pinning
depinning behavior. Also, pinning
depinning behavior is observed with the addition of nanoparticles to water on hydrophobic surfaces during evaporation and the dependence of the energy barriers on nanoparticle concentration may also be considered. Pure Liquids. At this point, we evaluate the forces involved during the depinning of the contact line. Figure 9 represents the region near the triple line, both at equilibrium (contact angle, θ0) and at a slightly smaller angle, (θ0
δθ), following some evaporation and assuming the triple line to be pinned. Clearly, at equilibrium there is zero net force given by Young’s equation (eq 2): 0 ¼ γSL
γSG þ γ cos θ0

Figure 8. Change in the contact angle, δθ (deg), for the different TiO2
water concentrations: 0.1% (squares), 0.05% (circles), 0.025% (triangles), 0.01% (diamonds), and 0.001% (hexagons) on PTFE. (Lines are present only to show trends.) However, what is very clear is that the steps in the contact line, δR, are noticeably more pronounced as the number of TiO2 nanoparticles in water is increased. In Figure 8, the change in the magnitude of contact angle jumps, δθ, is shown for different concentrations. The same trend as for the contact line steps is observed for the change in the contact angle, δθ. As mentioned above, depinning of the contact line causes an increase in the contact angle. The experimental results presented so far show very clear evidence of the correlation between the magnitude of the contact line steps, corresponding to contact line depinning and contact angle jumps, and the nanoparticle concentration. This supports the idea that nanoparticles play an important role in the pinning and depinning of the contact line. Evaporation of the droplet occurs mainly near the triple contact line, inducing the buildup of nanoparticles at the edge as the evaporation proceeds.17 Askounis et al. pointed out that the buildup of the deposits was proportional to the nanoparticle concentration; therefore, for higher concentrations, larger deposits at the contact line are

ð2Þ

With a slight decrease in the angle to (θ0
δθ), there will be a (horizontal) force acting toward the bulk liquid of magnitude δF B: δB F ¼ γ cosðθ0
δθÞ
γ cos θ0 ≈γ sin θ0 δθ

ð3Þ

Young’s equation has been used to eliminate (γSL
γSG). We postulate an intrinsic energy barrier, U, preventing tripleline motion, as previously reported.14,18 Therefore, its differential, ∂U/∂r, can be taken as a force locally opposing depinning, whereas δF B attempts to cause depinning (force/length). (The δ notation is used simply because the deviation from equilibrium will usually be small.) At the threshold of depinning, we have ∂U ð4Þ ¼ δB F ¼ γ sin θ0 δθ ∂r During the evaporation of a droplet, any decrease in the contact angle leads to the exertion of a force tending to contract the droplet. Depinning occurs when δθ has become sufficiently large (θ is sufficiently small) to supply a value of δF B that is large enough to overcome the intrinsic energy barrier preventing 12840

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

Figure 10. Results of the depinning force, δF, for the first jump calculated with eq 4 for the different systems: glass* + aluminum
ethanol (squares), C4F8
ethanol (circles), glass
water (triangles), silicon
water (hexagons), glass* + silicon
water (diamonds), glass* + aluminum
water (asterisks), and parylene
water (stars) vs cos θ0 (where the dotted line represents the barrier necessary to surmount for depinning to occur).

contact line motion, U. If θ0 is high enough for a given δF B, then δθ is small, thus subsequent microscopic jumps may become “smoothed” and visible as macroscopically continuous motion: the contact line appears to slide until the droplet vanishes. It seems that the unbalanced Young’s force, δF B, is insufficient to cause depinning of the contact line for small initial constant angles, θ0. This is clearly the case for ethanol on glass* and C4F8, where the contact line remains pinned for most of the droplet lifetime. On the contrary, for water on silicon, glass*, and parylene, where the initial contact angle is higher than 1 rad, the contact line recedes after a period of evaporation. Hydrophobic surfaces exhibit depinning of the contact line for both water and ethanol. This is consistent with the above theory where the depinning force is proportional to the sine of the initial contact angle. Using eq 4, we show in Figure 10 a quantitative analysis of the depinning force of the contact line, for the first jump, on different hydrophilic surfaces. We propose that a potential depinning force, δF B, exists that is related to the initial contact angle (before a jump) and the surface tension of the liquid, being greater for the high initial contact angle and high surface tension. Accepting a given force barrier, ∂U/∂r, for triple-line movement (depending on the system solid
liquid
gas), depinning of the contact line is not attained for small initial contact angles because γ sin θ0 is small. Thus, the depinning force is not great enough to overcome the force barrier in the cases of ethanol on C4F8 or glass*. However, for a barrier of the same magnitude, when γ sin θ0 is greater because of the higher initial contact angles, as in the water
PTFE and water
Cytop cases, there is (virtually) continuous motion of the triple line because a very small value of δθ induces movement. There is also an intermediate case where the contact angle requires a great change, δθ, for depinning to occur. This is encountered in the water on silicon and water on parylene systems. For δF B > 0.02 N m1
, there is depinning of the contact line: the barrier is

ARTICLE

~ , for the first jump (N m
1  10
7) Figure 11. Excess free energy, δG calculated for the different TiO2
water concentrations on PTFE using eq 5 (squares) and eq 6 (circles) (curves, polynomials of degree 2, are used to show trends).

surmounted. Although the theory indicates a greater depinning force for larger initial contact angles, there is at least one additional parameter that may affect the contact line dynamics. When a block of aluminum is inserted under the glass* substrate for the water case, it leads to a large increase in the necessary depinning force, as seen in Figure 10. Additional experiments on this surface showed different evolutions of the contact angle and the contact radius when different solids with different thermal properties were placed underneath the glass* coverslip (aluminum, PTFE, and silicon). This points to the fact that, in addition to hydrophobicity, the dynamics of the contact line and the wetting of droplets depend on the thermal resistance and hence the kinetics of evaporation. This question will be addressed in the last subsection of this article. TiO2
Water Nanofluids. In this section, the pinning
depinning of the triple line for the suspension TiO2 nanoparticleswater on silicon, Cytop, and PTFE (a hydrophobic surface), is considered (Figure 6). For hydrophobic surfaces (i.e., Cytop and PTFE), there is no significant pinning of the contact line for the case of pure liquids tested (ethanol and water) on the macroscale. It is noticed that adding a small quantity of TiO2 nanoparticles induces stick
slip behavior on hydrophobic substrates, and this is enhanced as the concentration of nanoparticles increases. On a hydrophilic substrate, a complete pinning of the drop is observed because of an increase in the pinning force resulting from both a low initial contact angle and the presence of nanoparticles. An explanation of the contact line pinning
depinning dependence on nanoparticle concentration is proposed in which consideration is given to the energy barrier that the contact line must overcome for a jump to ensue. Assuming ∂U/∂r to be a constant (for a given nanoparticle concentration), we see from eq 4 that δθ ≈ 1/sin θ0 for a given value of γ. Thus, jumps in a stick
slip cycle should be more frequent for higher values of θ, with other things being equal. However, water on PTFE, with a contact angle of typically 2 radians, requires the addition of only small quantities of nanoparticles (0.001% of TiO2) for noticeable pinning
depinning to occur. It is instructive to estimate values for these barriers to depinning with the data available. Two equivalent expressions have previously been derived to estimate free-energy barriers, 12841

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

ARTICLE

Figure 12. (Left) Evolution of the contact radius, R (mm), and (right) contact angle, θ (deg), of water on a borosilicate coverslip + silicon (squares), a borosilicate coverslip + PTFE (circles), and a borosilicate coverslip + aluminum (triangles) with time, t (s).

~ , at the jump threshold of stick
slip behavior.14,19 The choice δG depends simply on whether the jump is to be characterized in terms of a change in radius, δR (eq 5), or a change in the contact ~ is the excess free energy of the droplet (per angle, δθ (eq 6). δG unit length of the triple line) at the threshold of a jump and is due to Young’s equation not being satisfied and is therefore simply equivalent to U.14 ~ ¼ δG

γ sin2 θ0 ð2 þ cos θ0 ÞðδRÞ2 2R

ð5Þ

~ ¼ δG

γRðδθÞ2 2ð2 þ cos θ0 Þ

ð6Þ

The intrinsic energy barriers present at the triple line and due to the change in the contact angle are evaluated for the different TiO2 concentrations using eqs 5 and 6. The surface tension of water remains unchanged at 72.8 mN/m after the addition of TiO2 nanoparticles (which was confirmed using the pendent drop technique). The typical contact radius for a 3 μL water droplet on PTFE is ca. 0.9 mm before the first jump, and the initial contact angle is ca. 114° (ca. 2 radians). The use of eq 5 or 6 depends on the data available (i.e., δR or δθ). In our case, the evolution of both is available as explained in the Experimental Section, which allows us to compare the excess free energies using both equations. (Strictly speaking, they should of course be equivalent, but clearly we average over the drop rather than use one local part of the triple line). Average values of the contact radius step and the contact angle jump are extracted from Figures 7 and 8, respectively, for the different concentrations. The average values of the free energy found after substituting the experimental data into eqs 5 and 6 for each concentration are presented in Figure 11. The difference is probably due to uncertainties in measuring δR or δθ. It is clear that the excess free energy before the jump of the contact line due to a more thermodynamically favorable position is an increasing function of nanoparticle concentration. Even though eqs 5 and 6 do not include the concentration as an explicit variable, there is a direct correlation between the distance jumped by the contact line and the nanoparticle concentration, as shown in Figure 6. This may be explained by the buildup of particles

where for higher concentrations the number of nanoparticles deposited at the triple contact line is greater.20 These deposits act like heterogeneities or defects on the surface, inducing a greater pinning of the contact line as we increase the nanoparticle concentration. A longer pinning leads to a higher deviation from equilibrium before a jump and to greater steps of the contact line. Effect of the Thermal Resistance of the Substrate. In what follows, we attempt to explore the effect of the thermal resistance of the substrate on the pinning
depinning phenomenon of contact lines. Some experimental results in the section above seem to indicate that the dynamics of the contact line depends on the thermal resistance of the substrate and consequently on the kinetics of evaporation. A full appraisal of this question is, however, beyond the scope of this article and will be explored in future work. However, a few preliminary results are presented here. For this purpose, experiments using deionized water were performed with different solids put in contact underneath the thin glass* slide (of about 0.1 mm thickness). Three solids were tested: silicon, PTFE, and aluminum. In Figure 12 (left), the evolution of the contact radius with time is shown using different “under” solids. For a thermally insulating material (i.e., PTFE with a thermal conductivity of 0.23 W/K 3 m), complete pinning of the droplet throughout total evaporation was observed. However, for a conductive material (i.e., aluminum with a thermal conductivity of 237 W/K 3 m), depinning of the contact line was observed after ca. 40% of the total lifetime. In the case of the silicon under solid (thermal conductivity of 149 W/K 3 m), there was pinning for a shorter period of time followed by depinning of the contact line. In Figure 12 (right), the evolution of the contact angle, θ, for the three different cases is presented. A monotonic decrease in the contact angle for at least the first few minutes of evaporation is noticed for all three under solids as a result of the pinning of the contact line. For silicon, depinning of the contact line occurs before that of aluminum. The case where silicon is used underneath glass* shows some stick
slip behavior as noted from both the base radius and contact angle jumps in Figure 12. These results are at present unexplained satisfactorily, especially because the observed behavior seems not to follow any order expected from the relative values of thermal conductivities. Notwithstanding, the effect of the thermal conductivity seems to be very marked and requires further investigation. 12842

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843

Langmuir

’ CONCLUSIONS The dynamics of the three-phase contact line of evaporating droplets has been experimentally investigated. Two important variables have been considered: substrate hydrophobicity and the presence of nanoparticles. Substrates with varying hydrophobicity were used to investigate the evaporation of pure water and ethanol droplets. The experimental results consistently point to the fact that the depinning of the contact line is favored by more hydrophobic surfaces. These observations were satisfactorily explained using a simple theory based on the force balance in the vicinity of the contact line. In the second part of this article, TiO2
water nanofluid droplets were studied. The experimental results show clearly that the presence of nanoparticles promotes the pinning of the contact line on hydrophobic and hydrophilic substrates and stick
slip behavior on hydrophobic ones. The dependence of the magnitude of stick
slip on nanoparticle concentration is clearly evident. The depinning force and depinning energy barriers are estimated as a function of nanoparticle concentration. The trend found corroborates the idea that the energy barrier for depinning increases with increasing nanoparticle concentration.

ARTICLE

(21) Li, H.; Fowler, N.; Struck, C.; Sivasankar, S. Soft Matter 2011, 7, 5116–5119. (22) Anderson, D. M.; Davis, S. H. Phys. Fluids 1995, 7, 248–265. (23) Sefiane, K.; Tadrist, L. Int. Commun. Heat Mass Transfer 2006, 33, 482–490. (24) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (25) Shin, D. H.; Lee, S. H.; Jung, J.-Y.; Yoo, J. Y. Microelectron. Eng. 2009, 86, 1350–1353. (26) Ramos, S.; Tanguy, A. Eur. Phys. J. E 2006, 19, 433–440. (27) Grandas, L.; Reynard, C.; Santini, R.; Tadrist, L. Int. J. Therm. Sci. 2005, 44, 137–146. (28) Sharma, H.; Mutharasan, R. Appl. Phys. Lett. 2011, 98, 114101–114103. (29) Golovko, D. S.; Butt, H.-J.; Bonaccurso, E. Langmuir 2008, 25, 75–78. (30) Fujishima, A.; Rao, T. N.; Tryk, D. A. J. Photochem. Photobiol., C 2000, 1, 1–21. (31) Wang, H.; Duan, J.; Cheng, Q. Anal. Chem. 2011, 83, 1624– 1631.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: k.sefi[email protected].

’ REFERENCES (1) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Rev. Mod. Phys. 2009, 81, 739. (2) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334–1344. (3) Bigioni, T. P.; Lin, X-M; Nguyen, T. T.; Corwin, E. I.; Witten, T. A.; Jaeger, H. M. Nat. Mater. 2006, 5, 265–270. (4) Young, T. Philos. Trans. R. Soc. London 1805, 95, 65–87. (5) Birdi, K. S.; Vu, D. T. J. Adhes. Sci. Technol. 1993, 7, 485–493. (6) Bourges-Monnier, C.; Shanahan, M. E. R. Langmuir 1995, 11, 2820–2829. (7) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (8) Sefiane, K.; David, S.; Shanahan, M. E. R. J. Phys. Chem. B 2008, 112, 11317–11323. (9) Dunn, G. J.; Wilson, S. K.; Duffy, B. R.; David, S.; Sefiane, K. J. Fluid Mech. 2009, 623, 329–351. (10) Shanahan, M. E. R. J. Adhes. Sci. Technol. 1992, 6, 489–501. (11) McHale, G.; Rowan, S. M.; Newton, M. I.; Banerjee, M. K. J. Phys. Chem. B 1998, 102, 1964–1967. (12) Cazabat, A.-M.; Guena, G. Soft Matter 2010, 6, 2591–2612. (13) Shanahan, M. E. R.; Sefiane, K.; Moffat, J. R. Langmuir 2011, 27, 4572–4577. (14) Shanahan, M. E. R. Langmuir 1995, 11, 1041–1043. (15) Kaufui, V. W.; Omar De, L. Adv. Mech. Eng. 2010, 11. (16) Choi, S. U. S. Korea-U.S. Technical Conference on Strategic Technologies, Vienna, VA, October 22
24, 1998. Sponsoring Organization: US Department of Energy (US). (17) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756. (18) Moffat, J. R.; Sefiane, K.; Shanahan, M. E. R. J. Phys. Chem. B 2009, 113, 8860–8866. (19) Shanahan, M. E. R.; Sefiane, K. In Contact Angle, Wettability and Adhesion; Mittal, K. L., Ed.; Brill Academic Publishers: Leiden, The Netherlands, 2009; Vol. 6, p 19. (20) Askounis, A.; Orejon, D.; Koutsos, V.; Sefiane, K.; Shanahan, M. E. R. Soft Matter 2011, 7, 4152–4155. 12843

dx.doi.org/10.1021/la2026736 |Langmuir 2011, 27, 12834–12843