Mobility of Aqueous and Binary Mixture Drops on Lubricating Fluid

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Article Cite This: Langmuir 2019, 35, 7672−7679

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Mobility of Aqueous and Binary Mixture Drops on Lubricating FluidCoated Slippery Surfaces Meenaxi Sharma, Pritam Kumar Roy, Jitesh Barman,† and Krishnacharya Khare* Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India

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S Supporting Information *

ABSTRACT: The mobility of liquid drops on lubricant-infused slippery surfaces depends strongly on various system parameters, for example, surface energy and roughness of the underlying solid surface and surface tension and viscosity of the test and the lubricating fluids. Here, we investigate lubricant-coated slippery surfaces fabricated on smooth hydrophobic solid surfaces and examine the influence of thickness and viscosity of the lubricating oil on the velocity of aqueous drops. We also investigate the effect of surface tension of the test liquid using a binary mixture of water and ethanol, on the apparent contact angle, which further affects their slip velocity. A theoretical model, based on various dissipative forces acting in different regions of the lubricating oil and a test drop, is also presented, which elucidates the dependence of drop velocity on lubricating oil viscosity and base radius of drops of test liquids.

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INTRODUCTION The ubiquitous phenomenon of liquid drops moving on a solid surface is observed in nature on various plant leaves during rainy days and can also be experienced in our daily life, for example, in bathroom and kitchen sinks, raindrops on window panes, car windshields, to name a few. Such surfaces have a wide range of practical applications including coatings,1 microfluidics,2 fog harvesting,3 and so forth. Inspired by nature, a broad range of technological applications are based on surfaces with designed surface chemistry and topography on micro/nanoscales to produce and control its wetting/nonwetting performance.4−6 For example, artificial superhydrophobic surfaces7−9 are fabricated by mimicking the structure of a lotus leaf10 by generating micro and/or nanoscale textures, coated with a low-surface-energy material. Such superhydrophobic surfaces demonstrate extreme water repellency with rolling water drops, and are hence found suitable in various practical applications such as self-cleaning,11,12 water proofing,13 biomedical areas,14 and so forth. Superhydrophobic surfaces demonstrate their extreme nonwetting performance because of the air trapped in the textures of the solid surface underneath the drop. However, maintaining the air pockets can be extremely difficult as they could be destroyed by penetration of the liquid inside these air pockets under extreme environmental conditions such as high pressure,15,16 low temperature,17 and also upon mechanical damage of the surface.4,6 This would change the wetting state of the drop from Cassie−Baxter to Wenzel, resulting in pinned (immobile) drops.6 To overcome this difficulty, a new class of liquidrepellent surfaces, named as lubricating fluid-infused slippery surfaces (LISs), is designed by filling the micro- and nanoscale textures with a suitable low-surface-tension lubricating fluid.18−24 In nature also, similar characteristics are observed © 2019 American Chemical Society

in Nepenthes pitcher plants, which also inspired the fabrication of LISs.25,26 As an important pre-requisite for LIS behavior, the underlying solid surface should be hydrophobic; otherwise, top aqueous drops would sink into the lubricating oil film and the drops would not slip at all.18,22,24,27 The thin oil layer acts as a lubricating layer which shows very low-contact-angle hysteresis (CAH ≈ 1−2°) because of smooth movement of the threephase contact line.18 As a result, test liquid drops on such surfaces slip effortlessly at a very low tilt angle (∼2°). Additionally, LIS also acts as a potential candidate in a wide range of technological and industrial applications because of its excellent nonwetting and slippery performances, and is hence advantageous in self-cleaning,22,28 drag reduction,29 food packaging (commercial ketchup refill bottles),30 fog harvesting,31 enhancing condensation,32 anticorrosion,33,34 optical transparency,35,36 anti-icing,37−39 anti-biofoulings,40 and so forth. The common feature for most of these applications is to enhance the mobility of drops of pure and complex fluids in a controlled manner. Most research groups used topographically structured or porous solid substrates to infuse lubricating fluids, which requires an additional step of generating topographies or porosity. Alternatively, smooth solid surfaces can also be used with appropriate surface engineering to fabricate lubricantcoated slippery surfaces (LCSs).24,27,41,42 Because of the involvement of four different phases (solid, lubricating fluid, test liquid, and vapor), slippery surfaces offer enormous scope for fundamental research. Numerous studies have been done to investigate the effect of drop impact dynamics on lubricantReceived: February 18, 2019 Revised: April 23, 2019 Published: May 22, 2019 7672

DOI: 10.1021/acs.langmuir.9b00483 Langmuir 2019, 35, 7672−7679

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Langmuir infused surfaces for lubricating films of varying viscosity and thickness43,44 and also to study the drop mobility on such surfaces.28,45,46 For such four-phase systems, Varanasi et al. calculated various wetting configurations outside and underneath a test drop, which is very useful in determining the mobility of the drop on lubricant-infused structured solid surfaces.20 Many other research groups have also reported the drop motion on lubricant-infused surfaces considering various parameters involved in driving and dissipative forces.29,45−48 The interplay of various types of forces acting on a moving drop on LISs controls its motion and also decides its speed. On such slippery surfaces, a test liquid drop is always surrounded by a wetting ridge near the three-phase contact line, which is due to the balance of interfacial tensions. Various research groups have investigated the shape and size of wetting ridges using various microscopic techniques.19,20,41,45,49 On a thin lubricating fluid-coated surface, the contact angle is defined by Neumann’s angle at the three-phase contact point.19,50,51 However, it is not that easy to measure Neumann’s angle compared to Young’s angle. Hence, apparent contact angles are alternatively used to demonstrate the static behavior of slippery surfaces.52 The presence of a wetting ridge around moving drops also affects their velocity because of the viscous dissipation in the ridge.20,45,47 Taking into account the viscous dissipation in different regions (drop, lubricating film, and wetting ridge), Quéré et al. calculated the total frictional force acting on a drop based on capillary number and Reynolds number, and derived a scaling law to predict the slip velocity of the drop.45 Recently, Kusumaatmaja et al. investigated the role of the shape of lubricant meniscus on droplet mobility using free energy latticeBoltzmann simulation.47 They observed that for large apparent contact angles, contact line pinning dominates, which can be overcome by increasing the thickness of the lubricating film. For small apparent contact angles, viscous drag because of the wetting ridge dominates, which can be reduced by decreasing the thickness of the lubricating film. Another interesting aspect of droplet motion is its tunability and control, which is quite beneficial in a wide range of applications. Various ways to control the droplet mobility are achieved either by surface modification, which can be done by chemical pattering48,53 or physical topography of the surface, or by some external stimuli, for example, mechanical strain, temperature, and so forth.35,54,55 Aizenberg et al. demonstrated the tuning of drop motion via mechanical stretching of the substrate results in pinning and sliding of the drop in a reversible manner.35 Another way to tune the droplet mobility can be via changing various physical parameters (viscosity, surface tension, density) of the test drop.45,55 Although previous reports on drop mobility are quite useful in establishing a required fundamental understanding, the role of the properties of the test liquid and lubricating fluid still needs to be explored for the complete understanding of the system, which is the main focus of this study. In this article, we study the drop mobility on LCSs fabricated on smooth hydrophobic solid surfaces tilted by a small angle and investigate the effect of various physical parameters pertaining to the lubricant and test liquid on the drop mobility. The first part includes the effect of lubricating film thickness and viscosity on drop velocity and in the next part, the effect of surface tension of the test liquid (which affects the contact angle and base radius of the drop) on the velocity of slipping drops is discussed. Comparing viscous dissipations in various regions of the two liquids (lubricant and

test liquid), a scaling law for drop velocity is also developed, which supports our experimental observations.

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EXPERIMENTAL SECTION

Microscopic glass slides, having root mean square surface roughness of 8 (±2) nm, were cut with dimensions of 2 cm × 2 cm and used as solid substrates for all the experiments. For removal of organic and inorganic surface impurities, the substrates were cleaned in an ultrasonic bath of ethanol, acetone, and toluene for 10 min each followed by O2 plasma (Harrick Plasma, USA) cleaning for 30 s. The resulting samples were found completely hydrophilic with a water contact angle of 5 (±1)°. Substrates were made hydrophobic by grafting a self-assembled monolayer of octadecyltrichlorosilane (OTS) molecules. The cleaned substrates were immersed in 0.2% V/V solution of OTS in toluene for 20 min followed by drying with N2 and heating at 90 °C for 30 min. OTS-coated glass substrates were found hydrophobic and oleophilic with water and silicone oil contact angles as 110 (±2)° and 5 (±1)°, respectively. Silicone oil (Gelest Inc. USA) with kinematic viscosity 20 cSt ≤ ηo ≤ 100 000 cSt, density of 950 kg/ m3 ≤ ρo ≤ 978 kg/m3, and surface tension of 20.6 mN/m ≤ γo ≤ 21.6 mN/m was used as the lubricating fluid for all the experiments (see the Supporting Information, Table S1). The hydrophobic glass substrates were coated with a thin lubricating film of silicone oil by dip-coating followed by gravity drainage to remove the excess oil. Substrates immersed in different viscosity silicone oils resulted in different thicknesses. Hence, the dip-coated samples were subsequently spin-coated with different rotation speeds to achieve the same thickness of 6 μm for all silicone oil viscosities. Deionized (DI) water (ρ = 997 kg/m3) was used as the test liquid to study the effect of viscosity of the lubricating oil on slippery behavior. Later, a binary mixture of water and ethanol was used to study the effect of surface tension of the test liquid on slippery behavior. Varying the ethanol concentration from 0 to 100% (V/V) resulted in the surface tension of the binary mixture in the range from 72.8 mN/m (pure water) to 21.6 mN/m (pure ethanol). Surface tension measurement of all binary mixtures was done using the pendant drop method under ambient conditions (see the Supporting Information Figure S1). Surface tension and other interfacial tensions of all binary mixtures are summarized in Table S2 of the Supporting Information. The drop volume of the test liquids was kept fixed at 10 μL for all slippery experiments. Contact angle measurements were performed using a dynamic optical contact angle goniometer (OCA-35, DataPhysics Germany) equipped with a complementary metal-oxide semiconductor camera. The drop profile was extracted using the software SCA-20, which provided the information of drop base radius and apparent contact angles. Schematics of an aqueous drop on a dry and a thin lubricating fluid-coated solid surface indicating Young’s, Neumann’s, and apparent contact angles are shown in Figure S2 of the Supporting Information. Slippery behavior of lubricating fluid-coated surfaces was characterized by measuring the CAH and slip velocity of the test liquid drops. CAH was measured by the drop volume method. Supporting Information Table S3 summarizes various contact angles: static contact angles (dry θws and apparent on lubricated θwos), advancing, receding, and CAH on oil-coated samples (θadv, θrec, and Δθ) and apparent contact angles (θapp) for binary mixtures as a function of increasing ethanol concentrations. Experimentally measured CAH values for different lubricating oil viscosities and binary mixtures with different ethanol concentrations in water are reported in Figure S3 of the Supporting Information. For drop velocity measurement, the goniometer was tilted using its tilting base unit and the drop motion on the tilted substrate was recorded using the camera. Slip velocity of a drop was calculated only after the drop traveled a certain distance so that its velocity became constant (cf. Supporting Information, Figure S4). In experiments where dependence of oil viscosity on slippery behavior was investigated, tilt angle (α) was kept constant at 20°, whereas the remaining experiments were performed at a 15° tilt angle. To avoid mixing of ethanol with silicone oil, all experiments were 7673

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Langmuir performed at a temperature of 25 °C as ethanol and silicone oil are immiscible at this temperature.56 Also, to minimize ethanol evaporation, all experiments were performed in a closed environment chamber. All measurements were repeated at least three times on different spots of different samples to calculate the standard deviation.

ηw, the above scaling relation reduces to vi ≈ v

RESULTS AND DISCUSSION On lubricating oil-coated slippery surfaces, test liquid (aqueous) drops slip spontaneously the moment they are tilted by a small angle (equal to or larger than the critical tilt angle, α*, which is the minimum angle at which a drop starts moving). The presence of a lubricating film prevents direct contact between a test drop and a solid substrate and hence provides a smooth movement to the three-phase contact line of the drop. Slipping characteristics of aqueous drops on such slippery surfaces depend strongly on thickness and viscosity of the lubricating fluid and surface tension of the test liquid. Figure 1a illustrates the schematic of a test liquid drop moving

(

capillary number Ca =

ηw v γw

) is of the order of 10

FD ≈ ηw vR b

and

ηovi hfilm

FO ≈ ηw vR b

(

ηw (v − vi)

vi = v 1 +

Rb

ηoR b ηw hfilm

ηovi

=

hfilm

FR ≈ ηovR b

(1)

(2)

(3)

Combining all the dissipative forces and adding the pinning force into it gives the total retarding force which is balanced by the driving gravitational force as Fg = FD + FO + FR + FP

(4)

ρgRb3

where Fg = sin α is the gravitational force and FP = ρgRb3 sin α* is the pinning force. Imposing the condition ηo ≫ ηw, eq 4 reduces to v≈

ρg (sin α − sin α*) 2 Rb ηo

(5)

It is clear from eq 5 that the drop velocity scales as square of the base radius (Rb2) of a test drop and is inversely proportional to the viscosity of the lubricating oil ηo. Equation 5 can also be written in dimensionless form as ηw area Ca ≈ (sin α − sin α*) 2 (capillary length) ηo (6)

, respectively, where

which after simplifying becomes

where the area scales as Rb2, capillary length as γw /ρg , and capillary number Ca ≈ ηwv/γw. In the present case, as water/

−1

)

, which

Finally, the viscous stress in the wetting ridge of height K scales as ηov/K and integrating it over a surface area of KRb results in the dissipative force (FR) because of the wetting ridge as

vi is the velocity of the oil−water interface. In equilibrium, balancing the viscous stress of both sides of the interface provides

−6

As a drop on a thin oil-coated surface is surrounded by a wetting ridge made of the oil, viscous dissipation in the oil takes place in two different regions: (i) oil film underneath the drop and (ii) wetting ridge. Viscous stress underneath the oil film scales as ηovi/hfilm, which after integration gives the viscous force (FO) as ηoviRb2/hfilm. For ηo ≫ ηw, it can be simplified to

down on a tilted substrate at different time intervals. Figure 1b shows various system parameters, namely lubricating film thickness hfilm, drop base radius Rb, drop height H, slip velocity v, and tilt angle α of a slipping test drop. Test liquid drops on lubricating oil-coated solid substrates may be cloaked by a thin oil layer depending upon the surface tensions of oil and the test liquid to minimize its energy as shown in Figure 1b. Test drops on lubricating fluid-coated slippery surfaces are also surrounded by a wetting ridge, caused because of balance of the three interfacial tensions at the three-phase contact point, as shown in Figure 1b, which also affects the mobility of the drops. CAH (Δθ) and critical tilt angle (α*) are measures of the resistance for a test drop to slide on a slippery surface. Therefore, lower values of CAH and critical tilt angle indicate less pinning (see the Supporting Information Figure S3). Varanasi et al. derived a scaling model for the velocity of moving drops on a lubricating fluid-coated surface by balancing the driving (gravitational) and drag (pinning and viscous) forces.20 Drop motion is affected by different kinds of dissipations in both liquids, that is, drop as well as lubricating oil. Velocity of the oil−water interface can be deduced from the continuity of the viscous stress at the oil−water interface. Viscous stress on the water and oil sides of an oil−water Rb

. To get the

indicates that the dissipation is mainly caused by the surface tension force. Even though the viscosity of binary mixture drops (ηw) varies between 0.89 and 1.09 cSt for pure water to pure ethanol, we assumed it to be constant with value 1 cSt. Quéré et al. also suggested that for as long as ηw < ηo, v is found to be independent of ηw, which is also the case for our experiments and hence justifies the choice of constant ηw.45 Therefore, it can be concluded that the drop motion is only affected by the surface tension of the test liquid and is independent of its viscosity. Viscous stress in a drop scales as ηwv/Rb, which confirms that the dissipation in the drop is due to change in the drop base radius caused by a change of surface tension of the test liquid. Integrating the viscous stress in the aqueous drop over the surface area of the drop results in the viscous force (FD), which scales as

Figure 1. Schematics of an (a) experimental setup showing an aqueous drop at different positions while moving down a tilted slippery substrate and (b) various system parameters corresponding to a test drop on a lubricating fluid-coated slippery surface tilted by an angle α.

ηw (v − vi)

ηoR b

magnitude of v, we balance the driving force with the dissipating one for a drop moving on an oil-coated surface inclined at an angle α. We first collect various dissipative forces (viscous and pinning) because of the oil and the drop. For binary mixture drops with viscosity ηw ≈ 1 cSt, surface tension (γw) ≈ 21−72 mN/m, and drop velocity v ≈ 0.5 mm/s, the

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interface can be written as

ηw hfilm

. As, for our experimental system, ηo ≫ 7674

DOI: 10.1021/acs.langmuir.9b00483 Langmuir 2019, 35, 7672−7679

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Figure 2. Effect of lubricating oil on slip velocity of water drops (with a fixed drop volume of 10 μL and a tilt angle of 20°). (a) Slip velocity of water drops as a function of lubricating film thickness for three different lubricant viscosities; 350 cSt (black), 1000 cSt (red), and 5000 cSt (blue). (b) Schematics and optical images showing the wetting ridge around moving water drops for two different oil viscosities but same thickness. (c) shows slip velocity as a function of lubricating oil viscosity and (d) shows the same data in nondimensional form. Experimental data points are shown by black squares and solid red lines correspond to the fitted curve of the theoretical model (eqs 5 and 6).

binary mixture drops are always cloaked by a thin oil layer, γw in the expression should be replaced by the effective interfacial tension γeff = γov + γow where γov and γow are oil−vapor and oil−water interfacial tensions, respectively. During experiments, we first investigated the effect of film thickness (hfilm) and kinematic viscosity (ηo) of lubricating silicone oil on the slip velocity of water drops. Subsequently, we also investigated the effect of surface tension of the test liquid on the slip velocity. Figure 2a shows the variation of slip velocity of water drops as a function of lubricating film thickness, hfilm, for three different silicone oil viscosities, that is 350, 1000, and 5000 cSt. Zero film thickness corresponds to dry substrates where no drop motion is observed because of high friction and pinning. As the thickness of the lubricating film is increased, the drop velocity also increased as shown by the first few data points in Figure 2a. This is because the introduction of a thin oil layer covers defects and pinning sites of the solid surface and provides a lubricated surface and hence a smooth contact line motion to slipping drops. As the thickness of the lubricating layer is increased, the slip velocity of the drops is also increased as the surface became more lubricated with reduced pinning effects. For larger values of oil film thicknesses, water drops show a constant slip velocity, which is independent of film thickness (under lubrication approximation: film thickness ≪ lateral size of the film). This is because a sufficient amount of lubricant is present between a water drop and the solid surface and the drop shows a constant slip velocity, which is independent of the oil film thickness. Figure 2a also indicates that the slip velocity of water drops increases with increasing lubricant film thickness and becomes maximum at about hfilm = 6 (±2) μm for all viscosities. The figure also shows the effect of lubricating oil viscosity on the drop velocity. It is clear from the graph that the slip velocity of test drops decreases drastically with increasing lubricating oil viscosity.

Increasing oil viscosity induces larger viscous drag for slipping drops, resulting in increased frictional force between the drop and the surface. For high oil viscosity (ηo = 5000 cSt), slip velocity becomes approximately 10 times smaller than for the low viscosity (350 cSt) one. This is an important result, which indicates that smaller thickness of a lubricating film affects the slip velocity, whereas larger thickness does not affect it. Also, the viscosity of the lubricating oil plays a major role in the slippery behavior of lubricated surfaces. The wetting ridge around a test drop also affects the drop velocity as it offers a resistance against drop motion. It was observed that, for a fixed film thickness, the height of the wetting ridge around a moving test drop decreased with increasing oil viscosity, which is shown by schematics and optical images in Figure 2b. Because of the motion, the wetting ridge around a test drop could not attain its equilibrium value (the maximum value). Consequently, larger-viscosity silicone oil resulted in a smaller wetting ridge size and the smaller viscosity silicone oil yielded larger wetting ridge sizes. After carefully analyzing the results, we found that the size of meniscus also depends on the speed of the water drops. This is again because drops moving with a larger speed get lesser time to form a complete wetting ridge and vice versa. To investigate the role of oil viscosity on test drop velocity, slippery surfaces were prepared with oil films of the same thickness but different viscosities. Figure 2c shows the variation of slip velocity of water drops as a function of lubricating oil viscosity. It is clear from the figure that for silicone oil of 350 cSt viscosity, water drops slip very quickly with a velocity of about 0.9 mm/s, which slows down to 0.2 mm/s for oil of viscosity of 5000 cSt (see videos Movies S1 and S2 in the Supporting Information). For low viscosities, large variation (∼a factor of 100) in slip velocity is observed over a small viscosity range (20−5000 cSt), whereas not much variation is seen over the large viscosity range (5000−100 000 cSt). Therefore, the variation of slip velocity with oil viscosity is plotted in semilog scale in 7675

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(θwos) surfaces as a function of the surface tension of the mixture. Semprebon et al. derived an expression for an apparent contact angle on a thin oil-coated surface as γ −γ cos θapp = ov γ ow . Figure S2 in the Supporting Information

Figure 2c. The solid red line in Figure 2c represents the theoretical model (eq 5), which also suggests that the slip velocity of water drops is inversely proportional to the viscosity of lubricating oil. Figure 2d shows the same data plotted in nondimensional form fitted with eq 6, confirming the linear dependence between the capillary number (Ca) and inverse of lubricating oil viscosity (1/ηo). In addition to the viscosity of the lubricating fluid, physical properties of the test liquid (surface tension and viscosity) also play a paramount role in the resulting slippery behavior. The base radius (Rb) of a test liquid drop sitting on a lubricating oil-coated solid surface depends on the surface tensions of the test liquid and the lubricating oil and the interfacial tension between the two. For the present experimental system with an oleophilic and hydrophobic solid surface, which is designed for aqueous-based test liquid, oil-based lubricating fluids have been used, which have very low surface tension (∼21 mN/m). Hence, surface tension of the test liquid was varied by using a binary mixture of water and ethanol in different volume ratios. Figure 3a shows the surface tension of a water−ethanol binary

eff

shows schematics of various contact angles on dry and lubricated surfaces. In addition, Tables S2 and S3 in the Supporting Information contain experimental and calculated values of various interfacial tensions and contact angles for different binary mixtures with increasing ethanol concentration. Moving from pure ethanol to pure water, θws and θwos increases from 21° and 32° to 107° and 105°, respectively. The difference in θws and θwos is found to be significant for the ethanol−water mixture compared to pure water. Figure 3b (right Y-axis) shows the base radius of drops of a binary mixture as a function of its surface tension. It is clear from the graph that as the surface tension increases, the base radius of the drops decreases because their contact angle increases. Subsequently, slippery behavior with the binary mixture as test liquid was investigated with drop volume V = 10 μL and tilt angle α = 15°. Figure 4a shows the snapshots of the water (top row) and ethanol (bottom row) drops at different times moving down a tilted lubricated substrate. The figure shows the relative position of water and ethanol drops after the same time. The red dotted line in the first column indicates the reference point considered as t = 0 s for the motion of the water and ethanol drops. Subsequent columns indicate different times after t = 0 s as shown in Figure 4a. It is clear from the figure that ethanol drops of the same volume move faster than water drops. Calculation of slip velocity of binary mixture drops is described in Figure S4 in the Supporting Information. Figure 4b shows experimentally obtained slip velocity of binary mixture drops as a function of the surface tension of the binary mixture for slippery surfaces coated with silicone oil of a viscosity of 1000 cSt. It is clear from the graph that the drop velocity decreases with increase in their surface tension, or in other words, ethanol drops of the same volume move faster than water drops. For the same experimental system, the slip velocity of ethanol drops (0.76 mm/s) is about twice that of water drops (0.37 mm/s). As the radius, and hence the contact area, of ethanol drops is much larger on a lubricant-coated surface compared to water drops, intuitively one would expect a larger effective friction, and hence slower velocity for ethanol drops. Similar behavior for velocity was also observed on slippery surfaces with different viscosities of silicone oil, which is shown in Figure 4c. For lower viscosities (ηo < 1000 cSt), a large variation in drop velocity of binary mixture drops is observed; however, for ηo > 1000 cSt, the slip velocity does not change much with increase in surface tension as the viscous force dominates over the surface tension force. For ηo = 200 cSt, ethanol drops move very fast (3.57 mm/s) compared to water drops (2.06 mm/s); however, for ηo = 5000 cSt, a small variation in slip velocity (0.14 mm/s for ethanol and 0.10 mm/s for water) is perceived. We also noted that the dynamic apparent contact angle (contact angle while drops are moving) for the binary mixture drops did not change with time (see the Supporting Information Figure S5). It is clear from eq 5 of the theoretical model that the drop velocity scales as the square of the base radius (Rb2) of a drop and is inversely proportional to the lubricating oil viscosity ηo. Figure 5a shows the plot of drop velocity as a function of square of the base radius of a slipping drop as suggested by eq 5. Linear variation of V with Rb2 confirms the qualitative

Figure 3. (a) Surface tension of the ethanol−water mixture as a function of increasing ethanol volume concentration. 0% volume concentration corresponds to pure DI water (72.8 mN/m), whereas 100% corresponds to pure ethanol (21.6 mN/m). The inset shows optical images of water and ethanol drops with contact angles of 109° and 22°, respectively. (b) Left Y-axis shows contact angles on dry (θws) and lubricated (θwos) surfaces as a function of surface tension of the binary mixture. The right Y-axis shows the base radius (Rb) of the corresponding drops.

mixture as a function of ethanol volume concentration. The surface tension of the mixture was measured using the pendant drop method as shown in Table S2 in the Supporting Information. 0% ethanol concentration corresponds to pure DI water, whereas 100% corresponds to pure ethanol and the intermediate values represent binary mixtures of water and ethanol, which provide us a range of surface tensions from 72.8 to 21.6 mN/m. Figure 3b (left Y-axis) shows Young’s contact angle on dry (θws) and apparent contact angle on oil-coated 7676

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Figure 4. Effect of surface tension of the binary mixture on the drop velocity on lubricating fluid-coated slippery surfaces with a fixed drop volume of 10 μL and tilt angle of 15°. (a) Optical images of water (top row) and ethanol (bottom row) drops at different time intervals. The red dotted line corresponds to the reference time t = 0 s. (b) Variation of slip velocity as a function of surface tension of the binary mixture on a substrate coated with 1000 cSt silicone oil. (c) Slip velocity as a function of surface tension of the binary mixture on substrates coated with different viscosity silicone oils.

fall on the same master curve. This is due to the fact that the oil viscosity is now multiplied with the capillary number, making the expression independent of the viscosity. Therefore, the above study confirms that the surface tension of the test liquid plays a very crucial role in determining the slippery behavior on lubricating fluid-coated surfaces.

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CONCLUSIONS In this study, we report the effect of physical properties of the lubricating fluid and test liquid on the velocity of slipping drops on LCSs. With increasing film thickness, the drop velocity initially increases and then becomes constant, whereas with increasing viscosity the drop velocity decreases. Drop velocity becomes maximum for a fixed film thickness, which is the same for all the lubricants with different viscosities. The surface tension of the test liquid is another important property which affects the drop contact angle and hence the base radius of the drop, which subsequently affects the slip velocity. During this study, the surface tension of the test liquid was varied by using the binary mixture of ethanol and water and varying the volume concentration of ethanol in the mixture. For the same tilt angle, pure ethanol drops move much faster than pure water drops of the same volume and the slip velocity decreases as the surface tension of the binary mixture increases. This is due to the fact that the viscous dissipation, which is inversely proportional to the drop base radius, decreases as the surface tension of the test liquid decreases. Increasing the oil viscosity further decreases the slip velocity of the binary mixture drops. As long as the viscosity of the test liquid is much smaller than that of lubricating oil, the slip velocity is independent of the viscosity of the former liquid. A scaling model based on the balance of driving and various dissipative forces is developed to predict the dependence of the slip velocity on various system parameters. The model predicts that the slip velocity depends inversely on the viscosity of the lubricating fluid, whereas it varies linearly with the square of the base radius of test drops, which agrees with the experimental findings.

Figure 5. Effect of base radius of the test liquid drop (or surface tension of binary mixture) on slippery behavior. (a) Variation of drop velocity as a function of square of the base radius (Rb2) and (b) nondimensional form of the same data. Solid lines represent the theoretical model (eqs 5 and 6) fitted to the experimental data points.

agreement of the force balance-based analytical model with the experiment. With increasing lubricating oil viscosity, the slope of V with the Rb2 line decreases, which indicates the dominance of the viscous force over gravitational force. Equation 6, which represent the same scaling behavior in nondimensional form, is fitted to the experimental data, which is shown in Figure 5b in which all data points corresponding to different oil viscosities 7677

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.9b00483.

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Physical properties of the lubricating fluid and various interfacial tensions and contact angles of test liquids (PDF) Slipping of a 10 μL water drop on a solid surface coated with 350 cSt silicon oil tilted by 20° (AVI) Slipping of a 10 μL water drop on a solid surface coated with 5000 cSt silicon oil tilted by 20° (AVI) Slipping of a 10 μL binary mixture (0% ethanol) drop on a solid surface coated with 1000 cSt silicon oil tilted by 15° (AVI) Slipping of a 10 μL binary mixture (100% ethanol) drop on a solid surface coated with 1000 cSt silicon oil tilted by 15° (AVI)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Pritam Kumar Roy: 0000-0002-1929-8199 Krishnacharya Khare: 0000-0001-5669-5858 Present Address †

Electronic Paper Display Institute, South China Normal University, Higher Education Mega Center, Guangzhou 510006, China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research work was supported by Hindustan Unilever Limited, India, and DST, New Delhi, through its Unit of Excellence on Soft Nanofabrication at IIT Kanpur.

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REFERENCES

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DOI: 10.1021/acs.langmuir.9b00483 Langmuir 2019, 35, 7672−7679

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DOI: 10.1021/acs.langmuir.9b00483 Langmuir 2019, 35, 7672−7679