Mobility of Yield Stress Fluids on Lubricant-Impregnated Surfaces

Research Article Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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Mobility of Yield Stress Fluids on Lubricant-Impregnated Surfaces Leonid Rapoport, Brian R. Solomon, and Kripa K. Varanasi* Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States

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S Supporting Information *

ABSTRACT: A common problem which we encounter on a daily basis is dispensing of yield stress fluids such as condiments, lotions, toothpaste, etc. from containers. Beyond consumer products, assuring the flow of yield stress fluids such as crude oil, mud, blood, paint, pharmaceutical products, and others, is essential for the respective industries. Elimination of wall-induced friction can lead to significant savings in the energy required for flow of yield stress fluids, as well as associated product loss and cleaning costs. Lubricant-impregnated surfaces (LIS) have been shown to change the dynamic behavior of yield stress fluids and enable them to flow without shearing. Despite the wide applicability of this technology and its general appeal, the fundamental physics governing the flow of yield stress fluids on LIS have not yet been fully explained. In this work, we study the mobility of yield stress fluids on LIS, and explain the relationship between their macroscale flow behavior and the microscale properties of LIS. We show that for yield stress fluids the thermodynamic state of an LIS can be the difference between mobility and immobility. We demonstrate that LIS can induce mobility in yield stress fluids even below their yield stress allowing them to move as a plug without shearing with an infinite slip length. We identify different mobility mechanisms and establish a regime map for drag reduction in terms of the shear stress to yield stress ratio and the microscopic properties of the LIS. We demonstrate these regimes in a practical application of pipe flow thereby providing key insights for the design of LIS to induce mobility of yield stress fluids in a broad range of practical applications. KEYWORDS: lubricant-impregnated surfaces, yield stress, slip, drag reduction, spreading

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INTRODUCTION Yield stress fluids are ubiquitous across different industries ranging from cosmetics and food products to building materials and energy.1 These fluids exhibit solid-like properties when the applied shear stress is lower than the yield stress τy. Once the applied stress exceeds this value, flow is initiated. The fluid behavior can be described by the Herschel−Bulkley model, which relates the shear stress τ and strain rate γ :̇ τ = τy + ηγ ṅ

need to develop slippery surfaces that can increase the mobility of these fluids in a repeatable, controlled, and robust manner. Here we show how lubricant impregnated surfaces (LIS)18 can be designed to enhance mobility of yield stress fluids. These surfaces were shown to reduce water drag,19 alter the dynamic behavior of water droplets,20 and improve the performance of a suspension-based flow electrode by allowing the battery to flow as plug.21 An LIS consists of a textured solid impregnated with a lubricating fluid.20,22−27 A droplet on such a surface can exist in 1 of 12 thermodynamic states which depend on the properties of the solid, the impregnated lubricant, the working fluid, and the environment.20 These states can be divided into two classes of LIS which are determined by the spreading coefficient of the lubricant on the solid in the presence of the working fluid Sos(w) = γsw − γos − γow (γ is the surface energy and subscripts “o”, “s”, “w”, and “a” denote a lubricant, a smooth surface, a working fluid, and the environment, respectively). When the spreading coefficient is non-negative (Sos(w) ≥ 0), the case of spreading LIS, the lubricant wets the textured surface completely and the tops of the textures are covered by a thin van der Waals film (vdW) of the impregnated lubricant. When the spreading coefficient is negative (Sos(w) < 0), the case of nonspreading LIS, the tops of the textures remain exposed.20 For the class of the nonspreading LIS, stable lubricant impregnation is possible when

(1)

where η and n are the consistency and flow indices. Because of these properties, a key challenge with yield stress fluids is that they are difficult to flow and stick to surfaces resulting in significant additional energy required for flow as well as associated product loss and cleaning costs. For example, up to 25% of a product per container is wasted because it cannot be dispensed, resulting in an overall product loss that is estimated to be in the order of millions of tons.2 Hence reducing wall friction, improving flowability, and eliminating stiction of these fluids is of significant interest. Despite the vast existing knowledge on the drag reduction of Newtonian fluids,3−9 rheology of yield stress fluids,10−12 and the flow of yield stress fluids in various geometries,13−16 drag reduction of yield stress fluids remains a developing field as slip mechanisms differ depending on the type of fluid in question.17 Surfaces that reduce drag for Newtonian fluids do not necessarily have the same performance for yield stress fluids. Hence, there is a © XXXX American Chemical Society

Received: December 7, 2018 Accepted: February 24, 2019

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DOI: 10.1021/acsami.8b21478 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

Research Article

ACS Applied Materials & Interfaces the contact angle θos(a) of the lubricant on the smooth surface in the surrounding environment as well as the contact angle θos(w) of the lubricant on the smooth surface in the presence of the working fluid are smaller than the critical angle defined as: cos θcr =

1−φ r−φ

(2)

where r is the total surface area divided by the projected area, and φ is the solid fraction defined as the emerged surface area divided by the projected surface area. Commercial applications28 for the flow of yield stress fluids such as ketchup, mayonnaise, waxy crude oil, toothpaste, etc. on LIS have demonstrated its performance but have not explained the physical mechanism that govern the remarkable slip phenomenon. Herein we study the dynamic behavior of yield stress fluids on LIS, elucidate the key physical mechanisms that control slip, and establish mobility regimes.

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RESULTS A common example of a yield stress fluid is a suspension of particles in a solvent; these fluids exhibit a yield stress when the volume fraction of the particles is above a critical value.29,30 One example is Carbopol which is considered an ideal yield stress fluid whose slip mechanisms have been extensively studied.31−36 We use 1 wt % Carbopol (τy = 66.7 Pa, η = 55.6 Pa·s−n, n = 0.40) as a model fluid in our study.37,38 For example, a water droplet exhibits low contact angle hysteresis on flat polytetrafluoroethylene (PTFE), which allows it to rapidly roll when the surface is tilted as shown Figure 1A. However, a similar volume of Carbopol placed on the same surface sticks and stays immobile as shown in Figure 1B. Surprisingly, this is also the case for a superhydrophobic surface (static contact angle 165.3°, contact angle hysteresis 3.2°) on which water droplets exhibit high mobility while Carbopol stays immobile. A similar behavior is observed when Carbopol is placed on a nonspreading LIS impregnated with silicone oil that has a large enough φ as shown in Figure 1F (the LIS consists of an array of square microposts of size a and depth h with varying posts pitch b, see Materials and Methods). However, on a spreading LIS impregnated with silicone oil Carbopol moves readily along the surface as shown in Figure 1H. To understand this peculiar behavior, systematic experiments were conducted under a stress-controlled cone and plate rheometer on both spreading and a nonspreading LIS with different texture geometries. Spreading LIS. Figure 2A illustrates the experimental set up with a spreading LIS sample in which Carbopol is placed between a rotating stainless steel cone (20 mm diameter) and the surface of interest and sheared under a prescribed shear stress (see Materials and Methods). The control surface was the stationary plate of the rheometer (stainless steel) on which the Carbopol did not slip and its behavior is well described by a Herschel-Bulkley model as presented in Figure 2B. In contrast on a spreading LIS, the Carbopol is mobile even when the applied shear stress is below the yield stress for all values of texture pitch b. Moreover, for a given shear stress, the apparent strain rate (the strain rate measured by the rheometer) grows as the pitch increases. In fact, at high enough shear stresses, drag reduction was so high that Carbopol flew off the samples with the highest pitch (b = 25, 50 μm) due to centrifugal forces; hence measurements were restricted to lower shear stresses values for these samples. Drag reduction DR is

Figure 1. Performance of drag reduction solutions. (A) 187 μL water droplet moving down a PTFE tape. (B) 723 μL 1 wt % Carbopol sticking to a tilted Teflon tape. (C) 65 μL water droplet moving down a tilted superhydrophobic surface. (D) 57 μL 1 wt % Carbopol sticking to a tilted superhydrophobic surface. (E) Illustration of a nonspreading LIS where h is the height of the post, b is the pitch, and a is the width of a post with a square profile. (F) 165 μL 1 wt % Carbopol sticking to a tilted nonspreading LIS. (G) Illustration of a spreading LIS. (H) 118 μL 1 wt % Carbopol sliding on a tilted spreading LIS. Tilt angle is 30° for all experiments. All scale bars are 5 mm.

quantified in terms of the ratio of the apparent strain rate γċ measured on the control sample to that measured on an LIS γLIS ̇ . Since the measurements are performed in a stresscontrolled regime, the drag reduction is a function of the applied shear stress and is given by:8 DR(τ ) = 1 −

γċ γLIS ̇

τ

(3)

When DR = 0 the apparent strain rate on an LIS is equal to that on the control surface, and the LIS does not improve the mobility of the yield stress fluid. When DR = 1 the yield stress fluid is mobile on the LIS and immobile on the control surface under the same applied shear stress. In this case, drag reduction is complete as LIS is the difference between mobility and immobility of the yield stress fluid. As can be seen in Figure 2C, drag reduction grows inversely with the ratio of shear stress to yield stress. When this ratio is smaller than unity, complete drag reduction is attained since the fluid is immobile on the control surface. To understand the underlying phenomenon we focus on the regime in which the Carbopol does not undergo any shear and mobility comes entirely from slip on the LIS, τ < τy. Normally, in a cone and plate rheometer the angular velocity Ω of the rotating cone, will be used to calculate the apparent strain rate γapp ̇ = Ω/α ,12 where α is the cone angle. However, since the applied shear stress is smaller B


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ACS Applied Materials & Interfaces

Figure 2. Mobility on spreading LIS. (A) Illustration of experiment set up. Cone is 20 mm in diameter and has an angle of 4°. (B) Results for the control substrate and spreading LIS with varying post pitch. Solid line represents a Herschel-Bulkely model with τy = 66.7 Pa η = 55.6 Pa·s−n n = 0.40. (C) Drag reduction on LIS samples. (D) Stress vs strain rate in the lubricating layer. Solid lines represent linear fits. (E) Slip dominated regime and the transition regime. Solid line represents a linear fit with a slope of 0.75. (F) Transition regime and shear dominated regime. Solid line represents the Herschel-Bulkley model in panel A.

μγ ̇ ji τ h2 yzz ≈ o jjj1 + β zz τy τy jk (a + b)2 z{

than the yield stress the Carbopol does not shear and the measured velocity is exclusively due to slip which is caused by flow of the lubricant between the textures. For this case we approximate the system as a plate−plate rheometer in which the bottom face of the undeformed Carbopol is acting as the rotating top plate and the base of the LIS sample is acting as the stationary bottom plate. The relevant dimensions are shown in the inset of Figure 2A. Hence, the measured angular velocity is entirely due to the shearing of the impregnated lubricant so that the strain rate of the lubricant is given by:12 γȯ =

rΩ h

(5)

By plotting the measurements according to this relation we see in Figure 2E that the data collapses on a linear master curve with a fitted slope of 0.75 due to conversion from τr to τ (see SI).12 When the applied shear stress is larger than the yield stress of the material, the apparent strain rate has contributions from both shearing of the lubricant as well as shearing of the Carbopol. Strain rate due to the shearing of Carbopol can be expressed by γYS ̇ = (Ω − Ωs)/α , where Ωs is the angular velocity at the lubricant-Carbopol interface. When τ ≫ τy, the angular velocity at the lubricant-Carbopol interface becomes negligible compared to that measured by the rheometer (Ωs ≪ Ω), and the mobility is dominated by shear of the Carbopol so that we can approximate its strain rate by the apparent strain rate, γYS ̇ ≈ γapp ̇ . As a result, when τ ≫ τy using (1) we write the following relation between the applied shear stress and the apparent strain rate:

(4)

where r is the cone radius. Plotting the strain rate γȯ in the lubricating layer against the shear stress τr for a plate−plate rheometer (derivation in Supporting Information (SI)) shows that the relation between the two is linear for all values of pitch. Thus, LIS act as a Newtonian lubricating layer for which the applied shear is related to the strain rate in the oil by an effective viscosity τ = μeff γȯ . The effective viscosity of the LIS depends both on the viscosity of the lubricant as well as the geometry of the textures. The difference between the two is caused by flow of the lubricant past the posts,39 and the ratio between them depends on the ratio of post height to post pitch as μeff/μ − 1 ≈ βh2/(a + b)2 (SI Figure S1 where β is a constant). This scaling was shown previously in experiments studying wicking of fluids through microtextured surfaces.40 Thus, in the regime of low shear stress, the stress vs strain rate is linear and given by:

n n ηγapp ̇ ηγYS ̇ τ = +1≈ +1 τy τy τy

(6)

The above model is in good agreement with the experiments as shown in Figure 2F. To summarize, when the applied stress is smaller than the yield stress (τ < τy) the system is in the slip dominated regime where mobility comes from shearing of the oil. When τ > τy the C


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Effectively, this means that a nonspreading LIS is limited by its surface chemistry due to the exposed parts of the posts that can cause pinning. Hence, by minimizing the solid fraction of a nonspreading LIS we can induce high mobility similar to that of a spreading LIS. We demonstrate this effect by creating a vanishingly small solid fraction surface (φ ∼ 0) comprising of an array of close packed pyramidal structures with hierarchical features as shown in Figure 3C. For these structures the critical angle (defined by (2)) θcr = 63.4° is large enough so that the lubricant will be stably impregnated within the texture. As shown in Figure 3D and E, the mobility of Carbopol on the nonspreading LIS with low φ is similar to that of the spreading LIS. Indeed, rheometer experiments for both spreading and nonspreading low φ LIS show the dependence between stress and strain rate collapses onto each other as can be seen in Figure 3F. Note that this is in contrast to the immobility of Carbopol on both superhydrophobic surface (Figure 1D) and nonspreading LIS with high φ (Figure 1F). Application to Enclosed Conduits. Transportation of yield stress fluids in a traditional pipeline requires shear dominated flow, which leads to significant yield losses and high pumping costs. In contrast, an LIS coated pipe can allow for slip dominated regime that can minimize these losses. To demonstrate these advantages, we fabricated an LIS coated tube using an evaporation-based method (see Materials and Methods).26 We then compare the LIS coated tube to an unmodified tube by imaging the behavior of Carbopol under a constant pressure difference. On the unmodified glass tube Carbopol is immobile when the applied pressure induces a wall shear stress below the yield stress of the material. However, on a spreading LIS, the Carbopol moves without shearing as the system is in the slip dominated regime (τwall < τy). Consequently, Carbopol moves as a plug throughout the entire length of the coated tube at a constant speed of 0.5 mm/s which implies a lubricating layer thickness of 1.1 μm as shown in Figure 4A. Increasing the pressure so that the wall stress exceeds the yield stress (τwall = 2 τy) causes the Carbopol to shear as well as slip within the LIS coated tube. In Figure 4B, this flow behavior can be seen by the displacement of the free surface on which the pressure is applied as well as deformation of the Carbopol. When the wall stress is increased further (τwall = 4.5 τy), displacement due to slip is small compared to deformation due to shear as the system is in the shear dominated regime. This effect is represented in Figure 4C, where the Carbopol deforms in the LIS coated tube and the displacement of the free surface due to slip is relatively small such that the Carbopol smears on the tube walls. We quantify the mobility induced by LIS by introducing a parameter which compares translation due to slip with deformation due to shear ξ = Lt/[(Lf + Lt) − Li] where Li and Lf are the initial and final lengths of the Carbopol, and Lt is the translation length as shown in Figure 4A. When ξ = 0 mobility comes entirely from shearing as the following edge of the Carbopol stays immobile and Lt= 0. When ξ = 1 mobility comes entirely from slip as the Carbopol does not shear and its final length is equal to its initial length Li = Lf. The evolution of ξ as a function of time normalized by the time of Carbopol breakup tbreak is shown in Figure 4E. In the slip dominated regime (τwall = 0.6τy), ξ ≈ 1 throughout the experiment indicating pure translation with negligible deformation. In the shear dominated regime (τwall = 4.5τy) ξ < 1 for all times indicating that Carbopol mobility at any time is at least in part due to deformation. The deformed Carbopol which is sheared

system is in a transition regime where the apparent strain rate is both due to slip on the LIS as well as shearing of the Carbopol. Finally when τ ≫ τy the system is in a shear dominated regime where the mobility arises from shearing of the Carbopol. Nonspreading LIS. On nonspreading LIS (Figure 3A), we find that the behavior of Carbopol for τ < τy is no longer linear

Figure 3. Mobility on nonspreading LIS. (A) Illustration of nonspreading LIS on the experiment set up. View Z emphasizes the lubricant (in green) surrounding the bare post tops (in gray) and the regions in which the post tops pin the Carbopol (in red). (B) Results of nonspreading LIS with different pitch values (triangles) and flat silicon sample functionalized with FS (squares). Solid lines represent Herschel-Bulkley of the Carbopol (in black) and the samples in the region below yield stress (line colors correspond to the respective marker color). (C) A low solid fraction pyramidal surface with inset focusing on the small features on the face of the pyramid. Scale bars are 50 μm in the panel and 1 μm in the inset. (D) Carbopol sliding down a spreading low φ LIS. (E) Carbopol sliding down a nonspreading low φ LIS. (F) Stress versus strain rate for spreading and nonspreading low φ LIS. Solid line represents a Herschel-Bulkley model for a Carbopol.

but follows a Herschel-Bulkley model with parameters that depend on the pitch as shown in Figure 3B. Furthermore, we measure an effective yield stress which is lower than the actual yield stress because the contact area is limited to the post tops. This is similar to an effective yield stress reported previously for flat a hydrophobic surface.33 The ratio of the effective yield stress on a nonspreading LIS to the actual yield stress is found to be lower than the same ratio for a flat hydrophobic surface (φ = 1). Interestingly, the effective yield stress on a flat hydrophobic surface depends on the weight percent of the Carbopol and it is the upper boundary for effective yield stress on nonspreading LIS (see the SI). D


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Figure 4. Flow regimes in an enclosed geometry. Flow of Carbopol in a 0.25” outer diameter, 0.16” inner diameter borosilicate glass tube. Carbopol was dyed using a water-soluble dye at a 0.2 wt % concentration. (A) Slip dominated regime on a spreading LIS. (B) Transition regime on a spreading LIS. (C) Shear dominated regime on a spreading LIS. (D) Unmodified glass tube. (E) Mobility parameter as a function of the normalized time for the cases described in panels A (black squares), B (green diamonds), and C (blue triangles). For the case described in panel D ξ = 0 for all times. See SI Movies S1, S2, S3, and S4.

larger than the yield stress, LIS will not be as efficient in reducing drag as in applications where the applied shear stress is smaller than the yield stress. For the former case, a spreading LIS can induce mobility without shear (plug flow), which is of high importance in applications where the integrity of the fluid, and more specifically its suspended media, is crucial. Furthermore, a spreading LIS can avoid smearing of the product on the substrate, which is essential to eliminate product loss, cleaning costs, and ensure flowability. Thermodynamically stable spreading LIS requires θos(w) = 0°, which severely restricts material choice. Hence, designing spreading LIS becomes challenging for many practical applications due to material constraints. Another way to eliminate pinning sites is to use an excess layer of lubricant (when film thickness atop the texture is greater than the stable vdW thickness) that submerges the texture. However, slippery properties due to excess films will only be temporary as the excess lubricant will drain due to external forces and the resulting configuration will be based on the 12 possible thermodynamic states.20 In contrast, the criterion for nonspreading LIS θos(w) < θcr where θcr can be adjusted by tuning the texture parameters allows one to expand the materials space available for mobility applications. In this case mobility is dictated by the chemistry and the solid fraction of the exposed features as they induce pinning. We demonstrate that high mobility can be attained even for nonspreading LIS by developing surfaces with minimal solid fraction, thereby opening the door to applying LIS in many practical applications. However, for this technology to be adopted in real life situations, it also needs to be durable. Drainage of the lubricant can be caused by external forces such as gravity or interfacial shear due to continuous unidirectional flow over the LIS. This can be mitigated by adjusting the texture of the LIS (see SI) or the viscosity of the lubricant.41 However, over time

and deposited on the walls of the tube decreases the length of the mobile part of the plug and increases its velocity.38 This process is shown in Figure 4E by a continuous decrease in the value of ξ until a final value of 0.14 is attained when the Carbopol ruptures. A similar decrease in ξ can be seen at the final stages of the graph following Carbopol flow in the transition regime (τwall = 2.5τy) shown in Figure 4B. On an unmodified tube Carbopol displacement is exclusively due to shear (ξ = 0) as the Carbopol deforms without slipping until it ruptures and smears on the wall as shown in Figure 4D. The parameter ξ can be used as an indicator for the extent of shearing of the yield stress fluid which can be important in many application where the integrity of the working fluid depends on the shear it undergoes.

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DISCUSSION We show that LIS can be designed to allow mobility of yield stress fluids that would otherwise be immobile under the same flow conditions. This dramatic shift is in contrast to the 16% drag reduction LIS were shown to exhibit for Newtonian fluids19 and highlights the potential of LIS for applications involving yield stress fluids. We show that a spreading LIS in which the lubricant impregnates the microtextures as well as covers them, acts as a stable Newtonian lubricating layer with an effective viscosity that depends on the viscosity of the lubricating fluid and the post height to pitch ratio. When the shear stress is lower than the yield stress, the system is in the slip dominated regime, where the yield stress fluid moves without shearing. When the shear stress is sufficiently larger than the yield stress, the apparent strain rate is mainly due to shearing of the yield stress fluid, and the drag reduction due to LIS is negligible. In the transition regime, the contribution of slip to the apparent strain rate is comparable to that of shearing of the yield stress fluid. When the applied shear stress is much E


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Agitation continued for an hour, after which a solution of 18% NaOH in water (prepared by diluting a 50% NaOH solution by SigmaAldrich) was added in order to neutralize the pH. The base solution was introduced at a weight ratio of 2.3 in a dropwise manner. Since Carbopol consists mostly of water and its surface tension was shown to be close that of water,43 we use contact angles of the lubricants measured in the presence of water as a proxy for contact angles in the presence of Carbopol. Rheology experiments were performed using a torsional rheometer (AR-G2 by TA Instruments). A cone and plate geometry (20 mm diameter, 4° cone angle) was used in all experiments with silicon samples attached to the bottom flat plate using a double sided tape. Carbopol was then placed on the silicon samples and the cone was lowered until it was 30 μm above its truncation gap. Then, any excess of Carbopol was cleaned from the perimeter of the geometry before the cone was lowered further to the truncation gap. All tests were performed at atmospheric pressure and at 25 °C, which was regulated with a Peltier plate system. All samples were presheared at 100 s−1 prior to measurement and left to equilibrate for 4 min. The tests were performed by decreasing the applied shear rates to avoid possible transient shear banding.44 LIS in the glass tube was prepared by depositing 5 cSt silicone oil on the inner surface of a 0.25” outer diameter, 0.16” inner diameter borosilicate glass tube and annealing it under 300 °C for 5 min. This leads to the formation of a thin silicone layer on the surface which is then impregnated by dipping the tube in a 100 cSt silicone oil.26 The constant pressure set up consists of a syringe pump connected to a pressure transducer and a signal amplifier (PHD ULTRA syringe pump with an APT300 pressure transducer and a TAM-D amplifier, all by Harvard Apparatus). The behavior of the Carbopol was recorded with an optical camera (D800 with a 70−180 mm lens, both by Nikon).

under shear lubricant drainage is inevitable. In the case of spreading LIS drainage will first occur from in between the textures until a thin vdW film whose thickness is set by the disjoining pressure conformally covers them. This vdW film cannot be sheared of the surface easily, but the working fluid can still invade the textures without directly touching the solid surface and increase the effective viscosity. In the case of nonspreading LIS, the impregnated lubricant is stabilized by the texture under the condition that the critical angle θcr is larger than contact angles θos(a) and θos(w). When the lubricant drains the critical angle decreases, and when this criteria is no longer met the lubricant will completely drain from the surface. Hence, in order for the design of both spreading and nonspreading LIS to be robust, the use of LIS in practical applications should be coupled with implementation of approaches for lubricant replenishment.42

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MATERIALS AND METHODS

The textured silicon substrates used in this study were prepared by a standard photolithography process. The resulting microposts had a square geometry with width a = 10 μm, height h = 12 μm, and varying pitches b = 5, 10, 25, and 50 μm. The vanishingly small solid fraction surfaces were prepared using a 1064 nm Nd:YAG laser (TYMKA Electrox) which was used to ablate a flat silicon surface in a controlled pattern. The resulting texture consists of closely packed and reproducible pyramidal features spaced approximately 50 μm apart and 50 μm deep that are covered with submicrometer features. The samples were then cleaned in an oxygen plasma chamber (PDC-32G2 by Harrick Plasma) at 200 mTorr for 20 min and then treated with a low-energy silane Octadecyltrichlorosilane (denoted here as OTS, advancing and receding contact angle of water on a flat surface in the presence of air are θws(a),adv = 109.4° ± 0.5 θws(a),rec = 100.1° ± 1.1), or Perfluorooctyltrichlorosilane (denoted here as FS, θws(a),adv = 112.4° ± 0.7 and θws(a),rec = 93.4° ± 3.3, respectively). Both were purchased from Sigma-Aldrich and used without modification. To create a stable layer of lubricant the samples were lowered perpendicularly into a bath of silicone oil using a controlled dip coater (Multi Vessel Small by KSV Nima) at a speed of 10 mm/min to prevent entrapment of air bubbles on the surface. To avoid entraining excess films and ensure a thermodynamically stable impregnation, the sample was withdrawn at a speed such that the critical capillary number Cacr = μVcr/γ = 10−4 is attained,40 where μ is the viscosity of the lubricant (500 cP), γ is its surface tension (20 mN/m), and Vcr is the resulting critical withdrawal speed, 0.24 mm/min. Thus, to prevent an excess film, the samples were withdrawn at 0.20 mm/min. Surfaces used in panels A and B of Figure 1 were prepared by placing a 1” wide PTFE pipe thread sealant tape on a standard 1” wide glass slide. Contact angles of silicone oil were measured on the FS-coated silicon surfaces in the presence of air and deionized (DI) water using a Contact Angle Goniometer (model 500 by ramé-hart, Succasunna, NJ). The advancing and receding angles were taken as an average of at least three measurement on different location on the surface. The advancing angle was measured by adding silicone oil to a 5 μL oil droplet at a rate of 4.2 nL/s while measuring the diameter of the triple contact line. When the diameter started to increase, the measured contact angle was taken as the advancing contact angle. Similarly for the receding contact angle, oil was extracted from the droplet at a rate of 6.7 nL/s and the receding contact angle was taken as the contact angle when the triple contact diameter has started to decrease. The measured contact angles are reported in SI Table S1. The contact angles of silicone oil on OTS coated silicon surface are reported elsewhere20 and have also been included in SI Table S1 for completeness. Carbopol was prepared by slowly adding cross-linked poly(acrylic acid) polymer (Carbopol 940 by Lubrizol) into DI water that was agitated at a rate of 800 rpm by a mixing impeller (Cole-Parmer Compact Digital Mixer System, 50 to 2500 rpm by Cole Parmer). Before adding the dry polymer, any lumps were broken apart.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.8b21478. Additional information as noted in the text (PDF) Movie S1 (AVI) Movie S2 (AVI) Movie S3 (AVI) Movie S4 (AVI)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Leonid Rapoport: 0000-0002-9143-6226 Brian R. Solomon: 0000-0002-4723-6585 Kripa K. Varanasi: 0000-0002-6846-152X Author Contributions

L.R., B.R.S., and K.K.V. designed the research. L.R., and B.R.S. performed the research. L.R., B.R.S., and K.K.V. analyzed the data and wrote the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. G. H. McKinley for use of the AR-G2 Rheometer (TA Instruments), Prof. T. Buonassisi for use of the laser marking system (TYMKA Electrox), and V. Jayaprakash for use of the constant pressure set up (Harvard Apparatus). This work was supported by the Joint Center for Energy Storage Research, an Energy Innovation Hub funded F


Research Article


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by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. B.R.S. acknowledges financial support from the Martin Family Society of Fellows for Sustainability.

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Mobility of Yield Stress Fluids on Lubricant-Impregnated Surfaces

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