ARTICLE pubs.acs.org/Langmuir
Smart Design of Stripe-Patterned Gradient Surfaces to Control Droplet Motion O. Bliznyuk, H. Patrick Jansen, E. Stefan Kooij,* Harold J. W. Zandvliet, and Bene Poelsema Physics of Interfaces and Nanomaterials, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands ABSTRACT: The motion of droplets under the influence of lithographically created anisotropic chemically defined patterns is described and discussed. The patterns employed in our experiments consist of stripes of alternating wettability: hydrophobic stripes are created via fluorinated self-assembled monolayers, and for hydrophilic stripes, the SiO2 substrate is used. The energy gradient required to induce the motion of the droplets is created by varying the relative widths of the stripes in such a way that the fraction of the hydrophilic area increases. The anisotropic patterns create a preferential direction for liquid spreading parallel to the stripes and confine motion to the perpendicular direction, giving rise to markedly higher velocities as compared to nonstructured surface energy gradients. Consequently, the influence of the distinct pattern features on the overall motion as well as suggestions for design improvements from an application point of view are discussed.
’ INTRODUCTION Liquid motion on solid surfaces without any externally applied force was observed a long time ago: the “tears” of wine have been used for centuries to judge its quality.1 Nevertheless, it was not before the second half of the 19th century that the variation of the liquidvapor surface energy γlv was identified as the driving force for wine rising on the glass wall: Marangoni flows.2,3 Other examples of droplet motion resulting from Marangoni forces include thermal gradient surfaces,47 the surface tension being temperature-dependent, forcing droplets to colder areas, and also surfactant-induced motion811 in which γlv gradients arise from varying concentration of molecules at the liquid surface. The first models to predict droplet velocities were reported at the end of the previous century.12,13 Nevertheless, many questions concerning Marangoni flows are still to be elucidated.1417 Using a surface tension gradient of the solid surface γsv to induce motion avoids Marangoni flows within the droplet.18,19 A surface energy gradient as schematically shown in Figure 1 is typically achieved by controlled chemical modifications of the substrate.20,21 Alternatively, Zhu et al.22 reported the movement of a droplet on surfaces with a well-defined roughness gradient. The γsv increases in a specific direction, changing from hydrophobic (γsv1) to hydrophilic (γsv2). Owing to the different surface energy probed, the difference in dynamic contact angles (CAs) will induce movement in the direction of increasing γsv.2327 Experimental motion studies reveal the velocities to depend linearly on the radius of the wetted area; moreover, the droplet will move to the hydrophilic region only when the radius is above a certain critical value.2830 By summarizing existing descriptions for droplet motion on gradient wettability surfaces, the droplet velocity is generally determined by the balance of driving capillary and opposing r 2011 American Chemical Society
viscous forces.13,23,29,31 Confusingly, in the literature the energy and force are often intermixed,13,23 giving rise to erroneous expressions. For a ribbon of length l in the y direction, the driving force F = (dU)/(dx) for motion in the x directions is the unbalanced Young force F originating from different surface tensions on both sides of the droplet. The energy dU per unit length l is given by13 dU ¼ ½ðγsl γsv ÞB ðγsl γsv ÞA dx
ð1Þ
This corresponds to a driving force (again, per unit length l) of F ¼
dU ¼ ðγsv γsl ÞB ðγsv γsl ÞA dx
ð2Þ
The contact line at points A and B probes two different surface energies (γsv)B > (γsv)A and consequently adopts different contact angles θB < θA. These local dynamic contact angles can be used to rewrite eq 2: F ¼ γlv ðcos θB cos θA Þ
ð3Þ
Ideally, as soon as θB < θA, the ribbon experiences a driving force and will start to move in the direction of the higher γsv2. For a droplet in the shape of a spherical cap, the driving force FY can be represented by29 d cos θ 2 FY ¼ πR γlv ð4Þ dx Received: May 5, 2011 Revised: July 14, 2011 Published: July 25, 2011 11238
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Figure 1. Schematic representation of a sessile droplet on a wettability gradient changing from hydrophobic (low γsv1) to hydrophilic (high γsv2) (i.e., γsv2 > γsv1). The droplet will move in the direction of high γsv2 with a speed V.
where R is the radius of the base of the droplet and θ is the position-dependent contact angle of the liquid droplet. The motion of the droplet is hindered by viscous drag, also referred to as the friction force Fη. Using the lubrication approximation and assuming a circular shape of the wetted area (with radius R), it is given by13,29,32 Z xmax dx ð5Þ Fη ¼ 3ηπRV xmin ξðxÞ where η is the viscosity of the liquid, V is the droplet velocity, and ξ(x) is the height of the droplet, which depends on position x. Integration limits xmin and xmax are two cutoff lengths,29,32 the first being of molecular dimensions and the second being on the order of R. If only these two forces are considered, then the estimated viscous drag is orders of magnitude smaller than the driving force.33 As such, droplets are expected to move on all surfaces as soon as the CAs on both sides are different. Nevertheless, the experimental results reveal that in many cases droplets remain immobile despite the CA difference. This explanation is provided by the oversimplified initial model in which surfaces without hysteresis are considered. In general, surfaces exhibit hysteresis and as such provide an additional energy barrier for droplet motion.23,29,34 The effect of hysteresis can be estimated by the force acting on a thin strip of liquid parallel to the translation direction, with a thickness dy, and by integrating the force over the entire periphery of the droplet footprint: Z ð6Þ Fhys ¼ γlv ðcos θAd,B cos θRe, A Þ dy Here, θAd,B and θRe,A are the advancing and receding contact angles on the opposite ends of the thin strip.29 The aforementioned approach holds for free-standing droplets. However, in experimental situations, droplets are either (i) gently deposited while remaining attached to a dispensing unit23,25,27 or (ii) dropped from finite heights.35 In the latter case, the impact event itself should also be considered because it introduces kinetic energy into the system, which interferes with droplet motion. However, during controlled gentle deposition liquid surface interactions govern the motion of the droplet. Nevertheless, in the initial stages of motion the surface energy gradient induces a force on the droplet while it remains attached to the needle. The capillary force gives rise to an additional force that has to be taken into account. In many articles, this influence is overlooked and droplets are generally considered to be freestanding. In this article, we present a detailed investigation into the motion of droplets on chemically patterned surfaces. The droplets are gently deposited on a well-defined pattern, with a driving force being generated by a macroscopic wettability gradient.
Figure 2. Example of the gradient pattern design on a silicon wafer. Hydrophobic regions (blue) are created by PFDTS SAMs, and bare SiO2 (white) comprises the hydrophilic areas. The dark-blue circle depicts the droplet (2 μL) contact area during the initial spreading regime. Point x0 defines the center of the wetted area (i.e., where the droplet contacts the surface). The distance d between the point of contact and the border of the first patterned area is determined during the analysis of the movies. Below the respective patterns, the absolute widths of the stripes are indicated (in micrometers). This particular pattern is used for the experimental data presented in the side- and topview movies in the next section.
In fact, our patterns consist of regions with distinct wettability with sharp discontinuities between neighboring regions. As such, our experiments are similar to those described by Ondarc-uhu and Veyssie.36 In their work, they characterize the displacement of a liquid ribbon across a chemically defined discontinuity in the surface wettability. The results are analyzed in terms of the theoretical work described by Rapha€el.37 In this article, we describe the overall motion of droplets under the influence of the surface energy gradient. The different regimes in the droplet motion are identified and discussed. Finally, modifications of pattern designs to attain the desired droplet motion are discussed, with a view toward possible applications.
’ EXPERIMENTAL DETAILS Chemically Created Pattern. The surface patterns of selfassembled monolayers (SAMs) of 1H,1H,2H,2H-perfluorodecyltrichlorosilane (PFDTS, 97%, ABCR, Germany) on silicon wafers are created using standard clean room facilities. First, a positive photoresist is spin coated onto freshly cleaned wafers with a natural oxide film, followed by soft baking. Patterns are created via standard optical lithography, after which the exposed photoresist is washed off. The remaining photoresist is hard baked and will provide surface protection during the vapor deposition of PFDTS. The assembly creates a densely packed layer of molecules with a height on the order of 1 nm. Vapor deposition is done in a degassed chamber that is successively exposed to PFDTS and water reservoirs to introduce the respective vapors, initiating the reaction on the wafer surface.38 After SAM formation, the photoresist is washed off, leaving a chemically patterned surface. A typical layout of the patterns used in our experiments is shown in Figure 2. The droplet is deposited on the rectangular area of unpatterned PFDTS having a width of 2 mm (the footprint diameter of a 2 μL droplet amounts to 1.55 mm). On the right of the PFDTS rectangle, three patterns (respectively referred to as patterns I, II, and III) consisting of alternating hydrophobic (PFDTS) and hydrophilic (bare SiO2) stripes 11239
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Figure 4. The motion of a 2 μL glycerol/water droplet on a pattern with subsequent R values of 0.9, 0.5, and 0.3. (a) The suspended droplet (r = 0.78 mm) is brought into contact with the surface. (b) While spreading over the PFDTS rectangle, the droplet encounters pattern I. (c) The droplet is in contact with patterns I and II, (d) followed by the bridging of patterns I, II, and III. (e) The advancing side spreads on the unpatterned SiO2, giving rise to isotropic radial spreading. (f) Most of the droplet volume is now on SiO2; only pattern III remains covered by liquid. (g) Receding of the droplet from pattern III (h) to leave the patterned area and (i) finally come to a halt on SiO2. Figure 3. Snapshots taken from high-speed camera movies showing the side view of droplet motion (d = 0.36 mm). (a) The values for dynamic CAs on the advancing (right; θR) side and receding (left; θL) side during different regimes are presented. Vertical dashed lines indicate the borders between patterns, as introduced in Figure 2a. The droplet has a symmetrical shape. (b) The droplet at the end of the first regime: the shape is asymmetrical (ΔCA ≈ 9°) because of spreading of the right side over pattern I. (c) The droplet preferentially spreads over pattern I. (d) The end of the second regime when the “neck” breaks; the asymmetry of the liquidair interface is obvious. (e) The droplet during enhanced translation after breaking of the neck. (f) The droplet at the end of the third regime, covering all three striped patterns. are placed. The length of the individual striped patterns is either 1000 or 700 μm. The striped patterns give rise to anisotropic wetting properties in orthogonal directions, favoring the motion of the contact line parallel to the stripes but hindering it in the perpendicular direction.3941 The droplet translation is induced by the higher surface energies of the subsequent patterns, owing to an increasing fraction of the hydrophilic area. To quantify the relative hydrophobicity of the patterns, we introduced a dimensionless parameter R wPFDTS ð7Þ R¼ wSiO2 where wPFDTS and wSiO2 are the hydrophobic and hydrophilic stripe widths, respectively.39,40 Smaller R values imply a higher surface energy (i.e., a larger hydrophilicity of the patterns). All R values employed in our experiments are between 0.9 and 0.125 in different combinations. However, because the goal of this work is to present a general description of the motion over such anisotropic surfaces, we do not specifically discriminate between all different combinations of R in the presentation of the data. Droplet Deposition. Droplet deposition and characterization, including measurements of CAs, are done using an OCA 15+ goniometer (DataPhysics, Germany). The equipment enables the determination of CAs with an accuracy of 0.5°. Droplets are created using a computer-controlled syringe. For the experiments in this paper, we use a 60/40 vol % mixture of glycerol (ReagentPlus, Sigma, USA) and water (Millipore Simplicity 185 system). The mixture has a surface tension comparable to that of water, and the viscosity is approximately 10 times higher than that of water. For all droplets, the volume is fixed at 2 μL.
Droplet deposition is achieved by very slowly lowering the syringe with the suspended droplet until it contacts the patterned surface. From highspeed camera movies, the velocity of approach is determined. It is less than 5 mm/s to minimize the contribution of kinetic energy during the first stage of spreading. The time evolution of droplet shape and position is determined from side-view movies taken using a Photron SA3 highspeed camera, which is operated by Photron Fastcam Viewer 3 software. The frame rate is chosen such that it enables recording of the droplet motion over the entire pattern, typically 2000 fps for most of the acquired data. Movies are analyzed using a home-built Matlab program. A typical set of snapshots pertaining to the various regimes of motion as described in the following section are presented in Figure 3. Additionally, a standard CCD camera is mounted above the substrate to assess the motion of the droplets. The movies from the top-view camera are taken simultaneously with the side-view movies, therewith enabling a better visualization of the motion process.
’ RESULTS In Figure 4, top-view images of the motion of a droplet over the patterned surfaces provide a general overview. The droplet is brought into contact with the surface on the unpatterned PFDTS area (Figure 4a) and encounters pattern I before the static shape on the PFDTS is reached. Pattern I has a higher overall surface energy because of the presence of hydrophilic SiO2 stripes, inducing a preferential direction of spreading and inducing asymmetry in the droplet footprint (Figure 4b). Moreover, the contact line in the first striped pattern (pattern I) is distorted from a circular shape. In Figure 4c, the droplet has detached from the needle and has moved completely off of the unpatterned PFDTS rectangle onto patterns I and II. The droplet adopts an approximately cylindrical shape with two spherical caps, similar to those observed for static shapes on anisotropically patterned substrates.39,42 The macroscopic surface energy of the striped patterns increases for decreasing R, therewith inducing the motion of the liquid in the positive x direction. However, the droplet appears to be confined in the y direction by the energy barrier created by the PFDTS stripes. In Figure 4d, the advancing side of the droplet has crossed pattern III and starts to spread on the unpatterned SiO2. 11240
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Figure 5. (a) Evolution of the left (receding, red solid line) and right (advancing, blue solid line) edges as a function of time; the center position (black line) is the average of both edges. The middle of the syringe is taken as the zero position on the surface; x0 is uniquely defined for each experiment. A consequence of the side view is that spreading over the first 200 μm droplet size cannot be visualized.40,43 Horizontal dashed lines indicate borders between the chemically defined patterns, as indicated on the right. Patterns I, II, and III correspond to R = 0.9, 0.5, and 0.3, respectively. The vertical lines indicate transitions between the motion regimes (second, third, and fourth) as discussed in the text. (b) Time evolution of the droplet length in the x direction for the same pattern.
Simultaneously, the receding motion over pattern I starts. The image in Figure 4e reveals that this radial spreading on SiO2 affects the cylindrical shape. The droplet becomes wider in the y direction by partially wetting adjacent stripes on pattern III. The droplet seems to attempt to minimize its energy by adopting an approximately elliptical shape. Eventually, the droplet slowly recedes from pattern III (Figure 4h) and adopts a shape close to spherical. In the last images, the effect of impurities on SiO2 on the pinning of the contact line is clearly observed. In Figure 4ei, a thin residual layer of liquid can clearly be discerned, which remains after the droplet has passed. Zooming in on the trace reveals that only the hydrophilic SiO2 stripes are covered with continuous liquid stripes whereas hydrophobic PFDTS stripes remain liquid-free. However, occasionally small liquid bridges covering several adjacent stripes are formed. A quantitative study of the liquid traces remaining after droplet passage and their influence on the receding motion is not possible in the present experimental setup and will be the subject of future work. Nevertheless, the macroscopic overview of the liquid trace (Figure 4) can give us preliminary information concerning the contact line motion in the direction perpendicular to the stripes. More precisely, the size of the droplet in the direction perpendicular to the stripes (i.e., the width) can be estimated and compared for different patterns. The preliminary results reveal that the width values scatter around 1.7 ( 0.2 mm for all experimentally studied individual pattern lengths and combinations of R values. This is in agreement with previously reported results for static and kinetic droplet behavior on stripe patterns,39,40 where we found that the width of the droplet is solely defined by the hydrophobic part of the pattern and therefore exhibits similar values for all patterns. Indeed, the diameter on unpatterned PFDTS amounts to 1.55 mm for the droplet volumes considered in this work, which is within the experimental error of the data extracted from top-view movies. In the following text, a quantitative description of the droplet motion using a high-speed camera in a side-view geometry is given. Investigations are carried out only for the x direction. A typical transient obtained using the high-speed camera movies (Figure 3) is shown in Figure 5. The evolution of the right (advancing) and left (receding) edges of the droplet is presented
along with the overall length of the contact area in the x direction (i.e., parallel to the striped pattern). For clarity in the description, we distinguish four regimes in the droplet motion, as indicated by the vertical dotted lines in Figure 5. Only the second, third, and fourth regimes can be observed; the apparent absence of the first regime is due to its short duration. Furthermore, only the first three regimes will be addressed in detail; the fourth regime corresponding to isotropic spreading over the unpatterned SiO2 (Figure 4ei) will not be considered here. As described in the Experimental Details section, chemically defined patterns consist of PFDTS monolayers (transparent, approximately 0.7 nm thickness), which cannot be observed by the naked eye. Experimentally, this results in scatter in deposition position x0 for different experiments on a scale smaller than 1 mm. To enable a comparison of the results obtained in different experiments, the time is set to 0 s when the right side of the droplet crosses the border between the PFDTS rectangle and pattern I. Typically, this event occurs a few milliseconds after the droplet comes into contact with the surface. It turns out that initial position x0 is highly relevant to the subsequent spreading kinetics. The distance d is defined as the difference between x0 and the border of pattern I (see also Figure 2). Experimental values of d vary from 0.2 mm up to approximately 0.7 mm. First Regime. The first regime corresponds to the fast initial spreading of the droplet on a time scale (Δt1) from 6 to 10 ms. This stage of spreading is generally referred to as the inertial regime.40,43,44 The inertial regime starts when the droplet comes into contact with the substrate surface and ends when the radius of the wetted area reaches 90% (0.7 mm) of the radius of the droplet suspended to the needle prior to deposition (0.78 mm). The power law behavior of spreading and the involved timescales are consistent with previously published work. More importantly, no net translational motion is observed in the first regime. The liquid center of mass remains on the symmetry axis defined by the middle of the needle. During the inertial regime, the right side of the droplet advances over two distinct regions on the surface: (i) the hydrophobic PFDTS rectangle and (ii) pattern I consisting of alternating 11241
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Figure 6. Results are extracted from all studied patterns with different individual stripe-pattern lengths and various combinations of R values. Each color refers to a set of patterns having the same pattern I, II, and III lengths and R combination but different PFDTS and SiO2 stripe widths. Scaling of the data suggests that the absolute width of the stripes is not a relevant parameter for the description of motion. (a) Dynamic CAs at the moment the right side of the droplets reaches the border of pattern I plotted as a function of d. (The solid line is a guide to the eye.) The CA values on both sides of the droplets are equal because of the symmetric circular shape of the wetted area. (b) Dynamic CAs on the left side, plotted as a function of those on the right side of the droplet, at the end of the first regime. The solid line represents the situation for symmetric droplets (i.e., identical CAs on both sides of the droplet).
Figure 7. Length of the droplet footprint in the x direction (i.e., parallel to the stripes) at the moment of release from the needle as a function of d. The solid line is a guide to the eye.
hydrophilic SiO2 and hydrophobic PFDTS stripes. As mentioned above, d is between 0.2 and 0.7 mm, which implies that the extent of spreading on the respective regions varies between experiments. To study the effect of spreading over two distinct surface areas, dynamic CAs are shown in Figure 6. The values measured when the right edge of the droplet is at the border of the PFDTS rectangle are shown in Figure 6a as a function of the position where the droplet is deposited. Note that up to this point the droplet is symmetric and CAs on both sides of the droplet are the same. When reaching the border of the first pattern, the values scatter around a straight line as shown in Figure 6a. The decrease in the CA values from 145 to 110° with increasing d values is in agreement with expectations. For larger distances d, the spreading over the pure PFDTS area is more extensive. Lower contact angles are attained before the wetted area reaches the chemically defined border of the first pattern. The relatively large spread in data points in Figure 6a can be rationalized by considering that different symbols pertain to different experiments on a range of wafers, performed over an extended period of time, typically a few months. Although the reproducibility of the PFDTS coating on the wafers is good, often
slight variations within a few degrees in the equilibrium CA are observed. Also, the data in Figure 6 pertain to a wide range of patterns with varying R values. These also give rise to slight variations of the observed contact angles. Finally, the contact angles can be determined only within the accuracy as defined by the pixel dimensions in the images. This also introduces a slight scatter of the data points. In Figure 6b, the relation between CAs on both sides of the droplet at the end of the first (i.e., the inertial) regime is plotted. For completely symmetric droplets, the contact angles would be identical and would correspond to the solid line in Figure 6b. However, the dynamic CA values exhibit a difference of 9° between the right (pattern I) and left sides (PFDTS rectangle) of the droplet. The systematically lower dynamic CA values for the right side suggest that the footprint of the droplet becomes asymmetric in the inertial stage. Second Regime. Liquidsurface interactions take over and control the motion of the contact line in subsequent regimes. We designate the regime between the end of the inertial spreading and the moment at which the neck connecting the droplet to the needle breaks as the second regime. In this second regime, the left side of the droplet no longer advances in the negative x direction and will start moving in the opposite, positive x direction: from here on, we address the left side as receding (Figure 5). The right side continues to move over pattern I, and as such, it is referred to as the advancing side of the droplet. Overall, the center of mass of the droplet slowly shifts in the positive x direction: translational motion starts. From Figure 5, it is observed that the advancing motion over pattern I is faster as compared to the receding edge over the PFDTS, resulting in the elongation of the droplet in the direction parallel to the stripes. The duration Δt2 of the second regime typically varies from 50 to 200 ms, increasing as a function of d. To determine what triggers the release from the needle, the diameter of the footprint in the x direction (referred to as the length of the droplet) at the moment of release is plotted as a function of distance d in Figure 7. It appears that experimental length values at the moment the neck breaks scatter around a mean value of 2.05 mm for all patterns studied. The reasons for the scatter in the data are similar to those described for Figure 6 in the previous section. 11242
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Langmuir Apparently, attaining a specific length value is an essential parameter and triggers the release. This is consistent with the aforementioned increase in Δt2 as a function of d. The length of 2.05 mm cannot be achieved on pure PFDTS (static diameter of 1.55 mm), which requires that in most cases a significant part of the droplet volume shifts to pattern I. When the droplet is deposited further away from the border of pattern I, a larger part of the volume is on the unpatterned PFDTS and needs to be moved to achieve the required length, resulting in durations of the second regime of up to 200 ms. Third Regime. The third regime starts when the liquid neck connecting the droplet to the needle is broken and ends once the advancing side of the droplet reaches the border between pattern III and the unpatterned SiO2. During the third regime, the receding edge completely dewets the unpatterned PFDTS area and becomes pinned at the border of pattern I. As a result, the droplet is stretched over all three striped patterns, exhibiting a shape resembling a cylinder with two hemispherical caps (Figure 4c,d). The duration of the third regime varies between 300 and 700 ms (Δt3). Immediately after the release event, an increase in the speed of both the advancing and receding contact lines for a relatively short timescale is observed in Figure 5. The enhanced motion is more pronounced for the advancing side. It is difficult to conclude whether the release event induces spreading perpendicular to the stripes. To check whether the influence of the deposition position x0 is still detectable, average speeds for the advancing contact line over the whole length of pattern III are calculated from the time differences between the moment at which the advancing contact line reaches the border of pattern III and the moment it starts spreading over the SiO2. Dividing by the length of pattern III yields average speeds, which are approximately equal to 4 mm/s for all studied patterns. This confirms that in this stage of motion, there is no longer any influence of the deposition position.
’ DISCUSSION Capillary Spreading over Striped Patterns: Second and Third Regimes. The reason to separate the translational motion
over the patterned surface into two regimes is motivated by the fact that (i) during the second regime the droplet moves while still attached to the needle, experiencing an additional force that opposes the motion and (ii) to investigate the influence of the release event on the nonrestricted motion in the third regime. In Figure 3, the side-view snapshots taken from high-speed camera movies depict the droplet motion during the first three regimes. More specifically, the images in Figure 3bd can be used to illustrate the influence of the connection with the needle on the translational motion during the second regime. The droplet is in the capillary regime (i.e., liquidsurface interactions drive the motion of the droplet (eq 4), whereas viscous drag (eq 5) and hysteresis (eq 6) forces restrict the motion). A first estimate of the initial velocity can be obtained by neglecting hysteresis. In that case, the driving force is compensated for by the viscous force. By equating FY and Fη (eqs 4 and 5) and considering the approximation of a circular footprint of the droplet in the integration of eq 5,29 an expression for the initial steady-state velocity of the droplet follows γR sin θ d cos θ V ¼ ð8Þ 3η lnðxmax =xmin Þ dx
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Considering that the integration limits in eq 5 may be approximated by xmax ≈ 0.78 mm and xmin ≈ 109m, respectively, corresponding to the droplet radius and the molecular (nanometer) scale, we obtain ln(xmax/xmin) = 13.5, in good agreement with previous reports.13,32,36 For the surface tension of our water/glycerol mixture, we assume γ ≈ 70 mN/m; the viscosity of the mixture is about 10 times that of pure water, amounting to η ≈ 10ηwater = 102 Pa 3 s. For the radius of the droplet footprint, we take R = 0.7 mm. In the derivations leading to eq 8, a constant gradient of d cos θ/dx was considered. However, in our case we are dealing with a chemically defined discontinuity gradient similar to that described by Ondarc-uhu and Veyssie.36 A rough estimate follows by inserting Δ cos θ/Δx, where Δ cos θ is given by the different contact angles on both sides of the droplet (θPFDTS = 105° and θR=0.9 = 70°, respectively) and Δx = 2R is the spatial extent of the droplet. Inserting these numbers into eq 8 yields an estimated velocity of V = 52 mm/s. Comparing this value to the results shown in Figure 5 reveals that such high velocities are never attained in our experiments. The maximum velocity occurs at the start of regime II and amounts to 14.6 mm/s. Obviously, the effect of hysteresis has to be considered, as well as the fact that all equations were derived by considering a spherical droplet shape. The latter is clearly not the case (Figure 4). Moreover, we also have to consider the contribution arising from the connection of the droplet to the needle. When the center of mass of the droplet starts to move away from the symmetry axis of the needle, an additional liquidair interface area is created near the neck connecting the droplet to the needle (Figure 3c). The creation and subsequent increase in the additional liquidair surface while the droplet moves away from the needle costs energy. This in turns gives rise to an overall slowing down of the droplet motion. The substantial cost in energy for the creation of this additional surface manifests itself in enhancing the velocities of both advancing and receding contact lines after the connection with the needle is ruptured (Figure 3d and Figure 5). The velocity enhancement can be qualitatively explained by considering the neck, which connects the droplet volume to the liquid reservoir within the needle as a constrained spring. Once the spring is released (i.e., the neck breaks), the potential energy is released.44 Subsequently, the potential energy is converted into kinetic energy, leading to a rapid increase in the elongation of up to 25% of the value observed over the entire third regime approximately 6% of the time. More specifically, as shown in Figure 5, the droplet gains an additional 0.25 mm in length in 25 ms. Once the velocity peak has passed, the droplet motion is controlled by the balance of three forces, resulting in an overall decline in the measured velocities to a few mm/s, in agreement with other publications.23,24,29 Smart Design. The use of anisotropic striped patterns enables the creation of droplets with static shapes that are markedly different from spherical and defines a preferential direction for spreading.3941,45 Because of the confinement of the contact line motion in a direction perpendicular to the stripes, advancing motion parallel to the stripes is facilitated. Consequently, higher velocities of the contact line as compared to isotropic droplet spreading are usually observed. Furthermore, in the direction parallel to the stripes the static CAs are reasonably well predicted by the CassieBaxter equation,39 rewritten in terms of dimensionless parameter 11243
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Figure 8. The time span for the advancing edge of the droplet to wet all three striped patterns is presented as a function of d. The results pertain to the patterns with the same values for R but with different pattern lengths. The duration is obtained from the time difference between the moment at which the advancing edge reaches pattern I and the moment it reaches the border of the unpatterned SiO2. Results are shown for individual pattern lengths of (a) 700 μm (overall length of 2100 μm) and (b) 1000 μm (overall striped pattern length of 3000 μm).
R (eq 7) )
θ ¼ arccos
R cosðθPFDTS Þ þ cosðθSiO2 Þ 1 þ R
ð9Þ
where θPFDTS and θSiO2 represent the CAs on homogeneous PFDTS SAMs (105°) and on SiO2 (23°), respectively. From this equation, it follows that for the pattern design considered in the previous section with R values of 0.9, 0.5 and 0.3 corresponding static CAs are 68.8, 61.4, and 49.5°, respectively. The experimental dynamic CAs have been presented in Figure 3. During the capillary stage (i.e., the second, third, and forth regimes), the advancing CAs exhibit smaller values as compared to the receding ones. Also, the difference between CAs on both sides of the droplet is less than 10°. Furthermore, by comparing the experimental dynamic advancing CAs with the calculated static values ((eq 9), we find that the advancing CAs at the end of each pattern are at least 10° higher. On the basis of earlier studies reported in literature, in the case of chemically heterogeneous surfaces composed of two different chemical entities the advancing CA is defined by the more hydrophobic species whereas the receding CA is governed by the more hydrophilic one.46 For the unpatterned PFDTS SAMs, the value of the advancing angle is approximately 5° greater than the static value. We assume that this difference also holds for the stripe-patterned surfaces. On the basis of this, taking into account that our experimental results for advancing CAs show values that are more than 10° higher than the static CAs, the length of the striped patterns can be increased. Indeed, preliminary results on patterns with a length of up to 1500 μm (overall length of 4500 μm) have shown droplets moving over the entire design and being left on the unpatterned oxide surface. As expected, changing the length of the patterned areas has immediate consequences for the droplet velocity during its motion. To illustrate this influence, in Figure 8 we plot the time it takes the advancing edge of the droplet to move over the three striped patterns; patterns with the same combination of R values but different lengths are considered. First, the difference in timescales is surprising; the ratio of length scales does not correspond one-to-one to the time ratios. In the case of pattern lengths of 700 μm (i.e., the total length of the striped pattern amounts to 2100 μm), the overall time it takes the advancing droplet edge to wet all three patterns varies from 0.12 to 0.3 s (Figure 8a),
yielding average velocities typically above 10 mm/s. For patterns of length 1000 μm (total striped pattern length of 3000 μm), variations from 0.3 to 1 s (velocities below 9 mm/s) are observed, and there is considerably more scatter in the data (Figure 8b). As is to be expected, the time increases as a function of d for both pattern designs. To identify a more obvious trend and enable a quantitative discussion of pattern dimensions and droplet velocities, additional experiments covering a wider range of pattern lengths need to be performed. Another factor that influences the overall velocity of the droplet motion over the patterns is ΔR (i.e., the difference in macroscopic wettability among patterns I, II, and III). In agreement with intuitive expectation for larger differences in R, the droplet will wet and dewet the patterned surface more rapidly. During the experimental work presented here, for pattern I only values of R < 1 have been used, exhibiting static CAs below 68.8°. This in turn limits the possible combinations for velocity enhancements because successive R values must decrease. However, on the basis of observations of experimental dynamic CAs on the first pattern, CA value θSt = 75° is sufficient to initiate motion on this pattern. This indicates that the R value of the first pattern can be as high as 1.3, therewith enabling the use of a wider range of possible combinations. The lower limit of R is imposed by the fact that for the last pattern (pattern III) it is required that R > 0.2 to enable the droplet to dewet this pattern. Experimental results on designs with pattern III having R < 0.2 reveal that in most cases the receding motion of the droplet is inhibited; average velocities of typically well below 1 mm/s were observed. Another reason in favor of using higher R values is the consequent increase in receding contact angles over patterns. For all experimental sets, the receding motion over pattern I starts only when the advancing droplet edge initiates spreading on the SiO2, implying that the droplet first wets all three patterns. Employing higher R values may allow the dewetting of pattern I in an earlier stage of motion, resulting in shorter residence times or enabling the use of markedly longer overall pattern lengths.
’ CONCLUSIONS We present a detailed experimental study of glycerol/water mixture droplets over chemically defined linear-stripe-patterned surfaces. Droplets are gently deposited, after which their motion 11244
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Langmuir induced by a surface energy gradient is investigated. The motion of droplets over distances larger than 3 mm on a time scale of seconds is observed. To enable a clear description and allow adequate discussion, the motion process is separated into four regimes; the first three are discussed in detail. Using patterns consisting of alternating hydrophobic (PFDTS) and hydrophilic (SiO2) stripes gives rise to the confinement of motion in the direction parallel to the stripes, therewith enabling the transport of liquid in a controlled way. Moreover, a precisely defined pattern design on the surface allows a quantitative estimate of the macroscopic surface energy at any position during movement. This makes it possible ultimately to refine pattern designs for application purposes. Furthermore, the dependence of droplet velocities on the length and relative hydrophobicity of the patterns is discussed. Finally, chemically defined striped patterns seem to be a promising choice from an application point of view, owing to the combination of anisotropic spreading with enhanced contact line motion in the predefined direction as well as easily tunable surface energies.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: +31 (0)53 489 3148. Fax: +31 (0)53 489 1101.
’ ACKNOWLEDGMENT We thank Gor Manukyan (Physics of Complex Fluids, University of Twente) for hydrophobizing the substrate and James Seddon (Physics of Fluids, University of Twente) for helpful discussions. We gratefully acknowledge the support by MicroNed, a consortium to nurture microsystems technology in The Netherlands. ’ REFERENCES (1) Scriven, L. E.; Sternling, C. V. Nature 1960, 187, 186–188. (2) Thomson, J. Philos. Mag. 1855, 10, 330–333. (3) Marangoni, C. Ann. Phys. 1871, 219, 337–354. (4) Darhuber, A. A.; Valentino, J. P.; Troian, S. M.; Wagner, S. J. Microelectromech. Syst. 2003, 12, 873–879. (5) Tseng, Y. T.; Tseng, F. G.; Chen, Y. F.; Cheng, C. C. Sens. Actuators, A 2004, 114, 292–301. (6) Pratap, V.; Moumen, N.; Subramanian, R. S. Langmuir 2008, 24, 5185–5193. (7) Greco, E. F.; Grigoriev, R. O. Phys. Fluids 2009, 21, 042105. (8) Schwartz, L. W.; Roy, R. V.; Eley, R. R.; Princen, H. M. J. Eng. Math. 2004, 50, 157–175. (9) Furtado, K.; Pooley, C. M.; Yeomans, J. M. Phys. Rev. E 2008, 78, 045302. (10) Toyota, T.; Maru, N.; Hanczyc, M. M.; Ikegami, T.; Sugawara, T. J. Am. Chem. Soc. 2009, 131, 5012–5013. (11) Sumino, Y.; Magome, N.; Hamada, T.; Yoshikawa, K. Phys. Rev. Lett. 2005, 94, 068301. (12) Greenspan, H. P. J. Fluid Mech. 1978, 84, 125–143. (13) Brochard, F. Langmuir 1989, 5, 432–438. (14) Savino, R.; Paterna, D.; Lappa, M. J. Fluid Mech. 2003, 479, 307–326. (15) de Jong, J.; Reinten, H.; Wijshoff, H.; van den Berg, M.; Delescen, K.; van Dongen, R.; Mugele, F.; Versluis, M.; Lohse, D. Appl. Phys. Lett. 2007, 91, 204102. (16) Tadmor, R. J. Colloid Interface Sci. 2009, 332, 451–454. (17) Bahadur, P.; Yadav, P. S.; Chaurasia, K.; Leh, A.; Tadmor, R. J. Colloid Interface Sci. 2009, 332, 455–460.
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