Wenzel State Research Articles

Multiscale numerical research on nucleate boiling enhancement from microscale to nanoscale

Nucleate boiling enhancement from surfaces in energy industries is of fundamental significance for improving energy conversion and thermal management efficiency. This study investigates the microscale and nanoscale boiling processes on the hybrid wettability micropillar structured surface (MPS) to continuously enhance nucleate boiling. The microscale and nanoscale boiling processes and underlying enhancement mechanisms are studied by Lattice Boltzmann Method (LBM) and Molecular Dynamics (MD) simulations, respectively. It is revealed that MPS designed with a hydrophilic bottom surface and a hydrophobic top surface decorated with nanopillars can improve nucleate boiling throughout the microscale and nanoscale boiling process. The microscopic boiling process of the hybrid wettability MPS shows that the synergistic effect of wettability and surface structure is attributed to nucleation boiling enhancement due to higher bubble nucleation density and higher bubble departure frequency. The nanoscale boiling process on hydrophobic nanopillar structured surfaces (NPS) shows further nucleate boiling enhancement. The NPS with a nanopillar height of 1.6268 nm is in the Wenzel state with higher heat flux and lower thermal resistance, resulting in faster boiling onset and shorter separation time, while the hydrophobic NPSs in the Cassie state leads to a deterioration in the nucleate boiling.

Effect of Hydrophobic Nano-SiO2 Particle Concentration on Wetting Properties of Superhydrophobic Surfaces.

As a unique surface wettability, superhydrophobicity has great application value. A variety of preparation methods for superhydrophobic surfaces have been reported, which have the disadvantages of high cost and complicated process. In order to design a method that is easy to operate, low-cost, and suitable for large-scale preparation of superhydrophobic surfaces, in this paper, hydrophobic nano-SiO2 particles are used as spray fillers, and superhydrophobic surfaces are successfully obtained by the spraying process. According to the classical Cassie and Wenzel theory, the influence of the concentration change of hydrophobic nano-SiO2 particles on their wettability is explained, and the appropriate spray concentration parameters are obtained. The results show that the proportion of hydrophobic nano-SiO2 particles is lower than 0.05 g/mL, which will lead to insufficient microstructure on the surface of the coating, and cannot support the droplets to form the air bottom layer. However, an excessively high proportion of hydrophobic nano-SiO2 particles will reduce the connection effect of the silicone resin and affect the durability of the surface. Through theoretical analysis, there are Wenzel state, tiled Cassie state, and stacked Cassie state in the spraying process. When the substrate surface enters the Cassie state, the lower limit of the contact angle is 149°. This study has far-reaching implications for advancing the practical application of superhydrophobic surfaces.

Engulfed small Wenzel droplets on hierarchically structured superhydrophobic surface by large Cassie droplets: Experiments and molecular dynamics simulations

Lotus leaves boost the development of superhydrophobic surfaces (SHSs) and water droplets applied for measuring the superhydrophobicity are usual macroscopic. Recent years, it shows that the superhydrophobicity vanishes when nano-size water droplets form on SHSs resulting in the Wenzel state, such as condensation. In fact, SHSs such as lotus leaves always keep superhydrophobicity, and water droplets quickly roll on surfaces. Here, we suppose that small Wenzel water droplets could be engulfed by large Cassie water droplets and verify this hypothesis by experiments and molecular dynamics (MD) simulations. It experimentally shows that the rolling large Cassie droplet engulfs small Wenzel droplets. We fabricate a Cassie droplet on the nanopillared SHS with the same contact angle as the experiment using MD simulation, as well as small Wenzel droplets. It shows that the moving large Cassie droplet engulfs small Wenzel droplets. Moreover, engulfing small Wenzel droplets does not reduce the velocity of large Cassie droplets because the emit energy of merging overcomes the adhesion energy of small Wenzel droplets. Effects of the number, distribution, and size of small Wenzel droplets on motion state and velocity of large Cassie droplets are also investigated. We believe this study would contribute to understanding nanodroplets on SHSs in practical applications.

Effect of treatment time and radio frequency power on roughness and wettability of oxygen plasma-etched Cadmium Telluride thin films

The thermal evaporated Cadmium Telluride (CdTe) on Indium tin oxide substrates was etched using Oxygen plasma at various treatment times and radio frequency (RF) power. The roughness and wettability parameters were calculated using atomic force microscopy and contact angle (CA) analysis. The morphology evolution increases the interface width w and the lateral correlation length ξ with etching time and RF power. The local roughness exponent near-0.5 shows the self-affine of the surface during the etching process. The obtained experimental exponents in the present work introduce the universality class of the scaling exponents. The surface hydrophilicity of films was studied using the measurement of the two droplets CA on the film surface and the surface energy. The physical and chemical structure of the surface affected by oxygen plasma causes the surface to become more rough and hydroxyl group formation. Infra-Red spectra of the untreated and etched films using Fourier transform infrared spectroscopy confirmed the presence of the CdTe bond and a hydroxyl group. The wettability behavior of the etched films demonstrated the transition from the Cassie-Baxter state to the Wenzel state. Results show surface energy of the etched films increases, and theirs become hydrophilic.

A Study of the Critical Velocity of the Droplet Transition from the Cassie to Wenzel State on the Symmetric Pillared Surface

A droplet hitting a superhydrophobic surface will undergo the Cassie to Wenzel transition when the wetting force exceeds the anti-wetting force. The critical velocity of the droplet’s Cassie to Wenzel state transition can reflect the wettability of the surface. However, the critical velocity research is still at the microscale and has not been extended to the nanoscale mechanism. A cross-scale critical velocity prediction model for superhydrophobic surfaces with symmetric structures is proposed here based on a mechanical equilibrium system. The model’s applicability is verified by experimental data. It demonstrates that the mechanical equilibrium system of droplet impact with capillary pressure and Laplace pressure as anti-wetting forces is more comprehensive, and the model proposed in this study predicts the critical velocity more precisely with a maximum error of 12% compared to the simulation results. Furthermore, the correlation between the simulation at the nanoscale and the evaluation of the macroscopic symmetrical protrusion surface properties is established. Combined with the model and the correlation, the relationship between the microscopic mechanism and the macroscopic examination of droplet dynamics on the superhydrophobic surface be presented, and the wettability evaluation method of macroscopic surfaces based on the molecular simulation mechanism can be realized.

Vapor condensation on micropillar structured surface with lattice Boltzmann method

Pure vapor condensation process and heat transfer on micropillar structured surfaces with various wettabilities are simulated numerically based on an improved three-dimensional phase-change lattice Boltzmann method (LBM). Condensed droplet dynamic behaviors containing nucleation, growth and departure are mainly explored. Two preferable droplet nucleation sites are detected successfully: at the corner between micropillar sides and subcooled substrate, and at the center of substrate. The effects of contact angle, micropillar spacing and height on droplet nucleation time, departure diameter and departure frequency are investigated quantitatively. Results indicate that as the contact angle increases, nucleation of condensate is delayed, while the departure diameter is reduced and departure frequency is increased. The increase in micropillar spacing, height and contact angle changes droplet from Wenzel state to partial wetting state. Moreover, it is also shown that the highest temperature and maximum local heat flux appear at the three-phase contact line. Despite the very complex roles of micropillar structures and wettability on condensation heat transfer, an optimal heat transfer surface with configurations of contact angle of 90°, micropillar spacing of 12 and height of 18 is presented. This study provides a fundamental understanding in regards to vapor condensation on microscale structured surface from numerical view.

Work needed to force the water-air interface down in the re-entrant structured capillary pore

The re-entrant structure of the membrane surface has attracted researchers' attention recently, due to its ability to make the membrane surface more wetting resistant-either in water or in liquids of low surface tension. The underlying principle of this approach is that an energy barrier has to be overcome when the transition occurs from the Cassie Baxter state to the Wenzel state of the rough membrane surface, which prevents the passage of liquid through the membrane pore. In this work, the energy barrier was evaluated for the cone-shaped pore based on Young's theory of the capillary force. It was found that the energy barrier is enhanced by increasing the angle of the apex of the cone, the pore length, and the contact angle. The effects of the first two geometrical factors, the angle of apex of cone and pore length, are much stronger than the effect of the contact angle. It is believed that this work will offer a guideline for the rational membrane design to reduce, and even prevent, the pore wetting of membranes, particularly for oil/water separation and membrane distillation.

Dropwise condensation on single-micro-scale roughness hydrophobic surfaces

Dropwise condensation (DWC) usually occurs on superhydrophobic surfaces with dual-scale (or multi-scale) roughness in discrete droplets to avoid liquid film formation, enhancing overall heat transfer efficiency. In this study, we demonstrate that the dual-scale roughness hydrophobic surface is not a necessary condition for DWC to occur. A series of single-scale roughness surfaces of regular arrays of square micro-pillars are fabricated to investigate the effect of surface roughness on the wetting behavior of condensed droplets and DWC. A sequence of the wetting behavior of condensed water droplets larger than 200 μm in diameter on single-scale roughness hydrophobic surfaces: Wenzel state → Cassie state → partial Cassie (Cassie-Wenzel mixed) state → Wenzel state (with the irregular shape of three-phase-contact-line) is observed along with increasing surface roughness (pillar height). An in-house design inverted microscopy system is applied for further confirmation of the wetting behavior of condensed droplets. A tiny Wenzel droplet nucleated grow in the microstructure can be dewetted by colliding with a Cassie droplet. This coalescence-induced dewetting transition can effectively make Cassie DWC occur on these single-scale roughness substrates, providing the surface structure design of condensers for Cassie DWC much easier to implement than on dual-scale roughness surfaces.

Velocity-Dependent Contact Angle and Energy Dissipations of Dynamic Wetting Nanodroplets on Nanopillared Surfaces.

Dynamic wetting, described by a dynamic contact angle (DCA), is a fundamental behavior of fluid on surface. With the development of blue energy, the research of droplet nanogenerator is flourishing. There is a growing interest in the dynamic wetting behavior of nanodroplets on surfaces. Molecular dynamics simulations are performed to reveal the influence of the velocity of nanodroplets and the wetting state (Cassie and Wenzel) on the DCA and the energy dissipation on the contact line. The simulation results demonstrate a more complicated scenario of dynamic wetting than the static wetting: The increasing rate of advancing DCA is lower than the decreasing rate of the receding DCA with respect to the nanodroplet velocity. As for the Wenzel state, larger surface roughness increases the dynamic wetting hysteresis, while for Cassie nanodroplets, the larger surface roughness leads to smaller dynamic wetting hysteresis. It is found that a structural force exists on the rough surface. The energy dissipation of the dynamic wetting mainly comes from the motion of the contact line, which is positively correlated to the velocity and can be decomposed to the viscosity and friction dissipations, respectively. The Cassie state causes much lower energy dissipation than the Wenzel state. Furthermore, the quasi-static contact angle is proposed to describe the contact angle on a rough surface. These findings advance the understanding of dynamic wetting behavior and inspire theoretical guidance for the design of novel functional interfaces.

Molecular Dynamics Simulation on the Wettability of Nanoscale Wrinkles: High Water Adhesion of Rose Petals.

Understanding the high water adhesion of rose petals is of great significance in artificial surface design. With all-atom molecular dynamics simulation, the wettability of nanoscale wrinkles was explored and compared to that of nanoscale strips with favorable hydrophobicity. The dewetting and wetting of gaps between nanoscale structures represent the Cassie-Baxter (CB) and Wenzel (WZ) states of the macroscopic droplet deposited on the textured surface, respectively. We uncovered the intermediate state, which is different from the CB and WZ states for wrinkles. Structures and free-energy profiles of metastable and transition states under various pressures were also investigated. Moreover, free-energy barriers for the (de)wetting transitions were quantified. On this basis, the roles of pressure and the unique structures of nanoscale wrinkles in the high water adhesion of rose petals were identified.

Research progress and outlook of the effect of wettingtransition on the freezing of impinging droplets onsuperhydrophobic surfaces

<p indent="0mm">Freezing of impinging droplets widely appears in industrial applications, such as energy power, electric communications, aerospace, and many others, which seriously interferes with equipment operation. Due to this fact, how to inhibit the impinging droplet freezing is of great significance in practical applications. It is worth recalling that the droplet bounces off surfaces as it impacts on superhydrophobic surfaces, and hence the impinging droplet freezing is thoroughly inhibited by the rebound characteristics of superhydrophobic surfaces. However, superhydrophobicity is the basis for droplet rebound. As the Cassie-Wenzel irreversible wetting transition is triggered by droplet impact, this irreversible wetting transition causes the failure of superhydrophobicity such that droplets adhere to and freeze on cold superhydrophobic surfaces. As a result, from the viewpoint of wetting transition, how to enhance the rebound characteristics of superhydrophobic surfaces is essential to inhibit the impinging droplet freezing. This paper provides a review on the influence of wetting transition on the impinging droplet freezing on superhydrophobic surfaces, ranging from its effect on dynamic behaviors, its effect on freezing forms to energy paths and transition mechanisms for impact-induced wetting transition. Based on this review, it is found that as droplets impact on superhydrophobic surfaces, it can bounce off only when the Cassie-Wenzel irreversible wetting transition is not triggered, or Cassie-Wenzel-Cassie reversible wetting transition is triggered. Secondly, when the impinging droplet adheres to the cold superhydrophobic surface, the impinging droplet freezes in the form of the Wenzel state as the Cassie-Wenzel irreversible wetting transition is thoroughly triggered, in the form of the partial Wenzel state as the Cassie-Wenzel wetting transition or the Wenzel-Cassie dewetting transition is partially triggered, and in the form of the Cassie state as the Cassie-Wenzel-Cassie reversible wetting transition is triggered. Compared with the partial Wenzel state droplet and the Cassie state droplet, the freezing delay time is less for the Wenzel state droplet because the solid-liquid contact area is larger for the Wenzel state droplet than that for the partial Wenzel state droplet and the Cassie state droplet. Thirdly, on the superhydrophobic surfaces at room temperature, the energy paths and transition mechanisms have been revealed for the impact-induced Cassie-Wenzel and Wenzel-Cassie wetting transition. However, on cold superhydrophobic surfaces, these energy paths and transition mechanisms are absent, which should be revealed by researchers. Based on the above summary, the impinging droplet freezing can be thoroughly prevented on cold superhydrophobic surfaces as the Cassie-Wenzel irreversible wetting transition is inhibited or the Cassie-Wenzel-Cassie reversible wetting transition is promoted. The outlook is provided in the end of this review, which includes that by the design of surface topology, inhibiting the irreversible wetting transition and promoting the reversible wetting transition that is based on the energy paths and transition mechanisms of wetting and dewetting transition on cold superhydrophobic surfaces.

Theoretical analysis on condensation heat transfer on the hydrophobic–hydrophilic hybrid surfaces with the impact of the Marangoni convection

Condensation occurs in the forms of filmwise condensation and dropwise condensation. Over the past decade, hybrid hydrophobic–hydrophilic surfaces have received significant attention due to their potential to enhance the heat transfer rate compared to complete dropwise condensation. The maximum condensed droplet radius in the hydrophobic region has a considerable impact on the heat transfer characteristics. This paper discusses the effect of the maximum droplet radius on hybrid surface heat transfer characteristics. On top of that, Marangoni convection effects originated due to the temperature gradient as a heat transfer resistance on the heat transfer rate is considered, modelled and investigated. Three models were investigated in this paper. The results indicate that there is an optimum maximum droplet radius for each model that can improve the heat transfer rate. When the filmwise region width increases from 0.5 mm to 1.0 mm, the optimum maximum droplet radius increases from 0.25 mm to 0.3 mm. For a fixated droplet contact angle and filmwise and dropwise region widths, the hybrid heat flux of the smooth dropwise model can be up to 1.55 times higher than that of the Cassie–Baxter model, and the hybrid heat flux of the smooth dropwise model can be up to 1.38 time higher than that of the Wenzel state. Finally, considering Marangoni convection showed up to a 30% increase in the heat transfer coefficient in some cases.

Quantifying Wetting Dynamics with Triboelectrification

Wetting is often perceived as an intrinsic surface property of materials, but determining its evolution is complicated by its complex dependence on roughness across the scales. The Wenzel (W) state, where liquids have intimate contact with the rough surfaces, and the Cassie–Baxter (CB) state, where liquids sit onto air pockets formed between asperities, are only two states among the plethora of wetting behaviors. Furthermore, transitions from the CB to the Wenzel state dictate completely different surface performance, such as anti‐contamination, anti‐icing, drag reduction etc.; however, little is known about how transition occurs during time between the several wetting modes. In this paper, wetting dynamics can be accurately quantified and tracked using solid–liquid triboelectrification. Theoretical underpinning reveals how surface micro‐/nano‐geometries regulate stability/infiltration, also demonstrating the generality of the authors’ theoretical approach in understanding wetting transitions. It can clarify the functioning behavior of materials in real environment.

Droplet wettability and repellency on fluorinated lubricant-infused surfaces: A molecular dynamics study

Fluorinated lubricant-infused surfaces are gaining remarkable attention as a promising candidate of self-cleaning and antifouling materials and liquid-resistant surface coatings. Despite all the lubricant-infused surfaces are related to a surface lubrication stabilized in a porous or nanotextured solid, they may present varying droplet morphologies regarding to the state of cloaking, lubricant ridges, and the wetting state. In this work, molecular dynamics simulations were performed to investigate the droplet wettability and repellency on fluorinated lubricant-infused surfaces. A phase diagram of possible droplet configurations at static equilibration has been developed and compared with theoretical predictions by examining the effects of interfacial tensions and lubricant thickness comprehensively. The static and dynamic droplet repellencies were further quantified in terms of the static, advancing, and receding contact angles and the shedding velocity. In particular, the distinctive “slippery Cassie” surface could effectively conquer the droplet pinning instability by energetically favorably “slippery Wenzel-to-Cassie” transition as well as self-replenishing of lubricant, as compared to the superhydrophobic surface that is susceptible to the irreversible transition to Wenzel state. The findings in this work are believed to provide molecular scale understanding and intuitive guidelines for inspiring applications of fluorinated lubricant-infused surfaces by designing surface wettability and lubricant thickness level rationally.

Characterization of condensation on nanostructured surfaces and associated thermal hydraulics using a thermal lattice Boltzmann method

The dynamics of the condensation process on nanostructured surfaces can be modulated substantially by tuning the surface architecture. Present study uses the mesoscopic framework of lattice Boltzmann method (LBM) to explore the role of surface morphology and cold spot temperature in determining the visual state of the condensate droplet, mode of nucleation, and associated rates of energy and mass interactions. A multiple relaxation time-(MRT)-based LBM solver, coupled with pseudopotential model, has been developed to simulate a rectangular domain of saturated vapor, housing a cold spot on the bottom rough surface. Superhydrophobicity has been achieved for certain combinations of surface parameters, with the intercolumn spacing being the most influential one. Gradual increase in the spacing modifies the nucleation mode from top through side to bottom, while the droplet changes from Cassie to Wenzel state. The Cassie drop in top nucleation mode exhibits the largest contact angle and least rate of surface heat transfer. Both types of Wenzel drops display large rate of condensation and two peaks in heat transfer, along with very short nucleation time in comparison with Cassie drops. Couple of phase diagrams have been developed combining all four scenarios of condensation predicted by the present model. One important novelty of the present study is the consideration of nonisothermal condition within LB structure. Enhancement in the degree of subcooling at the cold spot encourages greater condensation and Cassie-to-Wenzel transition.

Graphene-assisted wetting transition on grooved surfaces: A molecular dynamics study

The various high aspect ratio micro/nano structures that are duplicated by the widely applicable micro/nanomolding process would require excellent wettability of the structured mold for full filling of the liquid-like materials into microcavities. Herein, by employing molecular dynamics (MD) simulations, the influence of a monolayer graphene (MLG) on the wetting behaviors of grooved copper is thoroughly investigated, indicating that MLG is an effective approach in modulating the wettability of the structured copper surfaces. Moreover, the extracted outcomes signify that the coating with MLG reduces remarkably the required activation energy for the infiltration of water molecules into the copper groove, thereby triggering the wetting transition from the Cassie-Baxter (CB) to the Wenzel (WZ) state. In addition, by varying the coating locations and dimension of the MLG, it is unveiled that the sidewall coating of MLG plays a crucial role in reducing the free energy barrier needed to surmount the transition state. Interestingly, as the coating height of sidewall MLG increases, the energy barrier is reduced, and the grooved surface becomes more attractive to water molecular, attaining a stable WZ state by employing a height beyond the critical value of MLG coating of 12.4 Å in our model. Our work provides useful insights into the tunable wettability of the grooved surfaces by nanocoating engineering, suggesting that MLG can be an effective coating solution in the fabrication of novel micro/nanostructures with high aspect ratios.

Wetting States and Departure Diameters of Bubbles on Micro-/Nanostructured Surfaces.

Wetting states for droplets have been extensively investigated in the past. As the counter phase of the droplets, bubbles' wetting states have rarely been systematically explored. The wetting state of a bubble is closely related to its departure diameter, which plays significant roles in bubble-generated processes in boiling heat transfer and gas-evolving reactions. Based on the principle of minimum surface energy, we explicitly define three equilibrium wetting states (hemi-wicking state, Wenzel state, and Cassie-Baxter state) for bubbles on micro-/nanostructured surfaces in this paper. We analyze the three-phase contact line profiles for bubbles under these wetting states and propose theoretical models for predicting departure diameters of hemi-wicking-state bubble and Wenzel-state bubble on micro-/nanostructured surfaces. We identify competing effects of bubble departure in Wenzel state: the augmentation of contact line length due to the roughness, which would delay bubble departure, and the decrease of contact line length due to the reduced apparent contact angle, which would facilitate bubble departure. We demonstrate that hemi-wicking-state bubble exhibits a much smaller departure diameter on the textured surfaces. These findings are supported by numerical simulations by the three-dimensional (3D) multiple-relaxation-time lattice Boltzmann method. It is found that the length of the outermost contact lines instead of all contact lines determines the departure diameter of hemi-wicking-state bubble based on bubble detachment processes captured by our 3D numerical simulations. This work offers an avenue for the accurate prediction and control of bubble departure behaviors from micro-/nanostructured surfaces, and therefore can guide optimal designs of micro-/nanostructured surfaces in a variety of applications in boiling, desalination, and hydrogen production by electrolysis.

Analytical prediction of electrowetting-induced jumping motion for droplets on textured hydrophobic substrates: Effects of the wetting states

In electrowetting, an applied electric voltage can induce spreading, sliding, or even jumping of an individual droplet by changing the intrinsic balance of the three-phase interfacial tensions. This technique has been widely used for manipulating droplets in microfluidics and by lab-on-a-chip devices in recent decades. In the present paper, we present an analytical prediction of the jumping velocity for droplets undergoing electrowetting on textured hydrophobic surfaces with different wetting states. In particular, we consider wetting a liquid droplet on a textured hydrophobic substrate with a voltage applied between the droplet and the substrate. Once the voltage is turned off, the energy stored in the droplet during electrowetting is released and could even result in the detachment of the droplet. The effects of the initial and electrowetting states, i.e., the Cassie–Baxter state and the Wenzel state, on the jumping velocity of droplets are systematically discussed. Based on energy conservation, the energy conversion between the surface energy, the elastic energy of the contact line, and the kinetic energy of droplets due to internal viscous dissipation in different wetting states is analyzed. Closed-form formulas for the jumping velocity of different droplet wetting states are systematically derived. Finally, a unified form for predicting the electrowetting-induced jumping velocity of droplets on both flat and textured substrates with different wetting states is obtained. It can describe the jumping motion under various wetting conditions, which is validated by some experimental results. This work provides theoretical insights into the accurate control of the electrowetting-induced jumping motion of droplets on textured hydrophobic surfaces.

Study of the droplet transition from Cassie to Wenzel state on laser-modified metal surfaces

The paper presents the experimental study of the influence of laser radiation on the texture formation on aluminum alloy, the droplet transition from Cassie to Wenzel state, as well as the main geometric characteristics of a droplet (contact angle, droplet diameter and height). It was found that laser methods for changing the characteristics and texture of metal surfaces are a modern, flexible tool that makes it possible to achieve unique results in controlling the properties of metal surfaces.

Rugotaxis: Droplet motion without external energy supply

Nano-patterned substrates offer possibilities for controlling the motion of fluids without external energy supply in novel technologies in microfluidics, coatings, etc. Here, we report on the rugotaxial motion of droplets on wrinkled substrates with gradient in the wavelength of the wrinkles by exploring a broad range of parameters, such as amplitude of the wrinkles, substrate wettability, droplet size and wavelength gradient. Adopting a theoretical and molecular dynamics approach, we determine the Cassie-Baxter and Wenzel states of the droplets, investigate the efficiency of rugotaxis as a function of different parameters, and discuss additional effects, such as pinning. We find that shallow wrinkles characterised by small wavelength gradients, and moderate adhesion of the droplet to the substrate favour the rugotaxis motion with growing droplet size, when pinning is avoided. We also find that the driving force in rugotaxis is the gain in interfacial energy between the droplet and the substrate as the droplet enters regions of denser wrinkles (smaller wavelengths of the wrinkles).