Sliding drops across alternating hydrophobic and hydrophilic stripes

Irreversible Charging Caused by Energy Dissipation from Depinning of Droplets on Polymer Surfaces

Interfacial energy dissipation during stick-slip motion of a liquid drop on a nonconductive polymer substrate is shown to lead to an irreversible increase in electrical charge. This previously unobserved phenomenon occurs during surface wetting, in contrast to the previously reported charge separation mechanism that occurs during dewetting. Understanding this electrification mechanism will facilitate the design of energy harvesters and aid the development of risk mitigation strategies for electrostatic buildup in liquid flow across a wide range of industrial applications.

Estimating sliding drop width via side-view features using recurrent neural networks

High speed side-view videos of sliding drops enable researchers to investigate drop dynamics and surface properties. However, understanding the physics of sliding requires knowledge of the drop width. A front-view perspective of the drop is necessary. In particular, the drop's width is a crucial parameter owing to its association with the friction force. Incorporating extra cameras or mirrors to monitor changes in the width of drops from a front-view perspective is cumbersome and limits the viewing area. This limitation impedes a comprehensive analysis of sliding drops, especially when they interact with surface defects. Our study explores the use of various regression and multivariate sequence analysis (MSA) models to estimate the drop width at a solid surface solely from side-view videos. This approach eliminates the need to incorporate additional equipment into the experimental setup. In addition, it ensures an unlimited viewing area of sliding drops. The Long Short Term Memory (LSTM) model with a 20 sliding window size has the best performance with the lowest root mean square error (RMSE) of 67 µm. Within the spectrum of drop widths in our dataset, ranging from 1.6 to 4.4 mm, this RMSE indicates that we can predict the width of sliding drops with an error of 2.4%. Furthermore, the applied LSTM model provides a drop width across the whole sliding length of 5 cm, previously unattainable.

Anomalous phase diagram of the elastic interface with nonlocal hydrodynamic interactions in the presence of quenched disorder

We investigate the influence of quenched disorder on the steady states of driven systems of the elastic interface with nonlocal hydrodynamic interactions. The generalized elastic model (GEM), which has been used to characterize numerous physical systems such as polymers, membranes, single-file systems, rough interfaces, and fluctuating surfaces, is a standard approach to studying the dynamics of elastic interfaces with nonlocal hydrodynamic interactions. The criticality and phase transition of the quenched generalized elastic model are investigated numerically and the results are presented in a phase diagram spanned by two tuning parameters. We demonstrate that in the one-dimensional disordered driven GEM, three qualitatively different behavior regimes are possible with a proper specification of the order parameter (mean velocity) for this system. In the vanishing order parameter regime, the steady-state order parameter approaches zero in the thermodynamic limit. A system with a nonzero mean velocity can be in either the continuous regime, which is characterized by a second-order phase transition, or the discontinuous regime, which is characterized by a first-order phase transition. The focus of this research is to investigate the critical scaling features near the pinning-depinning threshold. The behavior of the quenched generalized elastic model at the critical depinning force is explored. Near the depinning threshold, the critical exponent is obtained numerically.

Scanning Drop Friction Force Microscopy

Wetting imperfections are omnipresent on surfaces. They cause contact angle hysteresis and determine the wetting dynamics. Still, existing techniques (e.g., contact angle goniometry) are not sufficient to localize inhomogeneities and image wetting variations. We overcome these limitations through scanning drop friction force microscopy (sDoFFI). In sDoFFI, a 15 μL drop of Milli-Q water is raster-scanned over a surface. The friction force (lateral adhesion force) acting on the moving contact line is plotted against the drop position. Using sDoFFI, we obtained 2D wetting maps of the samples having sizes in the order of several square centimeters. We mapped areas with distinct wetting properties such as those present on a natural surface (e.g., a rose petal), a technically relevant superhydrophobic surface (e.g., Glaco paint), and an in-house prepared model of inhomogeneous surfaces featuring defined areas with low and high contact angle hysteresis. sDoFFI detects features that are smaller than 0.5 mm in size. Furthermore, we quantified the sliding behavior of drops across the boundary separating areas with different contact angles on the model sample. The sliding of a drop across this transition line follows a characteristic stick-slip motion. We use the variation in force signals, advancing and receding contact line velocities, and advancing and receding contact angles to identify zones of stick and slip. When scanning the drop from low to high contact angle hysteresis, the drop undergoes a stick-slip-stick-slip motion at the interline. Sliding from high to low contact angle hysteresis is characterized by the slip-stick-slip motion. The sDoFFI is a new tool for 2D characterization of wetting properties, which is applicable to laboratory-based samples but also characterizes biological and commercial surfaces.

Droplet Wetting Propagation on a Hybrid-Wettability Surface

Droplet impinging on the boundary between hydrophilic and hydrophobic regions of a hybrid-wettability surface is studied both experimentally and numerically in the present paper. The interfacial evolution and dynamic feature and the corresponding underlying mechanisms behind are mainly analyzed. Because of the unbalanced surface energy in the vicinity of a boundary, the droplet undergoes spreading-receding in the hydrophobic region before migration toward the hydrophilic region. This results in an increase first but then a decrease in the spreading factor in the hydrophobic region, while it increases continuously in the hydrophilic region. In addition, increasing Weber number leads to the increase in both the spreading factor and migration displacement of the droplet in the hydrophobic region, but the latter decreases in the hydrophilic region, resulting from different momentums of secondary spreading. The experimental determinations are verified in detail by a series of numerical simulations performed based on the single variable method by fixing contact angles in different regions separately and excluding the impact momentum. It is shown that the highly unsymmetrical pressure field is exactly one important reason for droplet migration on the hybrid-wettability surface. Despite the weak dependence of the spreading factor on the hydrophilic contact angle in the hydrophobic region, it has an appreciably positive effect on droplet migration, which is confirmed by the increased pressure gradient with its action area in the hydrophobic region when decreasing the hydrophilic contact angle. This paper advances the fundamental understanding for droplet migration on the hybrid-/gradient-wettability surface.

Wetting of Dehydrated Hydrophilic Pseudomonas fluorescens Biofilms under the Action of External Body Forces

Wetting of dehydrated Pseudomonas fluorescens biofilms grown on glass substrates by an external liquid is employed as a means to investigate the complex morphology of these biofilms along with their capability to interact with external fluids. The porous structure left behind after dehydration induces interesting droplet spreading on the external surface and imbibition into pores upon wetting. Static contact angles and volume loss by imbibition measured right upon droplet deposition indicate that biofilms of higher incubation times show a higher porosity and effective hydrophilicity. Furthermore, during subsequent rotation tests, using Kerberos device, these properties dictate a peculiar forced wetting/spreading behavior. As rotation speed increases a long liquid tail forms progressively at the rear part of the droplet, which stays pinned at all times, while only the front part of the droplet depins and spreads. Interestingly, the experimentally determined retention force for the onset of droplet sliding on biofilm external surface is lower than that on pure glass. An effort is made to describe such complex forced wetting phenomena by presenting apparent contact angles, droplet length, droplet shape contours, and edges position as obtained from detailed image analysis.

Molecular View of the Distortion and Pinning Force of a Receding Contact Line: Impact of the Nanocavity Geometry

We present a molecular view using many-body dissipative particle dynamics simulations to unravel the pinning phenomenon of a liquid film receding over a solid substrate with a nanocavity. We find that the pinning force and distortion of the pinned contact line vary across different nanocavity shapes. We show that the mechanism of a caterpillar motion, which has previously been proposed for advancing precursor films, persists in a partially pinned receding contact line. Our results also demonstrate a localized clamping effect, which is originated from the variation of the dynamic contact angle along the pinned contact line. The simulation results suggest that the clamping effect can be controlled by the geometry of the nanocavity and hydrophilicity of the underlying substrate.

Lattice Boltzmann method for thin-liquid-film hydrodynamics

We propose an approach to the numerical simulation of thin-film flows based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin-film equations are recovered, and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop toward its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.

Wetting boundaries for a ternary high-density-ratio lattice Boltzmann method

We extend a recently proposed ternary free-energy lattice Boltzmann model with high density contrast [Phys. Rev. Lett. 120, 234501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.234501] by incorporating wetting boundaries at solid walls. The approaches are based on forcing and geometric schemes, with implementations optimized for ternary (and, more generally, higher-order multicomponent) models. Advantages and disadvantages of each method are addressed by performing both static and dynamic tests, including the capillary filling dynamics of a liquid displacing the gas phase and the self-propelled motion of a train of drops. Furthermore, we measure dynamic angles and show that the slip length critically depends on the equilibrium value of the contact angles and whether it belongs to liquid-liquid or liquid-gas interfaces. These results validate the model capabilities of simulating complex ternary fluid dynamic problems near solid boundaries, for example, drop impact solid substrates covered by a lubricant layer.

Statics and dynamics of polymeric droplets on chemically homogeneous and heterogeneous substrates

We present a molecular dynamics study of the motion of cylindrical polymer droplets on striped surfaces. We first consider the equilibrium properties of droplets on different surfaces, we show that for small stripes the Cassie-Baxter equation gives a good approximation of the equilibrium contact angle. As the stripe width becomes nonnegligible compared to the dimension of the droplet, it has to deform significantly to minimize its free energy; this results in a smaller value of the contact angle than the continuum model predicts. We then evaluate the slip length and thus the damping coefficient as a function of the stripe width. For very small stripes, the heterogeneous surface behaves as an effective surface, with the same damping as a homogeneous surface with the same contact angle. However, as the stripe width increases, damping at the surface increases until reaching a plateau. Afterwards, we study the dynamics of droplets under a bulk force. We show that if the stripes are large enough the droplets are pinned until a critical force. The critical force increases linearly with stripe width. For large enough forces, the average velocity increases linearly with the force, we show that it can then be predicted by a model depending only on droplet size, contact angle, viscosity, and slip length. We show that the velocity of the droplet varies sinusoidally as a function of its position on the substrate. However, for bulk forces just above the depinning force we observe a characteristic stick-slip motion, with successive pinnings and depinnings.

Droplet Sliding: The Numerical Observation of Multiple Contact Angle Hysteresis

Droplets sliding on surfaces always exhibit an advancing and a receding contact angle. When exerting different driving forces on the droplet to force it to slide at different velocities, the droplet would alter its shape to adapt to the new motion. Hence, different advancing/receding contact angles are likely to be observed, leading to the multiple contact angle hysteresis on a given surface. To verify this hypothesis, many-body dissipative particle dynamics is employed to perform the sliding simulation on both chemically homogeneous and heterogeneous surfaces. By ensuring the droplet sliding in uniform motions under different driving forces, the advancing/receding contact angles are recorded for analysis. Simulation results show that, for homogeneous surfaces, a larger driving force can result in both larger advancing contact angle and smaller receding contact angle, while for heterogeneous surfaces, increasing the driving force only results in smaller receding contact angles. For both cases, multiple contact angle hysteresis can be observed. These observations are contrary to the currently prevailing opinion, which believes that the contact angle hysteresis should be unique on given surfaces. Our findings would advance the understanding of wetting phenomena and possibly inspire new guidance for the design of functional interfaces.

Anisotropic Wetting of Droplets on Stripe-Patterned Chemically Heterogeneous Surfaces: Effect of Length Ratio and Deposition Position

The equilibrium state of a droplet deposited on chemically heterogeneous surfaces is studied by using many-body dissipative particle dynamics. The length ratio covers 2 orders from 0.01 to 1 and allows a systematical inspection of the changes of the droplet shape, contact angle, and aspect ratio with this parameter. Moreover, a new parameter, global aspect ratio, is introduced to better characterize the distortion of the droplet. It is found that the droplet shape at the equilibrium stage strongly lies on the deposition position when the length ratio is beyond 0.1. Additionally, the lateral displacement is observed when depositing the droplet on the border of two stripes at large length ratios (over 0.1). On the other hand, the Cassie area fraction also has a significant effect on the wetting behaviors. When the droplet is driven by a body force with a 45° inclined angle to the stripes, the moving direction could be strictly in line with the force direction, deviating from the force direction, or totally in line with the stripes, depending on the length ratio.

Equilibrium Drop Shapes on a Tilted Substrate with a Chemical Step

We calculate the equilibrium shape of a droplet sitting on a tilted substrate with a "chemical step", that is, different lypophilicity at the two sides of the step. This problem can be generalized to that of a droplet experiencing a body force, pushing it from the lyophilic part to the lyophobic part of the substrate. We present phase diagrams, in which we show for which droplet sizes there are dynamically inaccessible equilibrium shapes. We also identify what determines the threshold volume. While this given system was studied previously in the literature using contact angle hysteresis laws, we present the full static thermodynamical solution of the interfacial energy including the contact energy, while omitting the hysteresis effects from the contact line.

Dynamics of Ferrofluid Drops on Magnetically Patterned Surfaces

The motion of liquid drops on solid surfaces is attracting a lot of attention because of its fundamental implications and wide technological applications. In this article, we present a comprehensive experimental study of the interaction between gravity-driven ferrofluid drops on very slippery oil-impregnated surfaces and a patterned magnetic field. The drop speed can be accurately tuned by the magnetic interaction, and more interestingly, drops are found to undergo a stick-slip motion whose contrast and phase can be easily tuned by changing either the strength of the magnetic field or the ferrofluid concentration. This motion is the result of the periodic modulation of the external magnetic field and can be accurately analyzed because the intrinsic pinning due to chemical defects is negligible on oil-impregnated surfaces.

Tuning Drop Motion by Chemical Chessboard-Patterned Surfaces: A Many-Body Dissipative Particle Dynamics Study

Controlling the motion of liquid drops on the solid surface has broad technological implications. In this study, the many-body dissipative particle dynamics (MDPD) was employed to study the drop behaviors on chemical chessboard-patterned surfaces formed by square or triangular tiles. The scaling relationship of the model was established based on the surface tension, viscosity, and density of a real fluid, and an improved contact angle measurement technique was introduced to the MDPD system. For drops on a horizontal plane with different tile sizes, the equilibrium morphology was examined. The critical Bond number, that is, the critical dimensionless force which is required to unpin the drop, was found strongly affected by the size and the shape of the tiles. Once the droplet begins to move, the tile pattern and the size strongly affect the velocity fluctuation while weakly affect the average velocity. Interestingly, besides the common straight forward path, two more route patterns (zigzag and oblique) were observed by only tuning the tile angle, indicating that the advancing routes of the drop may vary according to the tile angle. To the author's knowledge, this phenomenon has not been reported in the literature. This study provides a valuable tool to explore the possibility of passive control of the drop's motion by energy-free chemical heterogeneous surfaces and thus is helpful for engineers to design a surface that could manipulate the drop motion without external energy.

Stretching of viscoelastic drops in steady sliding

The sliding of non-Newtonian drops down planar surfaces results in a complex, entangled balance between interfacial forces and non-linear viscous dissipation, which has been scarcely inspected. In particular, a detailed understanding of the role played by the polymer flexibility and the resulting elasticity of the polymer solution is still lacking. To this aim, we have considered polyacrylamide (PAA) solutions of different molecular weights, suspended either in water or in glycerol/water mixtures. In contrast to drops of stiff polymers, drops of flexible polymers exhibit a remarkable elongation in steady sliding. This difference is most likely attributed to variation of viscous bending as a consequence of variation of shear thinning. Moreover, an "optimal elasticity" of the polymer seems to be required for this drop elongation to be visible. We have complemented experimental results with numerical simulations of a viscoelastic FENE-P drop. This has been a decisive step to unraveling how a change of the elastic parameters (e.g. polymer relaxation time, maximum extensibility) affects the dimensionless sliding velocity.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Energy Dissipation of Moving Drops on Superhydrophobic and Superoleophobic Surfaces

A water drop moving on a superhydrophobic surface or an oil drop moving on a superoleophobic surface dissipates energy by pinning/depinning at nano- and microprotrusions. Here, we calculate the work required to form, extend, and rupture capillary bridges between the protrusions and the drop. The energy dissipated at one protrusion W_S is derived from the observable apparent receding contact angle Θ_r^app and the density of protrusions n by W_s = γ(cos Θ_r^app + 1)/n, where γ is the surface tension of the liquid. To derive an expression for W_s that links the microscopic structure of the surface to apparent contact angles, two models are considered: A superhydrophobic array of cylindrical micropillars and a superoleophobic array of stacks of microspheres. For a radius of a protrusion R and a receding materials contact angle Θ_r, we calculate the energy dissipated per protrusion as W_s = πγR²[A - ln(R/κ)]f(Θ_r). Here, A = 0.60 for cylindrical micropillars and 2.9 for stacks of spheres. κ is the capillary length. f(Θ_r) is a function which depends on Θ_r and the specific geometry, f ranges from ≈0.25 to 0.96. Combining both equations above, we can correlate the macroscopically observed apparent receding contact angle with the microscopic structure of the surface and its material properties.

Deviation of sliding drops at a chemical step

The motion of partially wetting liquid drops in contact with a solid surface is strongly affected by contact angle hysteresis and interfacial pinning. However, the majority of models proposed for drops sliding over chemical surface patterns consistently neglect the difference between advancing and receding contact angles. In this article, we present a joint experimental and numerical study of the interaction of gravity-driven drops with a chemical step formed at the junction between a hydrophilic and a hydrophobic region. It demonstrates the strong impact of a contact angle hysteresis contrast on the motion of drops at a linear chemical step. Surprisingly, the smallest driving force required to drag the drop across the step onto the lower hydrophobic surface is not observed at a right angle of incidence. Our model reveals that the non-monotonous response of this passive drop 'filter' is solely due to the higher advancing contact angle on the lower surface, and creates an instance where drop motion is affected by dissipation at the contact line rather than by surface energy.

Altering Emulsion Stability with Heterogeneous Surface Wettability

Emulsions–liquid droplets dispersed in another immiscible liquid–are widely used in a broad spectrum of applications, including food, personal care, agrochemical, and pharmaceutical products. Emulsions are also commonly present in natural crude oil, hampering the production and quality of petroleum fuels. The stability of emulsions plays a crucial role in their applications, but controlling the stability without external driving forces has been proven to be difficult. Here we show how heterogeneous surface wettability can alter the stability and dynamics of oil-in-water emulsions, generated by a co-flow microfluidic device. We designed a useful methodology that can modify a micro-capillary of desired heterogeneous wettability (e.g., alternating hydrophilic and hydrophobic regions) without changing the hydraulic diameter. We subsequently investigated the effects of flow rates and heterogeneous wettability on the emulsion morphology and motion. The experimental data revealed a universal critical timescale of advective emulsions, above which the microfluidic emulsions remain stable and intact, whereas below they become adhesive or inverse. A simple theoretical model based on a force balance can be used to explain this critical transition of emulsion dynamics, depending on the droplet size and the Capillary number–the ratio of viscous to surface effects. These results give insight into how to control the stability and dynamics of emulsions in microfluidics with flow velocity and different wettability.

Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles

We present a ternary free-energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model presented here can be extended to include an arbitrary number of fluid components.

Slippery to Sticky Transition of Hydrophobic Nanochannels

Contrary to common intuition that hydrophobic surfaces trivially cause water to slip, we discover a slippery-to-sticky transition in tunable hydrophobic nanochannels. We demonstrate this remarkable phenomenon by bringing out hitherto unveiled interplay between ion inclusions in the water and the interfacial lattice configuration over molecular scales. The consequent alterations in frictional characteristics illustrate that so-called hydrophobic nanochannels can be switchable to manifest features that are otherwise typically associated with hydrophilicity, causing water to stick. Our proposition may bear immense consequences toward fluidically functionalizing a hydrophobic interface without necessitating elaborate surface treatment techniques, bringing in far-ranging implications in diverse applications ranging from nature to energy.

Sliding droplets of Xanthan solutions: A joint experimental and numerical study

We have investigated the sliding of droplets made of solutions of Xanthan, a stiff rodlike polysaccharide exhibiting a non-Newtonian behavior, notably characterized by a shear thinning viscosity accompanied by the emergence of normal stress difference as the polymer concentration is increased. These experimental results are quantitatively compared with those of Newtonian fluids (water). The impact of the non-Newtonian behavior on the sliding process was shown through the relation between the average dimensionless velocity (i.e. the capillary number) and the dimensionless volume forces (i.e. the Bond number). To this aim, it is needed to define operative strategies to compute the capillary number for the shear thinning fluids and compare with the corresponding Newtonian case. The resulting capillary number for the Xanthan solutions scales linearly with the Bond number at small inclinations, as well known for Newtonian fluids, while it shows a plateau as the Bond number is increased. Experimental data were complemented with lattice Boltzmann numerical simulations of sliding droplets, aimed to disentangle the specific contribution of shear thinning and elastic effects on the sliding behavior. In particular the deviation from the linear (Newtonian) trend is more likely attributed to the emergence of normal stresses inside the non-Newtonian droplet.

Adaptive Phase-Field Modeling of Anisotropic Wetting with Line Tension at the Triple Junction

Line tension could affect the contact angle at triple junction, especially in micro- to nanoscale wetting. We have developed an adaptive phase-field model to consider the line tension quantitatively. This model is coupled to the smoothed boundary method for treating the contact line with the solid phase, while the volume constraint is imposed. Our calculated contact angles are in good agreement with the modified Young's equation. Further examples are illustrated for the anisotropic wetting on hydrophilic/hydrophobic stripes and rectangular grooves.

Actuating Water Droplets on Graphene via Surface Wettability Gradients

A surface wettability gradient can break the equilibrium status of a liquid droplet and drives its unidirectional movement on the surface. We propose a conceptual design of the driving water droplet on a graphene surface and demonstrate that both speed and direction of the movement can be controlled via a continuous gradient of surface wettability using comprehensive molecular dynamics (MD) simulations. Controlling the water droplet toward linear and nonlinear arc paths is exemplified in one- and two-dimensional gradients of surface wettability, respectively. Unbalanced Young's equation is extended to understand the speed of the droplet movement, and the predications agree well with MD simulations.

Simulating droplet motion on virtual leaf surfaces

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235-261 (doi:10.1017/S0022112001007133)) with the addition of a disjoining pressure term, describes the gravity- and curvature-driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet's path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.

Lattice Boltzmann investigation of droplet inertial spreading on various porous surfaces

The spreading of liquid drops on solid surfaces is a wide-spread phenomenon of both fundamental and industrial interest. In many applications, surfaces are porous and spreading patterns are very complex with respect to the case on smooth surfaces. Focusing on the inertial spreading just before the Tanner-like viscous regime, this work investigates the spreading of a low-viscosity droplet on a porous surface using lattice Boltzmann numerical simulations. The case of a flat surface is first considered, and it reveals a dependence on the solid equilibrium contact angle θ(s)(eq), which is in good agreement with published experimental data. We conducted numerical experiments with various surfaces perforated by a regular pattern of holes of infinite length. The results show that the global spreading dynamics is independent of the porosity morphology. Through the assumption that, for wetting, the pores can be regarded as surface patches with a contact angle of θ(pore)(eq)=180°, we deduce an effective equilibrium contact angle θ(eff)(eq) on the porous surface from the Cassie-Baxter law. A spreading model is then proposed to describe both a prefactor and an exponent that are similar to a flat surface whose equilibrium contact angle is θ(eff)(eq). This model compares satisfactorily with a large number of numerical experiments under varying conditions.

Numerical Study on Droplet Sliding across Micropillars

Droplet sliding on surfaces is an important phenomenon since it widely happens in microfluidic industry. In this article, we simulate droplets sliding across micropillars on smooth substrates to test how the pillars with different intrinsic wettability influence the movement of droplets. The simulation is performed using a particle-based numerical method, many-body dissipative particle dynamics (MDPD). The simulated results show that the heterogeneous area (built by arranged micropillars) can influence the dynamical contact angles significantly. Both the advancing and receding contact angles increase when the droplet front slides on the heterogeneous area, and their difference is also enlarged, thus the contact line may be pinned. The droplet shows a creeping motion style when its front climbs over each pillar. We also find when the droplet enwraps all pillars, the composite liquid/solid surfaces have no effect on the advancing and receding contact angles. The outcomes support the viewpoint that the wettability is a contact-line-based problem instead of a contact-area-based one.

Numerical investigation of dynamic effects for sliding drops on wetting defects

The ability to trap or deflect sliding drops is of great interest in microfluidics, as it has several technological applications, ranging from self-cleaning and fog harvesting surfaces to laboratory-on-a-chip devices. We present a three-dimensional numerical model that describes sliding droplets interacting with wetting defects of variable strength and size. This approach provides relevant insight if compared to simplified analytic models, as it allows us to assess the relevance of the internal degrees of freedom of the droplet. We observe that the deformation of the drop enhances the effective strength and range of the defect, and we quantify this effect by comparison to a point-mass model. We also analyze the role of the steepness and strength of the defect on the drop motion, observing that small, strong defects are more effective at trapping than large, shallow traps of same excess surface energy. Finally, our results show quantitative agreement with previously reported electrowetting experiments, suggesting a universal behavior in droplet trapping that does not depend strongly on the nature of the defect.

Tuning drop motion by chemical patterning of surfaces

We report the results of extensive experimental studies of the sliding of water drops on chemically heterogeneous surfaces formed by square and triangular hydrophobic domains printed on glass surfaces and arranged in various symmetric patterns. Overall, the critical Bond number, that is, the critical dimensionless force needed to depin the drop, is found to be strongly affected by the shape and the spatial arrangement of the domains. Soon after the droplet begins to move, stick-slip motion is observed on all surfaces, although it is less pronounced than that on striped surfaces. On the triangular patterns, anisotropic behavior is found with drops sliding down faster when the tips of the glass hydrophilic triangles are pointing in the down-plane direction. Away from the critical Bond number, the dynamic regime depends mainly on the static contact angle and weakly on the actual surface pattern. Lattice Boltzmann numerical simulations are performed to validate the experimental results and test the importance of the viscous ratio between the droplet phase and the outer phase.