Lattice Boltzmann modeling of directional wetting: comparing simulations to experiments

Anisotropic Icephobic Mechanisms of Textured Surface: Barrier or Accelerator?

Icing has been seen as an economic and safety hazard due to its threats to aviation, power generation, offshore platforms, etc., where passive icephobic surfaces with a surface texturing design have the potential to address this problem. However, the intrinsic icephobic principles associated with the surface textures, energy, elasticity, and hybrid effects are still unclear. To explore the anisotropic wettability, ice nucleation, and ice detaching behaviors, a series of textured poly(dimethylsiloxane) (PDMS)-based coatings with various texture orientations were proposed through a simple stamping method with surface functionalization. The anisotropic hydrophobic/icephobic phenomena and mechanisms were discovered from wettability evaluation, experimentally studied by icing/deicing experiments, and finally verified by microscopic numerical simulations. One-way analysis of variance (one-way ANOVA analysis) was used to analyze the effect of surface textures on hydrophobic/icephobic properties, which assisted in understanding anisotropic phenomena. Typical anisotropic ice nucleation and growth on the textured coatings were clarified using in situ environmental scanning electron microscope (ESEM) characterization. The ice/coating interfacial stress responses were studied by numerical stimulation at the microscopic level, further verifying the localized, amplified, and propagated stress at the ice/coating interface. The theoretical anisotropic responses, barrier effect, and accelerating effect were verified to interpret the anisotropic wettability and icephobicity, depending on the specific surface conditions. This study revealed the basics of the anisotropic icephobic mechanisms of textured icephobic surfaces, further facilitating the R&D of passive icephobic surfaces.

Drying behaviour of nanofluid sessile droplets on self-affine vis-à-vis corrugated nanorough surfaces

In recent years, evaporative self-assembly of sessile droplets has gained considerable attention owing to its wide applicability in many areas. While the phenomenon is well studied for smooth and isotropically rough (self-affine) surfaces, investigations comparing the outcomes on self-affine vis-à-vis corrugated surfaces remains to be done. In this experimental work, we compare the wetting and evaporation dynamics of nano-colloidal microlitre droplets on self-affine and corrugated nanorough surfaces having identical roughnesses and interface properties. The coupled influence of particle size, concentration, and surface structuring has been explored. Differences in wettability and evaporation dynamics are observed, which are explained via the interaction between wetting fluid and anisotropic surface roughness. Our findings exhibit different temporal behaviour of contact radius and angle in the evaporation process of the droplets. Further, the corrugated surface exhibits anisotropic wettability with a monotonic change in droplet shape as evaporation proceeds, finally giving rise to irregular dried patterns. The scaled rim width and crack spacing of the particulate deposits are examined. Our results can inspire fabrication of surfaces that can facilitate direction-dependent droplet motion for specific applications.

Wetting Effect on Patterned Substrates

A droplet deposited on a solid substrate leads to the wetting phenomenon. A natural observation is the lotus effect, known for its superhydrophobicity. This special feature is engendered by the structured microstructure of the lotus leaf, namely, surface heterogeneity, as explained by the quintessential Cassie-Wenzel theory (CWT). In this work, recent designs of functional substrates are overviewed based on the CWT via manipulating the contact area between the liquid and the solid substrate as well as the intrinsic Young's contact angle. Moreover, the limitation of the CWT is discussed. When the droplet size is comparable to the surface heterogeneity, anisotropic wetting morphology often appears, which is beyond the scope of the Cassie-Wenzel work. In this case, several recent studies addressing the anisotropic wetting effect on chemically and mechanically patterned substrates are elucidated. Surface designs for anisotropic wetting morphologies are summarized with respect to the shape and the arrangement of the surface heterogeneity, the droplet volume, the deposition position of the droplet, as well as the mean curvature of the surface heterogeneity. A thermodynamic interpretation for the wetting effect and the corresponding open questions are presented at the end.

Molecular Dynamics Simulation of Spreading of Mixture Droplets on Chemically Heterogeneous Surfaces

The dynamic spreading process of mixed droplets on chemically heterogeneous surfaces has attracted significant attention owing to its extensive industrial applications. The spreading of mixture droplets on a chemically heterogeneous surface is more complex than that for pure fluid droplets and needs to be understood further. In this study, molecular dynamic simulations were performed to investigate the dynamic spreading process of R32/R1234yf mixture droplets and water/ethanol mixture droplets of radius 4.7-6.5 nm with different compositions, on chemically heterogeneous surfaces. The variation in the relative spreading radius with time was analyzed and compared with the molecular kinetic theory. It was observed that for the R32/R1234yf mixture, the actual component mole fraction did not deviate from the nominal one in the triple contact region, and the dynamic spreading behavior was identical to that for the pure fluids. Meanwhile, the converse was true for the ethanol/water mixture. The molecular kinetic theory could accurately predict the spreading of droplets for R32/R1234yf mixtures when the mixture properties were used. However, this was not feasible for ethanol/water mixtures. It was observed that the local physical properties in the triple contact line (including the mole fraction and the lyophilic and lyophobic area ratio) play key roles in the spreading of the ethanol/water mixture droplets. The prediction of the dynamic spreading of water/ethanol mixture droplets on chemically heterogeneous surfaces can be improved significantly by using local properties to modify the molecular kinetic theory.

Optimal Control of Droplets on a Solid Surface Using Distributed Contact Angles

Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, rarely involves model-based optimal control strategies. In this work, we demonstrate the optimal control of both the shape and position of a droplet sliding on an inclined surface. This basic test case is a fundamental building block in plenty of microfluidic designs. The static contact angle between the solid surface, the surrounding gas, and the liquid droplet serves as the control variable. By using several control patches, e.g., like that performed in electrowetting, the contact angles are allowed to vary in space and time. In computer experiments, we are able to calculate mathematically optimal contact angle distributions using gradient-based optimization. The dynamics of the droplet are described by the Cahn-Hilliard-Navier-Stokes equations. We anticipate our demonstration to be the starting point for more sophisticated optimal design and control concepts.

A Numerical Study of Micro-Droplet Spreading Behaviors on Wettability-Confined Tracks Using a Three-Dimensional Phase-Field Lattice Boltzmann Model

Wettability-confined tracks have been extensively used in open-surface microfluidic devices for their high capacity of transporting droplet pumplessly. Inspired by the experimental work of Sen et al. [ Langmuir 2018 , 34 , 1899 - 1907 ], in the present study, a three-dimensional phase-field lattice Boltzmann model is developed and used to investigate the spreading behaviors of microdroplet on a series of wettability-confined tracks. The experimental findings are successfully reproduced through our simulation, where three distinct stages of droplet spreading on the horizontal wettability-confined diverging track are fairly exhibited, that is, the initial stage with droplet front spreading quickly, the intermediate stage with both droplet front and bulge moving forward at a constant speed, and the final stage with droplet front decelerating gradually. Moreover, a parametric study of track divergence angle is further performed, and the influential mechanism of track divergence angle on droplet spreading is further revealed. It is demonstrated that track divergence is responsible for the Laplace pressure gradient and capillary force inside the droplet, which drives the droplet bulge to move forward on the diverging track. With an increase in divergence angle, the capillary force increases linearly, which increases the droplet spreading speed at the initial and intermediate stages, while the peak capillary force comes earlier, and consequently the final decelerating stage comes earlier. On the basis of the parametric study and droplet volume conservation rule, a power law relation between track divergence angle and droplet spreading is proposed, which helps to identify the start of final decelerating stage. Finally, the droplet spreading over various inclined tracks is explored, which can be achieved only when the capillary force at the beginning is larger than the droplet gravity component along the inclined track surface.

The effect of the liquid layer thickness on the dissolution of immersed surface droplets

Droplets on a liquid-immersed solid surface are key elements in many applications, such as high-throughput chemical analysis and droplet-templated porous materials. Such surface droplets dissolve when the surrounding liquid is undersaturated and the dissolution process is usually treated analogous to a sessile droplet evaporating in air. Typically, theoretical models predict the mass loss rate of dissolving droplets as a function of droplet geometrical factors (radius, constant angle), and droplet material properties (diffusion constant and densities), where the thickness of the surrounding liquid layer is neglected. Here, we investigate, both numerically and theoretically, the effect of the liquid layer thickness on the dissolution of surface droplets. We perform 3D lattice Boltzmann simulations and obtain the density distribution and time evolution of droplet height during dissolution. Moreover, we find that the dissolution slows down and the lifetime linearly increases with increasing the liquid layer thickness. We propose a theoretical model based on a quasistatic diffusion equation which agrees quantitatively with simulation results for thick liquid layers. Our results offer insight to the fundamental understanding of dissolving surface droplets and can provide valuable guidelines for the design of devices where the droplet lifetime is of importance.

Investigation of Equilibrium Droplet Shapes on Chemically Striped Patterned Surfaces Using Phase-Field Method

We systematically investigate the equilibrium shapes of droplets deposited on a set of chemically striped patterned surfaces by using an Allen?Cahn-type phase-field model. Varying the widths of the stripes d, the volume V, as well as the initial positions of the droplets, we release the droplets on the top of the surfaces and observe the final droplet shapes. It is found that there are either one or two equilibrium shapes for a fixed ratio of d/ V^1/3 and each equilibrium shape corresponds to an energy minimum state. The aspect ratio of the droplets ? shows a periodic oscillation behavior with a decreasing amplitude as d/ V^1/3 decreases, similar to the stick?slip?jump movement of a slowly condensing droplet on a chemically striped patterned surface. Additionally, by comparing the movements of slowly evaporating and condensing droplets, we have observed a hysteresis phenomenon, which reveals that the final shapes of droplets also rely on the moving paths. Through modifying the dynamic contact angle boundary condition, the contact line movements of droplets under condensation and evaporation, which are far from equilibrium, are addressed.

Fluid flow simulations meet high-speed video: Computer vision comparison of droplet dynamics

HYPOTHESIS

While multiphase flows, particularly droplet dynamics, are ordinary in nature as well as in industrial processes, their mathematical and computational modelling continue to pose challenging research tasks - patent approaches for tackling them are yet to be found. The lack of analytical flow field solutions for non-trivial droplet dynamics hinders validation of computer simulations and, hence, their application in research problems. High-speed videos and computer vision algorithms can provide a viable approach to validate simulations directly against experiments.

EXPERIMENTS

Droplets of water (or glycerol-water mixtures) impacting on both hydrophobic and superhydrophobic surfaces were imaged with a high-speed camera. The corresponding configurations were simulated using a lattice-Boltzmann multiphase scheme. Video frames from experiments and simulations were compared, by means of computer vision, over entire droplet impact events.

FINDINGS

The proposed experimental validation procedure provides a detailed, dynamic one-on-one comparison of a droplet impact. The procedure relies on high-speed video recording of the experiments, computer vision, and on a software package for the analyzation routines. The procedure is able to quantitatively validate computer simulations against experiments and it is widely applicable to multiphase flow systems in general.

Finite-element lattice Boltzmann simulations of contact line dynamics

The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.

Standing, lying, and sitting: translating building principles of the cell membrane to synthetic 2D material interfaces

Lessons can be drawn from cell membranes in controlling noncovalent functionalization of 2D materials to optimize interactions with the environment.

Sitting Phase Monolayers of Polymerizable Phospholipids Create Dimensional, Molecular-Scale Wetting Control for Scalable Solution-Based Patterning of Layered Materials

The use of dimensionally ordered ligands on layered materials to direct local electronic structure and interactions with the environment promises to streamline integration into nanostructured electronic, optoelectronic, sensing, and nanofluidic interfaces. Substantial progress has been made in using ligands to control substrate electronic structure. Conversely, using the exposed face of the ligand layer to structure wetting and binding interactions, particularly with scalable solution- or spray-processed materials, remains a significant challenge. However, nature routinely utilizes wetting control at scales from nanometer to micrometer to build interfaces of striking geometric precision and functional complexity, suggesting the possibility of leveraging similar control in synthetic materials. Here, we assemble striped "sitting" phases of polymerizable phospholipids on highly oriented pyrolytic graphite, producing a surface consisting of 1 nm wide hydrophilic stripes alternating with 5 nm wide hydrophobic stripes. Protruding, strongly wetting headgroup chemistries in these monolayers enable formation of rodlike wetted patterns with widths as little as ∼6 nm and lengths up to 100 nm from high-surface-tension liquids (aqueous solutions of glycerol) commonly utilized to assess interfacial wetting properties at larger length scales. In contrast, commonly used lying-down phases of diynoic acids with in-plane headgroups do not promote droplet sticking or directional spreading. These results point to a broadly applicable strategy for achieving high-resolution solution-based patterning on layered materials, utilizing nanometer-wide patterns of protruding, charged functional groups in a noncovalent monolayer to define pattern edges.

Droplet migration on hydrophobic–hydrophilic hybrid surfaces: a lattice Boltzmann study

Droplet migration on textured hydrophobic–hydrophilic surfaces.

Effect of nano structures on the nucleus wetting modes during water vapour condensation: from individual groove to nano-array surface

The geometrical structures of surfaces are important to the formation and growth of nuclei during water vapour condensation. Nucleus wetting modes on grooved surfaces are determined by the intrinsic contact angle and the cross sectional angle.

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.

Wettability effects on contact line dynamics of droplet motion in an inclined channel

The present work discusses the implications of wall wettability and inclination of the surface on droplet dynamics. In this work, mesoscopic illustration of droplet dynamics in a duct with different inclination angles, based on the two-phase lattice Boltzmann model, is reported. Temporal evolution of wetted length, wetted area, and maximum height of the droplet for surfaces with different inclination angles and wettabilities is furnished in detail in order to elucidate the droplet displacement dynamics. It has been observed that the effect of inclination of the surface on droplet dynamics is more pronounced on a hydrophobic surface as compared to a hydrophilic surface. The time evolution of height and contact line motion of the droplet shows that higher angle of inclination of substrate affects the dynamics strongly irrespective of wettability.

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.

Stick-jump mode in surface droplet dissolution

The analogy between evaporating surface droplets in air to dissolving long-chain alcohol droplets in water is worked out. We show that next to the three known modi for surface droplet evaporation or dissolution (constant contact angle mode, constant contact radius mode, and stick-slide mode), a fourth mode exists for small droplets on supposedly smooth substrates, the stick-jump mode: intermittent contact line pinning causes the droplet to switch between sticking and jumping during the dissolution. We present experimental data and compare them to theory to predict the dissolution time in this stick-jump mode. We also explain why these jumps were easily observed for microscale droplets but not for larger droplets.

Shape of picoliter droplets on chemically striped patterned substrates

We studied the shape of water droplets deposited using an inkjet nozzle on a chemically striped patterned substrate consisting of alternating hydrophobic and hydrophilic stripes. The droplet dimensions are comparable to the period of the stripes, typically covering up to 13 stripes. As such, our present results bridge the gap linking two regimes previously considered: (i) droplets on single stripes and (ii) droplets covering more than 50 stripes. In line with previous work on markedly smaller water droplets, the exact deposition position is important for the final shape of the droplets. A droplet with its center deposited on a hydrophobic stripe reaches a shape that is different than when it is deposited on a hydrophilic stripe. Experimental results of different droplet configurations on the same surface are in agreement with simulations using the lattice Boltzmann model. In addition, the simulations enable a detailed analysis of droplet free energies and the volume dependence. The latter reveals scaling properties of shape parameters in terms of droplet radius scaled to the period of the stripe pattern, which have remained unexplored until now.