Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models

Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows

This paper extends the partially saturated method (PSM), used for curved or complex walls, to the lattice Boltzmann (LB) pseudopotential multicomponent model and adapts the wetting boundary condition to model the contact angle. The pseudopotential model is widely used for various complex flow simulations due to its simplicity. To simulate the wetting phenomenon within this model, the mesoscopic interaction force between the boundary fluid and solid nodes is used to mimic the microscopic adhesive force between the fluid and the solid wall, and the bounce-back (BB) method is normally adopted to achieve the no-slip boundary condition. In this paper, the pseudopotential interaction forces are computed with eighth-order isotropy since fourth-order isotropy leads to the condensation of the dissolved component on curved walls. Due to the staircase approximation of curved walls in the BB method, the contact angle is sensitive to the shape of corners on curved walls. Furthermore, the staircase approximation makes the movement of the wetting droplet on curved walls not smooth. To solve this problem, the curved boundary method may be used, but due to the interpolation or extrapolation process, most curved boundary conditions suffer from massive mass leakage when applied to the LB pseudopotential model. Through three test cases, it is found that the improved PSM scheme is mass conservative, that nearly identical static contact angles are observed on flat and curved walls under the same wetting condition, and that the movement of a wetting droplet on curved and inclined walls is smoother compared to the usual BB method. The present method is expected to be a promising tool for modeling flows in porous media and in microfluidic channels.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method

Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.

Study on the Ways to Improve the CO2-H2O Displacement Efficiency in Heterogeneous Porous Media by Lattice Boltzmann Simulation

To improve the efficiency of CO₂ geological sequestration, it is of great significance to in-depth study the physical mechanism of the immiscible CO₂-water displacement process, where the influential factors can be divided into fluid-fluid and fluid-solid interactions and porous media characteristics. Based on the previous studies of the interfacial tension (capillary number) and viscosity ratio factors, we conduct a thorough study about the effects of fluid-solid interaction (i.e., wettability) and porous media characteristics (i.e., porosity and non-uniformity of granule size) on the two-phase displacement process by constructing porous media with various structural parameters and using a multiphase lattice Boltzmann method. The displacement efficiency of CO₂ is evaluated by the breakthrough time characterizing the displacement speed and the quasi-steady state saturation representing the displacement amount. It is shown that the breakthrough time of CO₂ becomes longer, but the quasi-steady state saturation increases markedly with the increase in CO₂ wettability with the surface, demonstrating an overall improvement of the displacement efficiency. Furthermore, the breakthrough time of CO₂ shortens and the saturation increases significantly with increasing porosity, granule size, and non-uniformity, showing the improvement of the displacement efficiency. Therefore, enhancing the wettability of CO₂ with the surface and selecting reservoirs with greater porosity, larger granule size, and non-uniformity can all contribute to the efficiency improvement of CO₂ geological sequestration.

Comparative investigation of a lattice Boltzmann boundary treatment of multiphase mass transport with heterogeneous chemical reactions

Multiphase reactive transport in porous media is an important component of many natural and engineering processes. In the present study, boundary schemes for the continuum species transport-lattice Boltzmann (CST-LB) mass transport model and the multicomponent pseudopotential model are proposed to simulate heterogeneous chemical reactions in a multiphase system. For the CST-LB model, a lattice-interface-tracking scheme for the heterogeneous chemical reaction boundary is provided. Meanwhile, a local-average virtual density boundary scheme for the multicomponent pseudopotential model is formulated based on the work of Li et al. [Li, Yu, and Luo, Phys. Rev. E 100, 053313 (2019)10.1103/PhysRevE.100.053313]. With these boundary treatments, a numerical implementation is put forward that couples the multiphase fluid flow, interfacial species transport, heterogeneous chemical reactions, and porous matrix structural evolution. A series of comparison benchmark cases are investigated to evaluate the numerical performance for different pseudopotential wetting boundary treatments, and an application case of multiphase dissolution in porous media is conducted to validate the present models' ability to solve complex problems. By applying the present LB models with reasonable boundary treatments, multiphase reactive transport in various natural or engineering scenarios can be simulated accurately.

How water wets and self-hydrophilizes nanopatterns of physisorbed hydrocarbons

HYPOTHESIS

Weakly bound, physisorbed hydrocarbons could in principle provide a similar water-repellency as obtained by chemisorption of strongly bound hydrophobic molecules at surfaces.

EXPERIMENTS

Here we present experiments and computer simulations on the wetting behaviour of water on molecularly thin, self-assembled alkane carpets of dotriacontane (n-C₃₂H₆₆ or C32) physisorbed on the hydrophilic native oxide layer of silicon surfaces during dip-coating from a binary alkane solution. By changing the dip-coating velocity we control the initial C32 surface coverage and achieve distinct film morphologies, encompassing homogeneous coatings with self-organised nanopatterns that range from dendritic nano-islands to stripes.

FINDINGS

These patterns exhibit a good water wettability even though the carpets are initially prepared with a high coverage of hydrophobic alkane molecules. Using in-liquid atomic force microscopy, along with molecular dynamics simulations, we trace this to a rearrangement of the alkane layers upon contact with water. This restructuring is correlated to the morphology of the C32 coatings, i.e. their fractal dimension. Water molecules displace to a large extent the first adsorbed alkane monolayer and thereby reduce the hydrophobic C32 surface coverage. Thus, our experiments evidence that water molecules can very effectively hydrophilize initially hydrophobic surfaces that consist of weakly bound hydrocarbon carpets.

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Hysteresis in spreading and retraction of liquid droplets on parallel fiber rails

Wetting and spreading of liquids on fibers occur in many natural and artificial processes. Unlike on a planar substrate, a droplet attached to one or more fibers can assume several different shapes depending on geometrical parameters such as liquid volume and fiber size and distance. This paper presents lattice Boltzmann simulations of the morphology of liquid droplets on two parallel cylindrical fibers. We investigate the final shapes resulting from spreading of an initially spherical droplet deposited on the fibers and from retraction of an initial liquid column deposited between the fibers. We observe three possible equilibrium configurations: barrel-shaped droplet, droplet bridges, and liquid columns. We determine the complete morphology diagram for varying inter-fiber spacings and liquid volumes and find a region of bistability that spans both the column regime and the droplet regime. We further present a simulation protocol that allows one to probe the hysteresis of transitions between different shapes. The results provide insights into energies and forces associated with shape transformations of droplets on fibers that can be used to develop fiber-based materials and microfluidic systems for manipulation of liquids at a small scale.

Modeling Immiscible Fluid Displacement in a Porous Medium Using Lattice Boltzmann Method

The numerical investigation of the interpenetrating flow dynamics of a gas injected into a homogeneous porous media saturated with liquid is presented. The analysis is undertaken as a function of the inlet velocity, liquid–gas viscosity ratio (D) and physical properties of the porous medium, such as porous geometry and surface wettability. The study aims to improve understanding of the interaction between the physical parameters involved in complex multiphase flow in porous media (e.g., CO2 sequestration in aquifers). The numerical simulation of a gaseous phase being introduced through a 2D porous medium constructed using seven staggered columns of either circular- or square-shaped micro-obstacles mimicking the solid walls of the pores is performed using the multiphase Lattice Boltzmann Method (LBM). The gas–liquid fingering phenomenon is triggered by a small geometrical asymmetry deliberately introduced in the first column of obstacles. Our study shows that the amount of gas penetration into the porous medium depends on surface wettability and on a set of parameters such as capillary number (Ca), liquid–gas viscosity ratio (D), pore geometry and surface wettability. The results demonstrate that increasing the capillary number and the surface wettability leads to an increase in the effective gas penetration rate, disregarding porous medium configuration, while increasing the viscosity ratio decreases the penetration rate, again disregarding porous medium configuration.

Validation of pore network modeling for determination of two-phase transport in fibrous porous media

Pore network modeling (PNM) has been widely investigated in the study of multiphase transport in porous media due to its high computational efficiency. The advantage of PNM is achieved in part at the cost of using simplified geometrical elements. Therefore, the validation of pore network modeling needs further verification. A Shan-Chen (SC) multiphase lattice Boltzmann model (LBM) was used to simulate the multiphase flow and provided as the benchmark. PNM using different definitions of throat radius was performed and compared. The results showed that the capillary pressure and saturation curves agreed well when throat radius was calculated using the area-equivalent radius. The discrepancy of predicted phase occupations from different methods was compared in slice images and the reason can be attributed to the capillary pressure gradients demonstrated in LBM. Finally, the relative permeability was also predicted using PNM and provided acceptable predictions when compared with the results using single-phase LBM.

Inhibiting Ostwald Ripening by Scaffolding Droplets

Nanoemulsions as colloidal dispersions of deformable nanodroplets promise wide range of applications in pharmaceuticals, cosmetics, and agriculture. The main limitation that reduces their industrial applications is stability, with Ostwald ripening acting as the main destabilization mechanism. Different from the conventional methods by functionalizing nanoemulsions with adequate ripening inhibitors, here we propose an alternative strategy to stabilize nanoemulsions by inhibiting Ostwald ripening. We report via Lattice Boltzmann method (LBM) and theoretical analysis that the evolution of droplets can be manipulated with the help of solid substrates, either along or against the direction of Ostwald ripening. It turns out that through pinning contact line of sessile droplets, heterogeneous substrates or solid nanoparticles can behave as a scaffold to suppress Ostwald ripening, to regulate droplet morphology and to enhance droplet stability. The identical curvature and unexpected stability of scaffolding droplets are then interpreted with free energy analysis. In addition, by simulating substrates with various heterogeneities and solid particles of different shapes, we demonstrate that it is a common phenomenon that scaffolding droplets can evolve beyond Ostwald ripening.

Benchmark cases for a multi-component Lattice-Boltzmann method in hydrostatic conditions

Hydrostatic properties of partially saturated granular materials at the pore scale are evaluated by the lattice Boltzmann method (LBM) using Palabos implementation of the multi-component multiphase Shan-Chen model. Benchmark cases are presented to quantify the discretization errors and the sensitivity to geometrical and physical properties. This work offers practical guidelines to design LBM simulations of multiphase problems in porous media. Namely, a solid walls retraction procedure is proposed to reduce discretization errors significantly, leading to quadratic convergence. On this basis the equilibrium shapes of pendular bridges simulated numerically are in good agreement with the Young-Laplace equation. Likewise, entry capillary pressure and meniscus profiles in tubes of various cross-sectional shapes are in agreement with analytical predictions. The main points of this article are summarized as:•Benchmark cases for a multi-component Lattice-Boltzmann method are illustrated to be a guideline to calibrate the method in hydrostatic conditions.•A wall retraction procedure is introduced to minimize discretization errors.

Effect of Wetting Transition during Multiphase Displacement in Porous Media

The effects of wettability on multiphase displacement in porous media have been studied extensively in the past, and the contact angle is identified as an important factor influencing the displacement patterns. At the same time, it has been found that the effective contact angle can vary drastically in a time-dependent manner on rough surfaces due to the Cassie-Wenzel wetting transition. In this study, we develop a theoretical model at the pore scale describing the apparent contact angle on a rough interface as a function of time. The theory is then incorporated into the lattice Boltzmann method for simulation of multiphase displacement in disordered porous media. A dimensionless time ratio, Dy, describing the relative speed of the wetting transition and pore invasion is defined. We show that the displacement patterns can be significantly influenced by Dy, where more trapped defending ganglia are observed at large Dy values, leading to lower displacement efficiency. We investigate the mobilization of trapped ganglia through identifying different mobilization dynamics during displacement, including translation, coalescence, and fragmentation. Agreement is observed between the mobilization statistics and the total pressure gradient across a wide range of Dy values. Understanding the effect of the wetting transition during multiphase displacement in porous media is of importance for applications such as carbon geosequestration and oil recovery, especially for porous media where solid surface roughness cannot be neglected.

Application of high-order lattice Boltzmann pseudopotential models

Higher-order lattice Boltzmann (LB) pseudopotential models have great potential for solving complex fluid dynamics in various areas of modern science. The discreteness of the lattice discretization makes these models an attractive choice due to their flexibility, capacity to capture hydrodynamic details, and inherent adaptability to parallel computations. Despite those advantages, the discreteness makes high-order LB models difficult to apply due to the larger lattice structure, for which basic fundamental properties, namely diffusion coefficient and contact angle, remain unknown. This work addresses this by providing general continuum solutions for those two basic properties and demonstrating these solutions to compare favorably against known theory. Various high-order LB models are shown to reproduce the sinusoidal decay of a binary miscible mixture accurately and consistently. Furthermore, these models are shown to reproduce neutral, hydrophobic, and hydrophilic contact angles. Discrete differences are shown to exist, which are captured at the discrete level and confirmed through droplet shape analysis. This work provides practical tools that allow for high-order LB pseudopotential models to be used to simulate multicomponent flows.

Implementation of contact angles in pseudopotential lattice Boltzmann simulations with curved boundaries

The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.

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.

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.

Hybrid Wettability-Induced Heat Transfer Enhancement for Condensation with NonCondensable Gas

Heat transfer enhancement in dropwise condensation is widely investigated on a superhydrophobic surface with the advances in surface engineering, but the influence of a large amount of noncondensable gas (NCG) has not been clarified. In this work, the condensation heat transfer with a large amount of NCG is investigated by developing a multiphase lattice Boltzmann model for a multicomponent system. First, the condensation of a single droplet on a hydrophobic surface with NCG is simulated, demonstrating the capacity of the present model to capture the behaviors of different components during phase change and predict the significant influence of even a small fraction of the NCG on heat transfer. Then, solid surfaces with mixed wettability are built by introducing a fraction of hydrophilic parts to enhance heat transfer. It is found that there exists an optimized proportion which could maximize the condensation heat transfer efficiency corresponding to a specific mass fraction of NCG. Furthermore, the mechanism of this optimized proportion is revealed by examining the dynamic behaviors of condensation in a typical case, as a balance between a promotion of the nucleation rate and a put off of transition to filmwise condensation.

Electrokinetic droplet transport from electroosmosis to electrophoresis

Droplet transport in microfluidic channels by electrically induced flows often entails the simultaneous presence of electroosmosis and electrophoresis. Here we make use of coupled lattice-Boltzmann/molecular dynamics simulations to compute the mobility of a droplet in a microchannel under the effect of an external electric field. By varying the droplet solvation free energy of the counterions released at the channel walls, we observe the continuous transition between the electroosmotic and electrophoretic regime. We show that it is possible to describe the mobility of a droplet in a unified, consistent way, by combining the theoretical description of the electroosmotic flow with, in this case, the Hückel limit of electrophoresis, modified in order to take into account the Hadamard-Rybczynski droplet drag.

Theoretical investigation of heterogeneous wettability in porous media using NMR

It is highly important to understand the heterogeneous wettability properties of porous media for enhanced oil recovery (EOR). However, wettability measurements are still challenging in directly investigating the wettability of porous media. In this paper, we propose a multidimensional nuclear magnetic resonance (NMR) method and the concept of apparent contact angles to characterize the heterogeneous wettability of porous media. The apparent contact angle, which is determined by both the wetting surface coverage and the local wettability (wetting contact angles of each homogeneous wetting regions or wetting patches), is first introduced as an indicator of the heterogeneous wettability of porous media using the NMR method. For homogeneously wetting patches, the relaxation time ratio T1/T2 is employed to probe the local wettabiity of wetting patches. The T2 - D is introduced to obtain the wetting surface coverage using the effective relaxivity. Numerical simulations are conducted to validate this method.

Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio

A thermodynamically consistent free energy model for fluid flows comprised of one gas and two liquid components is presented and implemented using the entropic lattice Boltzmann scheme. The model allows a high density ratio, up to the order of O(10^{3}), between the liquid and gas phases, and a broad range of surface tension ratios, covering partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of the fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive, and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.

From Dot to Ring: The Role of Friction in the Deposition Pattern of a Drying Colloidal Suspension Droplet

The deposition of particles on a substrate by drying a colloidal suspension droplet is at the core of applications ranging from traditional printing on paper to printable electronics or photovoltaic devices. The self-pinning induced by the accumulation of particles at the contact line plays an important role in the formation of a deposit. In this article, we investigate, both numerically and theoretically, the effect of friction between the particles and the substrate on the deposition pattern. Without friction, the contact line shows a stick-slip behavior and a dotlike deposit is left after the droplet is evaporated. By increasing the friction force, we observe a transition from a dotlike to a ringlike deposit. We propose a theoretical model to predict the effective radius of the particle deposit as a function of the friction force. Our theoretical model predicts a critical friction force when self-pinning happens and the effective radius of deposit increases with increasing friction force, confirmed by our simulation results. Our results can find implications for developing active control strategies for the deposition of drying droplets.

Effect of wettability on two-phase quasi-static displacement: Validation of two pore scale modeling approaches

Understanding of pore-scale physics for multiphase flow in porous media is essential for accurate description of various flow phenomena. In particular, capillarity and wettability strongly influence capillary pressure-saturation and relative permeability relationships. Wettability is quantified by the contact angle of the fluid-fluid interface at the pore walls. In this work we focus on the non-trivial interface equilibria in presence of non-neutral wetting and complex geometries. We quantify the accuracy of a volume-of-fluid (VOF) formulation, implemented in a popular open-source computational fluid dynamics code, compared with a new formulation of a level set (LS) method, specifically developed for quasi-static capillarity-dominated displacement. The methods are tested in rhomboidal packings of spheres for a range of contact angles and for different rhomboidal configurations and the accuracy is evaluated against the semi-analytical solutions obtained by Mason and Morrow (1994). While the VOF method is implemented in a general purpose code that solves the full Navier-Stokes (NS) dynamics in a finite volume formulation, with additional terms to model surface tension, the LS method is optimized for the quasi-static case and, therefore, less computationally expensive. To overcome the shortcomings of the finite volume NS-VOF system for low capillary number flows, and its computational cost, we introduce an overdamped dynamics and a local time stepping to speed up the convergence to the steady state, for every given imposed pressure gradient (and therefore saturation condition). Despite these modifications, the methods fundamentally differ in the way they capture the interface, as well as in the number of equations solved and in the way the mean curvature (or equivalently capillary pressure) is computed. This study is intended to provide a rigorous validation study and gives important indications on the errors committed by these methods in solving more complex geometry and dynamics, where usually many sources of errors are interplaying.

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.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Direct Assembly of Magnetic Janus Particles at a Droplet Interface

Self-assembly of nanoparticles at fluid-fluid interfaces is a promising route to fabricate functional materials from the bottom-up. However, directing and controlling particles into highly tunable and predictable structures, while essential, is a challenge. We present a liquid interface assisted approach to fabricate nanoparticle structures with tunable properties. To demonstrate its feasibility, we study magnetic Janus particles adsorbed at the interface of a spherical droplet placed on a substrate. With an external magnetic field turned on, a single particle moves to the location where its position vector relative to the droplet center is parallel to the direction of the applied field. Multiple magnetic Janus particles arrange into reconfigurable hexagonal lattice structures and can be directed to assemble at desirable locations on the droplet interface by simply varying the magnetic field direction. We develop an interface energy model to explain our observations, finding excellent agreement. Finally, we demonstrate that the external magnetic field allows one to tune the particle deposition pattern obtained when the droplet evaporates. Our results have implications for the fabrication of varied nanostructures on substrates for use in nanodevices, organic electronics, or advanced display, printing, and coating applications.

Insights into the Impact of Surface Hydrophobicity on Droplet Coalescence and Jumping Dynamics

Droplet coalescence jumping on superhydrophobic surfaces attracts much research attention owing to its capability in enhancing condensation for energy and water applications. In this work, we reveal the impact of the finite surface adhesion to explain velocity discrepancies observed in recent droplet jumping studies, particularly when droplet sizes are a few micrometers (1-10 μm). Surface adhesion, which is usually neglected, can significantly affect both droplet coalescence and departure dynamics. It causes oscillations on velocity and contact area in the droplet coalescence process, as observed numerically and experimentally. Comparing the increasing rate of jumping velocity with contact angle for three different droplet sizes, we show that smaller droplets exhibit higher sensitivity to the change of surface hydrophobicity. We also specify the range of surface superhydrophobicity where the jumping velocity monotonically decreases (θ ≳ 170°), increases (θ ≲ 160°), or changes non-monotonically in transition (160° ≲ θ ≲170°) with droplet size. As a result, there exists a broad jumping velocity range for micrometer-sized droplets on a superhydrophobic surface with a slight contact angle variation. This work offers an extended understanding of the droplet coalescence and jumping dynamics to resolve the discrepancies in recent experimental observations.

Direction Dependence of Adhesion Force for Droplets on Rough Substrates

Determination of solid surface free energy is still an open problem. At present, there are two leading theories on how to determine the adhesion of droplets on rough substrates: one theory stresses that the droplet adhesion force lies in the areas of contact and interaction energy between liquid and solid molecules, whereas the other holds that the length of the edge of drops is essential. In this work, we unify the two theories through lattice Boltzmann simulations and demonstrate that the adhesion force could depend on either the contact area or the contact line, depending on the direction of the adhesion force measured, that is, by vertically separating the two materials or laterally sliding the droplet on the substrate. We reveal that for separating droplets away from rough substrates, the vertical adhesion (pull-off) force depends more significantly on the contact area rather than on the contact line. However, for sliding a droplet on substrates, the lateral adhesion force depends on the contact line while being independent of the contact area.

Contact angle adjustment in equation-of-state-based pseudopotential model

The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

Bubble accumulation and its role in the evolution of magma reservoirs in the upper crust

Volcanic eruptions transfer huge amounts of gas to the atmosphere. In particular, the sulfur released during large silicic explosive eruptions can induce global cooling. A fundamental goal in volcanology, therefore, is to assess the potential for eruption of the large volumes of crystal-poor, silicic magma that are stored at shallow depths in the crust, and to obtain theoretical bounds for the amount of volatiles that can be released during these eruptions. It is puzzling that highly evolved, crystal-poor silicic magmas are more likely to generate volcanic rocks than plutonic rocks. This observation suggests that such magmas are more prone to erupting than are their crystal-rich counterparts. Moreover, well studied examples of largely crystal-poor eruptions (for example, Katmai, Taupo and Minoan) often exhibit a release of sulfur that is 10 to 20 times higher than the amount of sulfur estimated to be stored in the melt. Here we argue that these two observations rest on how the magmatic volatile phase (MVP) behaves as it rises buoyantly in zoned magma reservoirs. By investigating the fluid dynamics that controls the transport of the MVP in crystal-rich and crystal-poor magmas, we show how the interplay between capillary stresses and the viscosity contrast between the MVP and the host melt results in a counterintuitive dynamics, whereby the MVP tends to migrate efficiently in crystal-rich parts of a magma reservoir and accumulate in crystal-poor regions. The accumulation of low-density bubbles of MVP in crystal-poor magmas has implications for the eruptive potential of such magmas, and is the likely source of the excess sulfur released during explosive eruptions.

Droplets Can Rebound toward Both Directions on Textured Surfaces with a Wettability Gradient

The impact of water droplets on superhydrophobic surfaces with a wettability gradient is studied using the lattice Boltzmann simulation. Droplets impacting such textured surfaces have been previously reported to rebound obliquely following the wettability gradient due to the unbalanced interfacial forces created by the heterogeneous architectures. Here we demonstrate that droplets can rebound toward both directions on textured surfaces with a wettability gradient. Our simulation results indicate that the rebound trajectory of droplets is determined by the competition between the lateral recoil of the liquid and the penetration and capillary emptying of the penetrated liquid from the textures in the vertical direction. When the time scale for the droplet penetration and capillary emptying process is smaller than the time for the lateral spreading, the droplet will rebound following the wettability gradient. By contrast, the droplet will display a bouncing against the wettability gradient direction because of the significant capillary penetration and emptying in the transverse direction. We believe that our study provides important insight for the design of micro/nanotextured surfaces for controlled droplet manipulation.

Elucidating Nonwetting of Re-Entrant Surfaces with Impinging Droplets

Superomniphobic surfaces display both superoleophobic and superhydrophobic properties, having a contact angle greater than 150° for both water and oil droplets. In this work, lattice Boltzmann simulations on droplets impacting the surface textures of various topologies are performed to understand the mechanism of how the superomniphobic properties can be achieved by optimizing the geometry of re-entrant surfaces and the inherent hydrophobicity of substrates. Detailed kinetics for droplet impinging is analyzed for both liquid impalement and emptying, showing distinct dependences on geometrical details of re-entrant surfaces. The origins of the enhanced stability of Cassie states are ascribed to (i) the barrier of the Cassie-to-Wenzel transition for the impalement process, (ii) the driving force for liquid receding in the emptying process, and (iii) the contact line pinning from the entrance effect and the edge effect. Finally, we check the strategies proposed here by designing a new re-entrance structure that possesses an excellent property in maintaining the droplet Cassie state.

Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces

The recently introduced entropic lattice Boltzmann model (ELBM) for multiphase flows [A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015)] is extended to the simulation of dynamic fluid-solid interface problems. The thermodynamically consistent, nonlinearly stable ELBM together with a polynomial representation of the equation of state enables us to investigate the dynamics of the contact line in a wide range of applications, from capillary filling to liquid drop impact onto a flat surfaces with different wettability. The static interface behavior is tested by means of the liquid column in a channel to verify the Young-Laplace law. The numerical results of a capillary filling problem in a channel with wettability gradient show an excellent match with the existing analytical solution. Simulations of drop impact onto both wettable and nonwettable surfaces show that the ELBM reproduces the experimentally observed drop behavior in a quantitative manner. Results reported herein demonstrate that the present model is a promising alternative for studying the vapor-liquid-solid interface dynamics.

Effect of PEO coating on bubble behavior within a polycarbonate microchannel array: A model for hemodialysis

Obstruction of fluid flow by stationary bubbles in a microchannel hemodialyzer decreases filtration performance and increases damage to blood cells through flow maldistribution. A polyethylene oxide (PEO)-polybutadiene (PB)-polyethylene oxide surface modification, previously shown to reduce protein fouling and water/air contact angle in polycarbonate microchannel hemodialyzers, can improve microchannel wettability and may reduce bubble stagnation by lessening the resistive forces that compete with fluid flow. In this study, the effect of the PEO-PB-PEO coating on bubble retention in a microchannel array was investigated. Polycarbonate microchannel surfaces were coated with PEO-PB-PEO triblock polymer via radiolytic grafting. Channel obstruction was measured for coated and uncoated microchannels after injecting a short stream of air bubbles into the device under average nominal water velocities of 0.9 to 7.2 cm/s in the channels. The presence of the PEO coating reduced obstruction of microchannels by stationary bubbles within the range of 1.8 to 3.6 cm/s, average nominal velocity. Numerical simulations based on the lattice Boltzmann method indicate that beneficial effects may be due to the maintenance of a lubricating, thin liquid film around the bubble. The determined effective range of the PEO coating for bubble management serves as an important design constraint. These findings serve to validate the multiutility of the PEO-PB-PEO coating (bubble lubrication, biocompatibility, and therapeutic loading). © 2015 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 104B: 941-948, 2016.

Numerical Study of the Influence of Cavity on Immiscible Liquid Transport in Varied-Wettability Fractures

Field evidence indicates that cavities often occur in fractured rocks, especially in a Karst region. Once the immiscible liquid flows into the cavity, the cavity has the immiscible liquid entrapped and results in a low recovery ratio. In this paper, the immiscible liquid transport in cavity-fractures was simulated by Lattice Boltzmann Method (LBM). The interfacial and surface tensions were incorporated by Multicomponent Shan-Chen (MCSC) model. Three various fracture positions were generated to investigate the influence on the irreducible nonwetting phase saturation and displacement time. The influences of fracture aperture and wettability on the immiscible liquid transport were discussed and analyzed. It was found that the cavity resulted in a long displacement time. Increasing the fracture aperture with the corresponding decrease in displacement pressure led to the long displacement time. This consequently decreased the irreducible nonwetting phase saturation. The fracture positions had a significant effect on the displacement time and irreducible saturation. The distribution of the irreducible nonwetting phase was strongly dependent on wettability and fracture position. Furthermore, this study demonstrated that the LBM was very effective in simulating the immiscible two-phase flow in the cavity-fracture.

Lattice Boltzmann modeling of droplet condensation on superhydrophobic nanoarrays

Droplet nucleation and growth on superhydrophobic nanoarrays is simulated by employing a multiphase, multicomponent lattice Boltzmann (LB) model. Three typical preferential nucleation modes of condensate droplets are observed through LB simulations with various geometrical parameters of nanoarrays, which are found to influence the wetting properties of nanostructured surfaces significantly. The droplets nucleated at the top of posts (top nucleation) or in the upside interpost space of nanoarrays (side nucleation) will generate a nonwetting Cassie state, while the ones nucleated at the bottom corners between the posts of nanoarrays (bottom nucleation) produce a wetting Wenzel state. The simulated time evolutions of droplet pressures at different locations are analyzed, which offers insight into the underlying physics governing the motion of droplets growing from different nucleation modes. It is demonstrated that the nanostructures with taller posts and a high ratio of post height to interpost space (H/S) are beneficial to produce the top- and side-nucleation modes. The simulated wetting states of condensate droplets on the nanostructures, having various geometrical configurations, compare reasonably well with experimental observations. The established relationship between the geometrical parameters of nanoarrays and the preferential nucleation modes of condensate droplets provides guidance for the design of nanoarrays with desirable anticondensation superhydrophobic properties.

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.

Beyond Cassie equation: local structure of heterogeneous surfaces determines the contact angles of microdroplets

The application of Cassie equation to microscopic droplets is recently under intense debate because the microdroplet dimension is often of the same order of magnitude as the characteristic size of substrate heterogeneities, and the mechanism to describe the contact angle of microdroplets is not clear. By representing real surfaces statistically as an ensemble of patterned surfaces with randomly or regularly distributed heterogeneities (patches), lattice Boltzmann simulations here show that the contact angle of microdroplets has a wide distribution, either continuous or discrete, depending on the patch size. The origin of multiple contact angles observed is ascribed to the contact line pinning effect induced by substrate heterogeneities. We demonstrate that the local feature of substrate structure near the contact line determines the range of contact angles that can be stabilized, while the certain contact angle observed is closely related to the contact line width.