A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but also able to handle arbitrarily complex boundaries with prescribed contact angles. The developed method is first validated by the simulation of a Janus droplet resting on a flat surface, a perfect Janus droplet deposited on a cylinder, and the capillary intrusion of ternary fluids for various viscosity ratios. It is then used to study a compound droplet subject to a uniform incoming flow passing through a multi-pillar structure, where three different values of surface wettability are considered. The simulated results show that the surface wettability has significant impact on the droplet dynamic behavior and final fluid distribution.
The boundary treatment is fundamental for modeling fluid flows; especially, in the lattice Boltzmann method, the curved boundary conditions effectively improve the accuracy of single-phase simulations with complex-geometry boundaries. However, the conventional curved boundary conditions usually cause dramatic mass leakage or increase when they are directly used for multiphase flow simulations. We find that the principal reason is the absence of nonideal effect in the curved boundary conditions, followed by the calculation error. In this paper, incorporating the nonideal effect into the linear …
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, measuring contact angles in experiments and simulations is still complicated and time-consuming. In this paper, we present an efficient scheme for the real-time and on-the-spot measurement of contact angles on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions by the spherical cap method without conside…
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends …
We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite differenc…
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…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional hydrodynamic model for the velocity field at a contact point moving with constant velocity over a curved wall. The model is a perturbation of the classical Huh and Scriven hydrodynamic solution [11], which is only valid for flow over a flat wall. The purpose of the hydrodynamic model is to investigate the macroscopic behavior of the fluids close to a contact point. …
In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid-structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid…
Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily-shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups, and …
We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on a manifestly Galilean covariant modeling of the Navier-Stokes equations. The simulation of the magnetic induction equation within the lattice-Boltzmann approach to MHD has been usually devised along the lines of the simplest phenomenological description, the single relaxation time (SRT) model. In order to deal with well-known stability difficulties of the SRT framework, we introduce, alternatively, a multi-relaxation-time technique f…
The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits com…
Applying contact angles based on a continuously moving contact line in 2D VOF simulations
University of Chinese Academy of Sciences（中国科学院大学）；Sorbonne Université（索邦大学）；Xi’an Jiaotong University（西安交通大学）；Institut Universitaire de France（法国高等学术研究院）
We present a two-way coupled fluid-structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. Arbitrary Lagrangian-Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in a combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately desc…
We investigate Poiseuille channel flow through intrinsically curved media, equipped with localized metric perturbations. To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the parameters of the metric perturbations (amplitude, range and density). We find that the flux depends only on a specific combination of parameters, which we identify as the average metric perturbation, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently develop…
An improved wetting boundary implementation strategy is proposed based on lattice Boltzmann color-gradient model in this paper. In this strategy, an extra interface force condition is demonstrated based on the diffuse interface assumption and is employed in contact line region. It has been validated by three benchmark problems: static droplet wetting on a flat surface and a curved surface, and dynamic capillary filling. Good performances are shown in all three cases. Relied on the strict validation to our scheme, the viscous fingering phenomenon of immiscible fluids displacement in a two-dimen…
We use a hybrid method of lattice Boltzmann and finite differences to simulate flat and curved interfaces between the nematic and isotropic phases of a liquid crystal described by the Landau-de Gennes theory. For the flat interface, we measure the interfacial velocity at different temperatures around the coexistence. We show that the interface is completely static at the coexistence temperature and that the profile width is in line with the theoretical predictions. The interface is stable in a range of temperatures around coexistence and disappears when one of the two phases becomes mechanical…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent Lattice Boltzmann are accurate when the wall is aligned with the main axes of the lattice but fail otherwise. To solve this problem, we extend a strategy previously developed for multiphase models. As an example, we study the coalescence of two droplets on a curved surface in two dimensions. The strategy proposed here is of special relevance for binary flows in …
An algorithm is proposed to implement unsteady jump boundary conditions, presenting discontinuity in physical quantities, within the lattice Boltzmann method (LBM). This is useful to tackle problems involving mass or heat transfer through interfaces or membranes that exhibit resistance to transport. The algorithm is simple to implement within an existing LBM based code that computes diffusion and advection of a scalar field, either temperature or solute concentration. Analytical solutions are recovered numerically with acceptable accuracy for the limiting case of a planar membrane. The algorit…
We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In this paper we have excluded the heat transfer between two phases. The interface boundary conditions for the liquid and gas phases is presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction since the droplet moves inside the gas phase and its interface deforms with respect to time and space. Therefore, the similar meshfre…
We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to $10^3$. Subsequentl…
Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equations applicability for arbitrarily curved surface has been long debated and is a sever problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to static shapes and modelling the pressure at the interface nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale…
The LBM is combined with the Volume Penalization (VP LBM) approach to simulate flows in the presence of obstacles. The single relaxation time LBM and the multiple relaxation time LBM are used. For cases where the fluid motion is enhanced by moving boundaries, the comparison of our results with analytical results is satisfactory. The flow around a cylinder at a relatively high Reynolds number is also calculated. For that case,the VP LBM method was parallelized. A comparison of our results with those found in the literature, demonstrates the reliability of the VP LBM to treat complex flows.
Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible character of the problem. Using the example of a spherical surface, we demonstrate that the swimmer performance that follows this "Randers policy" always beats a more direct policy. A study of the shape of …
