A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor-Couette test case. To impose the boundary condition when the fluid-fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated

Interface-Resolving Simulations of Gas-Liquid Two-Phase Flows in Solid Structures of Different Wettability

This PhD study is devoted to numerical investigations of two-phase flows on and through elementary and complex solid structures of varying wettability. The phase-field method is developed and implemented in OpenFOAM®. The numerical method/code is verified by a series of test cases of two-phase flows, and then applied to investigate: (1) droplet wetting on solid surfaces; (2) air bubble rising and interacting with cellular structures and (3) gas-liquid interfacial flows in foam structures

A new approach for the implementation of contact line motion based on the phase-filed lattice Boltzmann method

This paper proposes a new strategy to implement the free-energy based wetting boundary condition within the phase-field lattice Boltzmann method. The greatest advantage of the proposed method is that the implementation of contact line motion can be significantly simplified while still maintaining good accuracy. For this purpose, the liquid-solid free energy is treated as a part of the chemical potential instead of the boundary condition, thus avoiding complicated interpolations with irregular geometries. Several numerical testing cases including the droplet spreading processes on the idea flat, inclined and curved boundaries are conducted, and the results demonstrate that the proposed method has good ability and satisfactory accuracy to simulate contact line motions

A simulation method for the wetting dynamics of liquid droplets on deformable membranes

Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios

A fully Eulerian hybrid immersed boundary-phase field model for contact line dynamics on complex geometries

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few)

A thermodynamically consistent diffuse interface model for the wetting phenomenon of miscible and immiscible ternary fluids

The wetting effect has attracted great scientific interest because of its natural significance as well as technical applications. Previous models mostly focus on one-component fluids or binary immiscible liquid mixtures. Modelling of the wetting phenomenon for multicomponent and multiphase fluids is a knotty issue. In this work, we present a thermodynamically consistent diffuse interface model to describe the wetting effect for ternary fluids, as an extension of Cahn\u27s theory for binary fluids. In particular, we consider both immiscible and miscible ternary fluids. For miscible fluids, we validate the equilibrium contact angle and the thermodynamic pressure with Young\u27s law and the Young–Laplace equation, respectively. Distinct flow patterns for dynamic wetting are presented when the surface tension and the viscous force dominate the wetting effect. For immiscible ternary fluids, we manipulate the wettability of two contact droplets deposited on a solid substrate according to three scenarios: (I) both droplets are hydrophilic; (II) a hydrophilic droplet in contact with a hydrophobic one; (III) both droplets are hydrophobic. The contact angles at each triple junction from the simulations are compared with Young\u27s contact angle and Neumann\u27s triangle rule. Simulations for the validation of our work are performed in two and three dimensions. In addition, we model the evaporation process of a ternary droplet and obtain the same power law as that of previous experiments. Our model allows one to relate the interfacial energies with surface composition, enabling the modelling of the coffee-ring phenomenon in further perspective