Related papers: Towards a quantitative phase-field model of two-ph…
Stably stratified fluids subject to sustained forcing are known to develop step-like density "staircases", where nearly homogeneous layers alternate with thin interfaces of strong stratification. However, long-time numerical investigations…
The diffuse-interface model for two-phase flows with soluble surfactants has garnered considerable attention due to its ability to circumvent the need for Robin boundary condition in the bulk surfactant transport equation. However, the…
We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…
The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase…
Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can…
We consider the interaction between a free flowing fluid and a porous medium flow, where the free flowing fluid is described using the time dependent Stokes equations, and the porous medium flow is described using Darcy's law in the primal…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…
Based on the two-phase macroscopic governing equations in the phase field model, the governing equations and analytical solutions for the steady-state layered Poiseuille flows in the diffuse interface (DI) model are derived and analyzed.…
The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn-Hilliard Volume-of-Fluid model to capture the dynamics of the air-sea interface at geophysically relevant Reynolds numbers. It…
In the above paper the authors treat the boundary layer flow along a stationary, vertical, permeable, flat plate within a vertical free stream. Fluid is sucked or injected through the vertical plate. The fluid species concentration at the…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…
We find actual evidence, relying upon vorticity time series taken in a high Reynolds number atmospheric experiment, that to a very good approximation the surface boundary layer flow may be described, in a statistical sense and under certain…
Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
We present a mesoscopic model, based on the Boltzmann Equation, for the interaction between a solid wall and a non-ideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas,…
We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate production codes. We focus on the interface between the vapor and…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…