Related papers: Coarse-grained description of thermo-capillary flo…
In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component…
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped…
We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase field approach is…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
A liquid in Cassie-Baxter state above a structured superhydrophobic surface is ideally suited for surface driven transport due to its large free surface fraction in close contact to a solid. We investigate thermal Marangoni flow over a…
We study a system describing the dynamics of a two-phase flow of incompressible viscous fluids influenced by the convective heat transfer of Caginalp-type. The separation of the fluids is expressed by the order parameter which is of diffuse…
The transient thermocapillary migration of drops with nontrivial deformation is studied. The finite difference method is employed to solve the incompressible Navier-Stokes equations coupled with the energy equation; the front-tracking…
A novel way to handle surface tension gradient driven flows is developed in the volume-of-fluid (VoF) framework. Using an open source Navier-Stokes solver, {\it Basilisk}, and the present formulation, we investigate thermocapillary…
We consider a model of a two phase flow proposed by Anderson, McFadden and Wheeler taking into account possible thermal fluctuations. The mathematical model consists of the compressible Navier-Stokes system coupled with the Cahn-Hilliard…
A systematic theoretical study of temperature-gradient-induced electrokinetic flow and thermoelectric potential of electrolyte solutions in a micro-/nanocapillary is presented. The study is based on a semi-analytical model developed by…
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
We use the Navier-Stokes-Cahn-Hilliard model equations to simulate phase separation with flow. We study coarsening - the growth of extended domains wherein the binary mixture phase separates into its component parts. The coarsening is…
In this article we calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In a first stage we study the semi-infinite system consisting of an isotropic fluid in contact with a single hard…
The computational study of strongly-coupled, gas-solid flows at scales relevant to most environmental and engineering applications requires the use of `coarse-grained' methodologies such as the two-fluid model, particle-in-cell approach or…
We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…
The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid…