Related papers: On a thermodynamic framework for developing bounda…
We present an explicit finite difference method to simulate the non-ideal multi-phase fluid flow. The local density and the momentum transport are modeled by the Navier-Stokes (N-S) equations and the pressure is computed by the Van der…
Following a cell-method due to van Kampen for the calculation of a coarse-grained free energy functional for the van der Waals gas, we compute a corresponding entropy functional from microscopic principles. This entropy functional is one of…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
Within the theory of interacting continua, we develop a model for a heat conducting mixture of two interacting fluids described in terms of the densities and the velocities for each fluid and the temperature field for the mixture as a…
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
In most electronic devices, electric current of both types (electrons and holes) flows through a junction. Usually the boundary conditions have been formulated exclusively for open circuit. The boundary conditions proposed here bypass this…
The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical effects: convection, diffusion and capillary…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
In this paper, we consider a resolvent problem arising from the free boundary problem for the compressible fluid model of the Korteweg type, which is called the Navier-Stokes-Korteweg system, with surface tension in general domains. The…
A general diffuse interface model with a realistic equation of state (e.g. Peng-Robinson equation of state) is proposed to describe the multi-component two-phase fluid flow based on the principles of the NVT-based framework which is a…
A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal…
We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous…
We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition,…
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…
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,…
The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for…
Based on a rigorous thermodynamic framework, this work develops a two-fluid magnetohydrodynamic model grounded in the Helmholtz free energy formalism. The model maintains full thermodynamic consistency by simultaneously satisfying energy…