相关论文: Integral Representation of Hydraulic Permeability
A concentration difference of particles across a membrane perforated by pores will induce a diffusive flux. If the diffusing objects are of the same length scale as the the pores, diffusion may not be simple, objects can move into the pore…
This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $\rho$ within the water-air interface is assumed to…
Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational…
A fluid in a pore can form diverse heterogeneous structures. We combine a capillary description with the cubic-plus-association equation of state to study the thermodynamic stability of droplets, bubbles and films of water at 358 K in a…
Magnetohydrodynamically induced interface instability in liquid metal batteries is analyzed. The batteries are represented by a simplified system in the form of a rectangular cell, in which strong vertical electric current flows through…
The transport properties of one-dimensional Fermi gases at low-temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipation one needs to examine interactions beyond the LL model. In this work we provide…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…
We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion, surface…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane $\mathbb{R}^2$ or a bounded strip…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
We prove a local variant of Einstein's formula for the effective viscosity of dilute suspensions, that is $\mu^\prime=\mu (1+\frac 5 2\phi+o(\phi))$, where $\phi$ is the volume fraction of the suspended particles. Up to now rigorous…
We consider a fluid of $d$-dimensional spherical particles interacting via a pair potential $\phi(r)$ which takes a finite value $\epsilon$ if the two spheres are overlapped ($r<\sigma$) and 0 otherwise. This penetrable-sphere model has…