Related papers: Including van der Waals Forces in Diffusion-Convec…
The work investigates a model that combines a convection-diffusion-reaction equation for solute concentration with an unsteady Darcy-Brinkman equation for the flow field, including the Kortweg stress. Additionally, the flow field…
In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
We discuss a class of diffusion-type partial differential equations on a bounded interval and discuss the possibility of replacing the boundary conditions by certain linear conditions on the moments of order 0 (the total mass) and of…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
We perform linear and nonlinear stability analysis for thermal convection in a fluid overlying a saturated porous medium. We use a coupled system, with the Navier-Stokes equations and Darcy's equation governing the free-flow and the porous…
In this paper we reconsider the classical nonlinear diffusivity equation of real gas in an heterogenous porous medium in light of the recent studies about the generalized fractional equation of conservation of mass. We first recall the…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
A bidisperse porous medium is one with two porosity scales. There are the usual pores known as macro pores but also cracks or fissures in the skeleton which give rise to micro pores. In this article we develop and analyse a model for…
We present a theoretical study of wetting phenomena and interactions between liquid-vapor interfaces based on the density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid…
Studies of the transport of wet water vapour are relevant for various areas of human activity, including the construction and production of building materials, mining, agriculture, environmental safety of technological processes, scientific…
Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the…
In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of…
In this article, a finite element model is implemented to analyze hydro-thermal convective flow in a porous medium. The mathematical model encompasses Darcy's law for incompressible fluid behavior, which is coupled with a…
In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…