Related papers: Describing diffusion, reaction and convection on p…

In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The…

We present a theoretical model describing the current transient behavior observed during electrodeposition in an opal modified electrode. As a basic unit we consider a cylindrical vessel with a porous and corrugated surface, whose radius…

The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…

Opals are structures composed of the closed packing of spheres in the size range of nano-to-micro meter. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation…

In a recent paper [1] we developed a theoretical model to describe current transients arising during electrochemical deposition experiments performed at the bottom of sub-micrometric cylindrical vessels with permeable walls. In the present…

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…

Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…

We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is…

Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…

This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution…

We propose an analytical model based on diffusion-reaction equation approach for electrochemical electron transfer reaction, where the rate is limited by the electron transfer process. The electron transfer from an ion in solution to the…

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical…

A cross-diffusion system describing ion transport through biological membranes or nanopores in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. The ion concentrations solve strongly coupled diffusion equations…

We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…

Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…

In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…

We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…