Related papers: A Mathematical Model for Two Solutes Transport in …
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was…
We present the state-of-the-art theoretical modeling, molecular simulation, and coarse-graining strategies for the transport of gases and liquids in nanoporous materials (pore size 1-100 nm). Special emphasis is placed on the transport of…
We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…
In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are…
This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists…
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…
Mechanical properties of cellular structures, including the cell cytoskeleton, are increasingly used as biomarkers for disease diagnosis and fundamental studies in cell biology. Recent experiments suggest that the cell cytoskeleton and its…
The paper provides a macro-microscopic coupled constitutive model for fluid-saturated porous media with respect to the compressibility of the solid skeleton, the real solid material and the fluid phase. The derivation of the model is…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particles trajectories, we derive the corresponding governing equations for the concentration of the mobile and…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
We present and derive a novel double-continuum transport model based on pore-scale characteristics. Our approach relies on building a simplified unit cell made up of immobile and mobile continua. We employ a numerically resolved pore-scale…
In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
A mathematical model is developed to analyze the growth/decay rate of surface perturbations of an ultrathin metal film on an amorphous substrate (SiO_{2}). The formulation combines the approach of Mullins [J. Appl. Phys. v30, 77, 1959] for…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…