We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of f-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the...

We consider a system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition ux = vx , v = ψ(u) on the contact line S. First we prove existence and uniqueness of a solution (u, v) on a bounded domain. Furthermore, we are interested in the behaviour of the interface of the porous medium equation when it crosses t...

We address the small-time evolution of interfaces (fronts) for the pseudoparabolic generalization ∂u ∂t = ∂ ∂x ( u ∂u ∂x + u ∂2u ∂x∂t ) of the porous-medium equation, identifying regimes in which the local behavior remains fixed for some finite time and others in which it changes instantaneously. A number of phenomena beyond those exhibited by the porous-medium equation are elucidated, includin...

Abstract. The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem in a Gelfand triple with the pivot space H. This allows to employ methods of the theory of monotone operators in order to study fully discrete approximations combining a Galerkin method (including conforming finite element methods) with the backward Euler scheme. Convergence is shown eve...

We construct global L∞ entropy weak solutions to the initial boundary value problem for the damped compressible Euler equations on bounded domain with physical boundaries. Time asymptotically, the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical Darcy’s law. Based on entropy principle, we showed that the physical weak solutions converges to st...

A numerical investigation of jamming effect during the spontaneous interparticle percolation process of small beads through an unconsolidated porous media has been performed. The size ratio between the moving beads and the ones building up the porous medium was chosen larger than the geometrical trapping threshold: ξ(c)=(2/√3]-1)(-1)=6.464.... In this paper, we used the discrete element method ...

The purpose of this study is to quantify experimentally the evolution of dissolved species in porous media from 2D resistivity models. Transport experiments are carried out at the laboratory scale by performing flow in a model porous medium obtained by filling a transparent container with mono disperse glass beads. A tracer made by mixing a dissolved of blue dye and a known NaCl concentration i...

We consider a fractured porous medium that is studied at a scale such that the fractures can be modeled individually. Models for flow in which the fractures are interfaces between subdomains are presented. These models take into account interactions between the fractures and the surrounding porous medium. Existence and uniqueness of the solution to the model problem are proved. Error estimates ...

Unsteady mixed convection flows in a lid-driven square cavity filled with a fluid-saturated porous medium is investigated numerically. The two vertical walls of the enclosure are insulated while the bottom wall is cooled. The top wall is heated sinusoidally and moving at a constant speed. The governing equations are solved numerically by using finite volume method with SIMPLE algorithm. The res...

A free convective unsteady visco-elastic flow through porous medium bounded by an infinite vertical porous plate with variable suction, constant heat flux under the influence of transverse uniform magnetic field along with permeability in the presence of radiation has been investigated in the present study. The suction velocity of the porous medium fluctuates with time about the constant mean. ...