Efflorescence refers to crystallized salt structures that form at the surface of a porous medium. The challenge is to understand why these structures do not form everywhere at the surface of the porous medium but at some specific locations and why there exists an exclusion distance around an efflorescence where no new efflorescence forms. These are explained from a visualization experiment, por...

To improve the feasibility of soil-aquifer remediation using bioaugmentation, more efficient methods are needed to widely disperse pollutant-degrading bacteria in porous media. Under water-saturated conditions, bacteria readily adhere to soil particles, but under unsaturated conditions, bacteria preferentially accumulate at the air-water interface. Air sparging a saturated porous medium produce...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...

A simplified model for bacterial remediation of wastes in a porous medium is proposed. The mathematical model consists of a coupled set of nonlinear partial differential equations and an ordinary differential equation. Basic existence, uniqueness and regularity of the system can be proved in three space dimensions, globally in time. The existence of traveling waves can also be established. In a...

We study the existence of solutions to the porous medium equation with a nonnegative, finite Radon measure on the right hand side. We show that such problems have solutions in a wide class of supersolutions. These supersolutions are defined as lower semicontinuous functions obeying a parabolic comparison principle with respect to continuous solutions. We also consider the question of how the in...

Sponge phases are phases of randomly connected membranes. We

The purpose of the present paper is to study an unsteady laminar flow of an incompressible conducting viscous dusty fluid between two infinitely non-conducting parallel plates, where above plate is bounded by porous medium. The flow is influenced by pulsatile pressure gradient, uniform magnetic field which is applied perpendicular to the plates and due to oscillations of the plates under the ef...

Porous medium vacuum drying is a complicated heat and mass transfer process. Based on the theory of heat and mass transfer, a coupled model for the porous medium vacuum drying process is constructed. The model is implemented and solved using COMSOL software. The water evaporation rate is determined using a nonequilibrium method with the rate constant parameter Kr. Kr values of 1, 10, 1000, and ...

The thin film and quantum drift diffusion equations belong to a fourth-order family of evolution equations proposed in [21] to be analogous to the (second-order) porous medium family. They are 2Wasserstein (= d2) gradient flows of the generalized Fisher information I(v) just as the porous medium family was shown to be the d2 gradient flow of the generalized entropy E(v) by Otto [40]. The identi...

the effect of different juice extraction treatments on the qualitative properties of lime juice was investigated. samples were selected from jahromi lime variety and lime juice extracted by means of a screw type juice extraction device. the mechanical parameters of the helical juice extractor [screw velocity (270, 360 and 450 rpm), outlet pressure (minimum, medium vs. maximum)] and lime pretrea...