Renormalization Group Approach to the Problem of Flow Through Irregular Packed Beds

TL;DR

This paper develops a renormalization group method to analyze nonlinear diffusion in irregular packed beds, accounting for strong porosity fluctuations and providing asymptotic solutions for flow behavior.

Contribution

It introduces a novel renormalization group approach to model flow through irregular packed beds with strong porosity fluctuations, extending analysis to arbitrary dimensions and covariance structures.

Findings

Derived asymptotic Green's function for nonlinear diffusion in porous media.

Established the effect of porosity fluctuations on flow asymptotics.

Provided a general framework applicable to various dimensions and fluctuation covariances.

Abstract

We have calculated the asymptotics of Green's function of the differential equation of nonlinear diffusion in the microscopic range with strong porosity fluctuations in the problem of flow through irregular packed beds for arbitrary space dimension and arbitrary covariance of porosity fluctuations.