Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

TL;DR

This paper introduces a pore-scale modeling method for viscous flow in dense sphere packings, accurately estimating forces on particles and permeability, validated against detailed FEM simulations.

Contribution

The paper presents a novel upscaling approach using pore-level equations and Delaunay triangulation for dense sphere packings, improving force and permeability predictions.

Findings

Good agreement with FEM simulations in force calculations

Accurate permeability coefficients obtained

Applicable to large random sphere assemblies

Abstract

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.