Simulation of Flow of Mixtures Through Anisotropic Porous Media using a Lattice Boltzmann Model

TL;DR

This paper introduces a lattice Boltzmann model for simulating the transient flow of miscible and immiscible fluid mixtures through anisotropic porous media, incorporating hydrodynamics, diffusion, surface tension, and viscosity variations.

Contribution

It presents a novel LB-based simulation framework capable of modeling complex fluid interactions and porous structures, validated on standard and real-world geometries.

Findings

Model accurately reproduces Poiseuille flow and drop-interface interactions.

Successfully simulates fluid invasion in wood samples.

Handles viscosity variations and surface tension effects.

Abstract

We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations to consider various types of hardening fluids. The miscible mixture consists of two fluids, one governed by the hydrodynamic equations and one by diffusion equations. We validate our model on standard problems like Poiseuille flow, the collision of a drop with an impermeable, hydrophobic interface and the deformation of the fluid due to surface tension forces. To demonstrate the applicability to complex geometries, we simulate the invasion process of mixtures into wood spruce samples.