Population balance models for particulate flows in porous media:breakage and shear-induced events

TL;DR

This paper develops a multiscale population balance model for particulate flows in porous media, incorporating aggregation, breakage, and shear effects, with derivations for macroscopic descriptions from pore-scale dynamics.

Contribution

It introduces a novel framework for upscaling particle transport models in porous media, including a new collision-induced breakage mechanism and shear-dependent processes.

Findings

Derived upscaled breakage frequencies for different geometries

Presented results for 2D channel and 3D sphere arrangements

Analyzed shear-induced collision effects in particulate flows

Abstract

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from non-linear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.