Dynamics of suspended rigid aggregating particles in flowing medium: theory, analysis and scientific computing

TL;DR

This paper presents a comprehensive multi-scale model to analyze the dynamics of rigid aggregating particles in viscous flow, integrating micro-scale adhesion kinetics, meso-scale distribution evolution, and macro-scale equation-free patch methods.

Contribution

It introduces a unified multi-scale framework combining micro, meso, and macro scales for particle aggregation in flow, including an equation-free macro domain approach.

Findings

The model captures collision and aggregation dynamics accurately.

The micro-meso coupling effectively links adhesion kinetics with particle size evolution.

The macro domain simulation demonstrates efficient multiscale analysis.

Abstract

We develop and present a unified multi-scale model (involving three scales of spatial organisation) to study the dynamics of rigid aggregating particles suspended in a viscous fluid medium and subject to a steady poiseuille flow. At micro-level, the theory of adhesion describing the attachment / detachment kinetics of two rigid spheres coated with binding ligands, is utilized to describe the collision frequency function. The meso-scale dynamics is outlined through a continuous general dynamic equation governing the time rate of change of the particle size distribution function. The micro-meso coupling is achieved via the balancing of the mesoscale drag forces and couples with the micro-scale forces associated with the binder kinetics. Inside the macro domain (i.e., a long pipe), the model is equation free and divided into equal sized patches. The macroscale solution within each patch is obtained via appropriate (extrapolatory) coupling and amplitude conditions.