A mathematical treatment of bump structure for the particle laden flows with particle features

TL;DR

This paper provides a mathematical analysis of bump structures in particle-laden flows on inclined planes, focusing on how particle size and concentration influence the flow morphology using shock wave theory.

Contribution

It introduces a mathematical framework incorporating particle size and concentration effects into the analysis of bump structures in particle-laden flows.

Findings

Particle size and concentration significantly affect bump morphology.

The study links bump structures to shock wave solutions in conservation laws.

Explicit dependence of flow features on particle parameters is established.

Abstract

In this paper, we consider the particle laden flows on a inclined plane under the effect of the gravity. It is observed from preceding experimental works that the particle-rich ridge is generated near the contact line. The bump structure observed in particle-rich ridge is studied in terms of Lax's shock waves in the mathematical theory of conservation laws. In the present study, the effect of particles with nontrivial radii on morphology of particle laden flows is explicitly considered, and dependence of radius and concentration of particles on the bump structure is extracted.