Models for the two-phase flow of concentrated suspensions

TL;DR

This paper introduces a novel two-phase model for concentrated suspensions that captures yield-stress behavior and jammed regions, providing analytical and numerical insights into suspension flow dynamics in confined geometries.

Contribution

It develops a new constitutive law combining suspension and granular rheology, deriving a drift-flux model for dynamic analysis of jammed regions in suspensions.

Findings

Existence of jammed zones in steady flow.

Analytical reduction to boundary value problems.

Numerical simulation of unyielded region evolution.

Abstract

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behavior of the suspension flow including the appearance and evolution of an unyielded or jammed region.