A solid-liquid two-phase flow is the motion of a mixture that is composed of solid particulates and filling liquids. The deformation of a solid block or a fluid under external loading has been well studied and understood as a continuum of single constituent. Each of these materials has a respective constitutive relation that specifies the stress and strain (rate) relationship, which can be employed in the theory of continuum mechanics to describe its motion with prescribed boundary conditions.

For a solid-plus-liquid mixture, however, the interactions between the heterogeneous constituents and the flow boundaries make the mixture dynamics an intrinsically multi-scale problem, which falls beyond the realm of continuum mechanics. Both solid-solid and solid-liquid interactions will contribute to the mechanisms for mixture momentum transfer and energy dissipation. However complicated, when one of the two phases is dynamically insignificant, the mixture dynamics can be greatly simplified, leading to two well investigated fields: granular materials and suspensions.

Granular flow is the motion of a group of dry particles whose motion only depends on the interaction between solid particles while the interstitial fluid is negligible. Similar gas dynamics, where molecular dynamics sums up to an averaged gas behavior, kinetic theory has been applied successfully to describe the motion of granular flows. On the other extreme, in a suspension system, the solid particles possess too little inertia to overcome the force from the surrounding liquid. The particles often follow the fluid motion and direct particle collisions rarely occur. Thus, the theory on a suspension system was originated from classical fluid mechanics in the low Reynolds number regime. Modifications on how the presence of new solid boundary at the particle surface lead to new constitutive relations.

Thus, this course will be divided evenly into three parts. The first two will cover the classical topics in the fields of granular flows and suspensions. Though both fields require extensive theoretical background, we will focus on the physical meaning and the concepts behind the theory and learn from dimension analysis, if applicable. The learning should help to understand the third part—the recent theories on solid-liquid flows where both the solid and the liquid possess comparable inertia in the mixture.