Dense Suspension Flows: A Mathematical Model Consistent With Thermodynamics

We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of Landau and Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.

Automated summary

This paper addresses the flows of dense suspensions of particles within the framework of the two-velocity continuum, developing the thermodynamics of such a continuum using the approach suggested by Landau and Khalatnikov. As an application, the authors consider the convective settling problem and capture the Boycott effect, proving that enhanced sedimentation occurs in a tilted vessel due to vortices. Instead of relying on additional interphase forces, they apply a generalized Fick's law for the particle mass concentration flux vector.