On drag and lift forces in two-dimensional flows of a particulate mixture: A theoretical study

Abstract

In this paper we propose and derive expressions for the drag and lift forces in a two-phase particulate mixture. The analysis is limited to two-dimensional laminar flows. In the Section after the Introduction, a brief review of the single particle approach is provided; it is then shown that in most multiphase flow problems some generalization of these forces acting on a single particle is used. We then describe a different way of defining the lift force and the drag force, an approach used in non-Newtonian fluid mechanics. In the following Section, the essential equations of Mixture Theory are provided and the specific approach of [1] is used. In this scheme, the lift force is part of the interaction mechanisms, which are to be modeled as constitutive parameters. In the final Section, we derive an expression for the lift force, whereby it is shown that the normal component of the force acting on the body, obtained by integrating the traction vector of the mixture acting on a single isolated particle, will give us the desired expression for the lift force in multi-component flows.