Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows

Constitutive relations for the lift force on the particulate phase and the effect of Brownian motion are presented. These constitutive relations are derived subject to three new principles of constitutive equations. The effects of lift and Brownian motion in basic parallel flows are considered in order to determine the importance and the consequences of these effects. The relation of the Brownian motion model involving momentum balance to the diffusive model of particle motions is studied. Dimensional and scaling arguments are given.