Local drag law for suspensions from particle-scale simulations
Two-phase continuum descriptions of the dynamical behavior of particulate suspensions require, among others, the formulation of a "local drag law". Such a "law" specifies the mean force f(l) on particles as a function of averaged local properties, most notably, the mean difference velocity Delta  of particles and fluid and the local volume fraction Phi(l). The subscript l shall indicate the dependence of these quantities on the size l of the averaging cell. We study f(l) by direct numerical simulation, solving the incompressible Navier-Stokes equation on a fixed, regular grid on a scale much smaller than the particle diameter. The particle-fluid interaction is computed by a method similar to the one proposed in [Fogelson and Peskin J. Comp. Phys. 79, 50 (1988)]. We find a relation similar to the law of Richardson & Zaki, Delta  similar to (1 - Phi(l))(3.7), which relates the local phase difference velocity to the local volume fraction of the particles.
drag law suspensions particle-fluid mixtures averaging techniques