Estimation of hindered settling velocity of suspensions

Four effective-medium models (EM-I, II, III, IV) are utilized and compared for determining hindered settling velocity of equi-sized particles in a viscous fluid. Among the models, EM-IV model is found to accurately predict the effective viscosity and the hindered settling velocity of monodisperse suspensions. In EM-IV model which was developed for determining the diffusivity of proteins in a biological membrane by Dodd et al. [T.L. Dodd, D. A. Hammer, A.S. Sangani, D.L. Koch, J. Fluid Mech. 293 (1995) 147], the effective-medium region begins at the distance R = a[(1 − S(0))/ϕ]1/3 from the origin where the center of the test particle is located, where a is the radius of the particle, ϕ is the volume fraction of the particles in the suspension, and S(0) is the zero wavenumber limit of the structure factor. The estimations by EM-IV model agree very well with the exact calculations and the experimental observations. The hindered settling velocity U of the particles is given, in Richardson–Zaki form, by U/U0 = (1 − ϕ)5.5, where U0 is the settling velocity for an isolated particle.