Continuum approximations and particle interactions in concentrated suspensions

Abstract

Falling‐ball rheometry is used to study hydrodynamic forces in concentrated suspensions. The suspensions consist of large, uniform spheres (diameter ds=0.32 cm) neutrally buoyant in a viscous, Newtonian liquid. Falling‐ball experiments are performed by dropping steel balls of various diameters (df) through suspensions held in cylindrical containers of several diameters. In these optically opaque suspensions, the passage of the falling ball is observed with real‐time radiography and is recorded with digitized, high‐speed video. The average terminal velocities of the falling balls are used to calculate an apparent viscosity of each suspension (ηs). Extrapolation of the data to estimate the velocity which would occur in a cylinder of infinite diameter is used to find the apparent viscosity with zero wall effects (ηs∞). Each ηs∞ agrees with independent measurements throughout the solids concentration range of the data (0.0≤φ≤0.45). In the absence of wall effects, ηs∞ is independent of ds /df. That is, all sizes of falling balls (0.75≤df /ds≤12.0) experience the same mean stress field. In addition, it is seen that in dilute and moderately concentrated suspensions (0.0<φ<0.30), wall effects are identical to those in equivalent Newtonian liquids. At higher solids loadings, we observe additional wall effects that can act over much greater distances than in equivalent Newtonian liquids. The magnitude of additional wall effects increase rapidly as φ increases above 0.30.