Effect of velocity slip on settling of assemblages of spherical particles in power-law liquids at low to moderate Reynolds numbers

Abstract

Combined effects of the velocity slip, volume fraction of spherical particles and power-law behavior index on the flow and drag phenomena of assemblages of spherical particles in power-law liquids with velocity slip at the interface are numerically investigated. The effects of varying degrees of the velocity slip at interfaces of the fluid–solid particles are incorporated in the solver by making use of a linear slip velocity model. Further, the assemblages of particles are mathematically simplified as clusters of mono-size spherical particles equidistant from each other and the effect of neighboring particles on the target particle nullified at midpoint between the centers of two neighboring spherical particles. Within the combination of these two models, the dimensionless governing conservation equations of mass and momentum for power-law fluids are solved using a simplified marker and cell method in spherical coordinates on a staggered grid arrangement. The convective and non-Newtonian terms of the momentum equation are discretized using quadratic upstream interpolation for convective kinematics scheme and a second-order central differencing scheme, respectively. The presented numerical solver is extensively tested for its reliability via routes of the grid independence and validation with the existing literature counterparts. Furthermore, extensive new results were obtained in the range of dimensionless parameters such as the holdup of spheres, \(\Phi = 0.1{-}0.5\); dimensionless slip number, \(\lambda = 0.01{-}100\); Reynolds number, \(Re = 0.1{-}200\); and power-law behavior index, \(n = 0.6{-}1.6\). Briefly, some results indicate that the drag coefficients of assemblages of spheres decrease with the decreasing slip number and/or decreasing power-law index and/or with the decreasing holdup of the spheres.