Numerical study of two balls settling in viscoelastic fluids from an initial vertical configuration

Abstract

In this article, we have investigated, via numerical simulation, the interaction of two identical balls settling in a vertical square tube filled with a viscoelastic fluid. For two balls released in Oldroyd-B fluids, one on top of the other initially, we have observed two possible scenarios, among others: either the trailing ball catches up the leading one to form a doublet (dipole) or the balls separate with a stable final distance. If the ball density is slightly larger than the fluid density, the two balls form a doublet, either vertical or tilted. If one further increases the ball density, the two balls still form a doublet if the initial distance is small enough, but for larger initial distances at higher elasticity numbers, the balls move away from each other and their distance reaches a stable constant. Factors influencing doublet formation are (possibly among others) the ball density, the ball initial distance, and the fluid elasticity number. When settling in finite extendable nonlinear elastic-Chilcott and Rallison fluids, low values of the coil maximal extension limit enhance ball separation.