Numerical simulation of finite Reynolds number suspension drops settling under gravity

Abstract

A suspension drop is a swarm of particles that are suspended in initially still fluid. When settling under the influence of gravity a suspension drop may undergo a complex shape evolution including the formation of a torus and eventual disintegration. In the present work the settling process of initially spherical suspension drops is investigated numerically for low and moderate drop Reynolds numbers Red. In the simulations a pseudospectral method is used for the liquid phase combined with a Lagrangian point-particle model for the particulate phase. In the case of low Reynolds numbers (Red<1) the suspension drop retains a roughly spherical shape while settling. A few particles leak away into a tail emanating from the rear of the drop. Due to the use of periodic boundaries a hindered settling effect is observed: the drop settling velocity is decreased compared to a suspension drop in infinite fluid. In the Reynolds number range 1⩽Red⩽100 the suspension drop deforms into a torus that eventually becomes unstable and breaks up into a number of secondary blobs. This Reynolds number range has not been investigated systematically in previous studies and is the focus of the present work. It is shown that the number of secondary blobs is primarily determined by the Reynolds number and the particle distribution inside the initial drop. An increased number of particles making up the suspension, i.e., a finer drop discretization, may result in a delayed torus disintegration with a larger number of secondary blobs. The influence of the initial particle distribution as a source of (natural) perturbations and the effect of initially imposed (artificial) shape perturbations on the breakup process are examined in detail. To gain a better understanding of the substructural effects (inside the suspension) leading to torus breakup, the particle field is analyzed from a spectral point of view. To this end, the time evolution of the Fourier coefficients associated with the particle distribution in the azimuthal direction of the torus is studied.