Gravitational settling of particles through density interfaces

Abstract

Gravitational settling of dense particles through density interfaces is common in many environmental and engineering flow situations, yet very little research has been done to understand the mechanics of particle–stratification interactions. To this end, a detailed experimental study was carried out to investigate the settling of solid spherical particles through density interfaces. In these experiments, the solid particles first descended through a deep homogeneous layer, entered a thick pycnocline and then descended to another denser homogeneous layer. It was found that the stratification has a significant impact on the settling of particles in the approximate parameter range 1.5<Re1<15, where Re1=U1dp/v is the Reynolds number based on the particle entry velocity U1 to the stratified layer, dp is the particle diameter and v is the kinematic viscosity of the fluid. In the above parameter range, the particles tend to drag lighter fluid from the upper layer into the stratified region, thus increasing the drag on them substantially and decelerating them within the stratified layer. In the Froude number Fr1=U1/Ndp range investigated, 3<Fr1<10, where N is the buoyancy frequency of the stratified layer, the drag coefficient was found to be an order of magnitude larger than its homogeneous-fluid counterpart. The internal-wave contribution to the drag was small compared to that of fluid dragged into the stratified layer, but substantial internal-wave activity could be detected after the fluid dragged from the lighter layer (the caudal fluid) detached from the particle.The minimum velocity of the solid particle within the stratified layer was found to be given by Umin/U1= 5.5×10−2Fr9/101, occurring on a time scale tmin/ (d2p/v)= 1.4×102Re−1.71, where tmin was measured relative to the time of the particle's entry into the stratified region. Outside the parameter range 1.5<Re1<15, the drag on the sphere in the density-stratified layer could be approximated to that in a homogeneous fluid, whence the bringing of lighter fluid into the stratified layer as a tail behind the descending particle was found to be negligible.