Gravitational settling of particles through density interfaces

Gravitational settling of dense particles through density interfaces is com mon in many environmental and engineering flow situations, yet very little research has been done to understand the mechanics of particle-stratificati on interactions. To this end, a detailed experimental study was carried out to investigate the settling of solid spherical particles through density i nterfaces. In these experiments, the solid particles first descended throug h a deep homogeneous layer, entered a thick pycnocline and then descended t o another denser homogeneous layer. It was found that the stratification ha s a significant impact on the settling of particles in the approximate para meter range 1.5 < Re-1 < 15, where Re-1 = U(1)d(p)/nu is the Reynolds numbe r based on the particle entry velocity U-1 to the stratified layer, d(p) is the particle diameter and nu is the kinematic viscosity of the fluid. In t he above parameter range, the particles tend to drag lighter fluid from the upper layer into the stratified region, thus increasing the drag on them s ubstantially and decelerating them within the stratified layer. In the Frou de number Fr-1 = U-1/Nd-p range investigated, 3 < Fr-1 < 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 f luid dragged into the stratified layer, but substantial internal-wave activ ity could be detected after the fluid dragged from the lighter layer (the c audal fluid) detached from the particle. The minimum velocity of the solid particle within the stratified layer was found to be given by U-min/U-1 = 5.5 x 10(-2)Fr(1)(9/10), occurring on a ti me scale t(min)/(d(p)(2)/nu) = 1.4 x 10(2) Re-1(-1.7), where t(min) was mea sured relative to the time of the particle's entry into the stratified regi on. Outside the parameter range 1.5 < Re-1 < 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.