Stability criteria and convective mass transfer from the falling spherical drops, part I: bingham plastic fluids

Abstract

This work deals with the flow and mass transfer around a falling spherical drop in Bingham plastic fluids. Bubbles, drops, and particles are often dispersed in a suspending fluid of non-Newtonian nature. For example, suspensions of particles in a polymer solution are used in hydraulic fracturing slurries and swarms of bubbles are used in airlift bioreactors containing various biomacromolecules, as well as in foam production, degassing, and devolatilization of polymer melts. Governing equations for momentum and mass transfer and the Bingham constitutive equation are solved over a wide range of dimensionless groups as Reynolds number, 1≤Re ≤150 ; Schmidt number, 1≤Sc≤100 ; Bingham number, 0≤Bn ≤50 ; and viscosity ratio (0.1 and 10). The local underline transport processes are expressed using streamlines, concentration contours, and sheared and un-sheared regions, whereas the average transport quantities are reported in terms of drag coefficient, critical yieldstress parameter, and Sherwood number. A co-existence of sheared and unsheared regions occurs within the flow domain due to the fluid-yield stress. The sheared regions progressively diminish with the increasing value of the Bingham number. On the other hand, inertial effects (increasing Re) promotes the expansion of the sheared region in the flow domain. The new modified dimensionless groups are defined by re-scaling the governing equations based on the effective viscosity of the fluid. Finally, the present numerical values of the drag and average Sherwood number are correlated using the new modified dimensionless numbers