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
