WALL EFFECTS ON MASS TRANSFER FROM A FLUID SPHERE FALLING IN POWER-LAW FLUIDS AT FINITE REYNOLDS NUMBERS
The present study aims to elucidate the effect of severe confinement of walls and viscosity ratio on the steady-state convective mass transfer from a single Newtonian fluid sphere steadily falling along the axis of a long cylindrical tube filled with power-law fluids. The species transport equations along with momentum transport equations of both phases, have been solved numerically using the finite element method. The effects of the external Reynolds Number (Re), Schmidt number (Sc), power-law index (n), internal to external fluid characteristic viscosity ratio (k), and confinement ratio (λ) on the local and average Sherwood number (Sh) have been analyzed over the following ranges of conditions: Re = 25, 1 ≤ Sc ≤ 100, 0.4 ≤ n ≤ 1.8, 0.1 ≤ k ≤ 10 and 0.5 ≤ λ ≤ 0.9, and the results are discussed in terms of iso-concentration contours, and plots of local and surface-averaged Sherwood number. It has been observed that for a moderate to high value of the Schmidt number, irrespective of the value of the power-law index and viscosity ratio, as the value of confinement ratio increases, the average Sherwood number increases. As the value of the power-law index increases, the mass transfer rate decreases for all values of Schmidt number and viscosity ratio hereby suggesting that shear-thinning behavior facilitates mass transfer, whereas shear-thickening behavior impedes it. It is also observed that at low values of the viscosity ratio, mass transfer rate is always higher than that for the high viscosity ratio at a fixed Reynolds Number, Schmidt number, confinement ratio and power-law index.