Mass transfer from ensembles of fluid spheres to a power-law liquid at moderate Reynolds and Peclet numbers

Abstract

The steady convective mass transfer from ensembles of mono-size Newtonian fluid spheres to power-law liquids has been studied at moderate Reynolds and Peclet numbers. The species continuity equation segregated from momentum equations has been solved numerically using a finite difference method. A simple cell model has been used to account for the modification of the flow field due to the neighbouring droplets. Extensive numerical results have been obtained which elucidate effects of the Reynolds number ( Re o ) , Schmidt number ( Sc), power-law index ( n o ) , internal to external fluid characteristic viscosity ratio ( k ) and the volume fraction of the dispersed phase ( Φ ) on the rate of mass transfer. The ranges of parameters considered herein are: 1 ⩽ Re o ⩽ 200 , 1 ⩽ Sc ⩽ 10000 , 0.6 ⩽ n o ⩽ 1.6 , 0.1 ⩽ k ⩽ 50 and 0.2 ⩽ Φ ⩽ 0.6 . For shear-thinning fluids ( n o < 1 ) , the rate of mass transfer is somewhat enhanced whereas for shear-thickening fluids ( n o > 1 ) , it decreased as compared to that in Newtonian fluids ( n o = 1 ) . A simple predictive correlation has been proposed which can be used to estimate the rate of mass transfer in liquid–liquid systems in a new application involving power-law continuous phase.