Convection–diffusion–reaction inside a porous sphere under oscillatory flow including external mass transfer

Abstract

This study aims to show the effect of oscillation and external mass transfer on nutrient transport inside a porous sphere when the flow external to the porous sphere is of oscillatory nature. Unsteady Stokes equations are used for the flow outside the porous sphere and Darcy's law is used inside the sphere. We employ a complete general solution of oscillatory Stokes equations in order to solve the corresponding hydrodynamic problem. Then the convection–diffusion–reaction problem is formulated and solved analytically for both zeroth- and first-order rates of nutrient uptake. The Robin-type boundary condition is used to quantify the external mass transfer at the porous–liquid interface. Further, in the case of zeroth-order reaction, a general condition is derived between the Peclet number and the Thiele modulus to preclude the nutrient reduction everywhere inside the sphere.