A criterion to avoid starvation zones for convection–diffusion–reaction problem inside a porous biological pellet under oscillatory flow

The behavior of nutrient transport inside a porous spherical pellet in an oscillatory Stokes flow is investigated analytically. Unsteady Stokes equations are used for the flow outside the porous pellet and Darcy’s law is used inside the pellet. A solenoidal decomposition method is employed for the derivation of the flow field outside the pellet. The corresponding convection–diffusion–reaction problem is formulated and solved analytically for a zeroth-order nutrient consumption rate. From the obtained solution a general condition between the Peclet number and Thiele modulus is derived to obviate the nutrient reduction everywhere in the pellet. For the correct modeling of the processes involving flow through biological catalysts this becomes a necessary and sufficient condition.