Convection–diffusion–reaction inside a permeable cylindrical porous pellet under oscillatory flow: the effect of Robin boundary condition

Abstract

A semi analytical solution is presented considering the interaction of mass transfer with a homogeneous chemical reaction of zero order/ first order reaction inside a cylindrical porous pellet. The corresponding hydrodynamic problem is formulated as a problem of flow past a porous circular cylinder for Stokes-Darcy coupled system. This is solved using a stream function approach employing the continuity of pressure, continuity of normal velocity component and Saffman slip condition for the tangential velocity component at the porous-liquid interface. The velocity field obtained inside the porous pellet is used to study the combined convection–diffusion–reaction problem subject to Robin type boundary condition, which takes into account the external mass transfer resistance. It is seen that in case of zero order reaction, for a particular combination of physical parameters, concentration takes negative values at some points inside the pellet, which is generally termed as starvation. A necessary and sufficient condition is derived ensuring the non-negativity of the concentration inside the pellet.