The modelling of imperfect mixing in buffer tanks

A model flow configuration in a buffer tank with a two layer flow stratification is considered. The lower, denser stream is presumed to short-circuit to the outlet, driving a recirculating cavity flow in the upper layer. As the upper layer can be argued, due to strong convective dispersion, to be well mixed, mass transfer to the upper layer from the dense stream is the limiting step. In analogy with a plug flow reactor, a shell balance on the material fluxes in a slug of the lower stream leads to a lumped parameter mixing model with two limiting conditions: (1) no mixing at infinite superficial velocity of throughput; and (2) perfect mixing with infinite mass transfer coefficient.