A countercurrent mechanism with transverse diffusion

A simple treatment is given for the stationary state distribution of a substance dissolved in two liquids flowing in opposite directions in two tubes with a common wall that is permeable to the substance. The transverse diffusion is taken into account. It is shown how in the case of sufficiently fast diffusion the permeability constant of the wall can be obtained from the concentrations of the substance at the ends of the tubes, the velocities in the tubes, and the length of the tubes.