Mass transfer under laminar flow conditions is discussed on the basis of the Navier-Stokes equations and the axially dispersed plug-flow model. By fitting the results with these two approaches, relationships can be derived for predicting the mass-transfer coefficient and the Peclet number in a parallel-plate laminar flow system with on impermeable wall and an opposite wall at which the concentration is uniform. This single-stream relationship can be utilized for calculating the mass-transfer coefficients in both channels of a co-current parallel-plate dialyser. It is shown that the Peclet number in the axially dispersed plug-flow model derived for a parallel-plate flow where both sides are impermeable gives better results when applied to the co-current dialyser than the single-stream relationship. The results obtained allow the mathematical modelling of process and analytical flow-through manifolds incorporating a dialysis module.