A Comparison of Two Methods for Solving Transport Equations with Weak Diffusion

The equations that describe the transport of material through a separation system often take the form of diffusion-convection equations in which diffusion plays a minor role. It is possible to derive approximate solutions to such equations using singular perturbation theory. At least two such theories have been developed, one by van Kampen and the second by Weiss and Dishon. We compare results generated by the two theories on two exactly solvable equations, one equivalent to the Lamm equation and the second related to electrophoresis in a gradient. In both cases the van Kampen approximation proved to be more accurate in a neighborhood of the peak for a pulse-loaded system.