PERTURBATION SOLUTION TO THE CONVECTION-DIFFUSION EQUATION WITH MOVING FRONTS

Electrophoresis of a solute through a column in which its transport is governed by the convection-diffusion equation is described. Approxima te solutions to the convection-diffusion equation in the limit of smal l diffusion are developed using perturbation methods. The diffusion co efficient and velocity are assumed to be functions of space and time s uch that both undergo a sudden change from one constant value to anoth er within a thin transition zone that itself translates with a constan t velocity. Two cases are considered: (1) the thickness epsilon(f) of the transition zone is negligible compared to the diffusional length s cale, so the zone may be treated as a singular boundary across which t he diffusion constant and velocity suffer discontinuous changes; (2) t he transition zone is considerably wider than the diffusional length s cale, so the diffusion coefficient and velocity although sharply varyi ng, are smooth functions of position and time. A systematic perturbati on expansion of the concentration distribution is presented for case 1 in terms of the small parameter epsilon = 1/Pe. A lowest order approx imation is given for case 2. A suitably configured system analyzed her e can lead to progressive accumulation, oi focusing, of the transporte d solute. The degree of focusing in case 1 scales with epsilon(-1), wh ereas in case 2 it scales with (epsilon(f) epsilon)(-1/2), and thus in creases much more weakly with increasing Pe. A separation based on thi s concept requires development of materials and devices that allow dyn amic tuning of the mass-transport properties of a medium. This would m ake it possible to achieve progressive focusing and separation of solu tes, such as proteins and DNA fragments, in electrophoretic media with an unprecedented degree of control.