Time and length scales in governing equations and boundary conditions for on-chip electrophoretic sample separation

Abstract

Microfluidics is the science of miniaturization of conventional lab devices to microchips; electrophoresis is one of the techniques for on-chip DNA and protein separation. In this article, nondimensionalization of the problem governing equations and boundary conditions is presented as preliminary preparation for performing computational and physical experiments. With the objective of designing an optimized sample-separation microchip, non-dimensionalization plays a key role in guiding this design and avoiding redundant efforts whether they be computational or experimental. The current article presents a comprehensive approach to the nondimensionalization of the electric potential field, flow field, and concentration field, including both governing equations and boundary conditions. For the case of a cross-shaped microchannel, used to control the sample shape in the vicinity of the injection site, the role of the applied voltages and other involved dimensionless parameters, such as Reynolds number, Peclet number, electrokinetic mobilities and velocities, are presented. The possible choices of reference values for length scale, electric potential, velocity, and concentration are studied in detail and, in particular, the use of a convective time scale is compared with that of a diffusive time scale. In the end, the wall electroosmotic velocity, the convective time scale, and the injection/separation channel width are adopted for non-dimensionalization of the problem.