Semiphenomenological model for the dispersion of DNA during electrophoresis in a microfluidic array of posts

A lattice Monte Carlo model is proposed for quantifying the dispersion of DNA during microfluidic electrophoresis in a quasiperiodic array of posts similar to that encountered in the microfluidic self-assembly of magnetic bead columns. The transport model is semiphenomenological in the sense that all parameters, such as the post geometry, average collision time, and collision probability, are assumed to be accessible either directly from experiment or from a model of the microscale physics. Asymptotically exact formulas are obtained for the mean velocity and dispersivity using Taylor-Aris dispersion theory, which permits a straightforward analysis of the separation efficiency. The model is applicable to a variety of situations involving collision-retardation processes.