Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1μm posts with a 3μm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. On the contrary, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device.
- Brownian dynamics
- DNA electrophoresis