| The drift and diffusion motions of biased particles are commonly studied using random walks on lattices. We present a novel theoretical approach that makes it possible to calculate exact mobilities in the presence of lattice obstacles. Several two-dimensional examples are studied and a particular attention is given to separation techniques and how our model can be used to study such devices. We also broach the problems related to the field-dependence of the diffusion coefficient during random walks, and we present new algorithms that remove these difficulties. We develop new Monte Carlo algorithms that make it possible to study both drift and diffusion processes simultaneously, even in presence of very strong fields. Finally, we present two brief discussions about the addition of curved field lines and viscosity gradients to our lattice models. This work opens the door to a wide range of applications, especially for the study of electrophoretic technologies. |
