Reducing the diffusional spreading rate of a Brownian particle by an appropriate non-uniform external force field

The variance of the probabilistic distribution of positions for a Brownian particle acted upon by an external force depends on whether the force field is uniform or not. If the field is uniform, the variance is independent of the field strength and, in fact, it is equal to that found for a pure Brownian process (free particle). If the force field acting on the particle is not uniform, the variance can be larger or smaller than that for a free particle depending on whether the particle, on the average, moves, respectively, toward increasing or decreasing absolute values of the field. This important result may find an immediate application in the design of high-resolution differential mobility analyzers for nanoparticles: the diffusional broadening of the transfer function can be dramatically reduced by simply reversing the direction of the aerosol particle motion between the electrodes.