ASYMPTOTIC RESULTS FOR A PERSISTENT DIFFUSION-MODEL OF TAYLOR DISPERSION OF PARTICLES

We study Taylor diffusion for the case when the diffusion transverse t o the bulk motion is a persistent random walk on a one-dimensional lat tice. This is mapped onto a Markovian walk where each lattice site has two internal states. For such a model we find the effective diffusion coefficient which depends on the rate of transition among internal st ates of the lattice. The Markovian limit is recovered in the limit of infinite rate of transitions among internal states; the initial condit ions have no role in the leading-order time-dependent term of the effe ctive dispersion, but a strong effect on the constant term. We derive a continuum limit of the problem presented and study the asymptotic be havior of such limit.