Classical Advection-Diffusion in Heterogeneous Media

A method is proposed for solving the problem of impurity transport in heterogeneous medium due to the classical diffusion and advection. The case when advection is absent was analyzed separately. It focuses on distances from the impurity source, which are much larger than the main body of its localization, and the asymptotic approach developed by one of the authors (P.S.K.) is used. The problem is reduced to solving a differential equation of the first order, which determines the linear trajectory of the concentration signal from the source that arises with this approach to the point of observation. The result for concentration is expressed in terms of one-dimensional integrals along the concentration signal line. The solution of the transport problem in the presence of advection is obtained by transition into the coordinate system accompanying advection. The key elements entering the resulting concentration expression are the effective time and impurity displacement, both are caused by advection.