A multi-length-scale theory of the anomalous mixing-length growth for tracer flow in heterogeneous porous media

We develop a multi-length-scale (multifractal) theory for the effect of rock heterogeneity on the growth of the mixing layer of the flow of a passive tracer through porous media. The multifractal exponent of the size of the mixing layer is determined analytically from the statistical properties of a random velocity (permeability) field. The anomalous diffusion of the mixing layer can occur both on finite and on asymptotic length scales.