On the growth of the mixing zone in miscible viscous fingering

We investigate the growth of a mixing zone in the displacement of oil by a solvent. Such a zone usually takes the form of long thin fingers of solvent which protrude into the oil. However, despite the existence of reasonably good empirical models for the evolution of mixing zones, there is limited theoretical understanding of the observed growth. Of particular interest is the rate at which the leading edge of the mixing zone grows. In this paper we establish the structure of the mixing zone, and reveal a critical mechanism that plays a role in the growth of the leading edge of the mixing zone. It turns out that there is a close link between the growth rate of the mixing zone and a shape selection problem for Saffman-Taylor fingers.