Dynamics of an oil drop in an aqueous suspension

Abstract

The proposed manuscript is the first of articles, devoted to the dynamics of oil displacement by aqueous
suspension in the pore space of a solid skeleton. We assume that the liquids are separated by some unknown interface. The
solid skeleton has a given periodic structure with a dimensionless pore size " 1 . It is a free boundary problem, since
in the microscopic description the interface between oil and suspension must be determined. Such problems are among
the most difficult problems in the theory of partial differential equations, and, as a rule, existence results are possible only
locally in time. We will obtain global in time result by reducing the free boundary problem to the problem of finding the
viscosity of liquids, which will be described by the transport equation. The main purpose of this article is to describe the
joint motion of a single oil drop in the surrounding water suspension.