9704746 Siegel The goal of the proposed project is to study the effects of surfactant on free surface flows in their highly nonlinear regime. This includes the time-dependent evolution of an interface that is severely deformed and contains many excited wavelengths. Attention will be focused on a simple model system, namely the displacement of a viscous fluid by a less viscous fluid in a Hele-Shaw cell (a cell consisting of two closely spaced glass plates). The interface between the fluids is subject to the Saffman-Taylor instability and develops a finger-like pattern. This system serves as a model for flow through porous media. Moreover, since the Saffman-Taylor instability is an undesirable phenomena in crude oil recovery, the problem is industrially important. The main emphasis will be on examining the effects of surfactants on steady and time-dependent finger patterns, and their role in enhancing or suppressing finger-tip splitting and side-branching instabilities. This differs from studies of surfactant effects in most other systems, since typically the free surfaces are assumed to be fixed in space or only slightly deformed, or close to a steady state configuration. Methods employed will include asymptotic analysis and numerical simulation. The practical goal of such studies is to control the size and shape of fingers, in the hopes of enhancing oil recovery. Free surface motions, such as waves on water or bubbles rising in a liquid, are important in many areas of science and engineering. A number of modern technological processes involve free surface flows. Examples include coating processes, ink jet printing processes, and oil recovery. The presence of surfactant on a free surface can significantly affect the properties of the surface. Common surfactants include detergents, fatty acids, and alcohols. Even very small amounts of surfactant can cause significant variation in the value of surface tension at a fluid-fluid interface. Thi s can have a dramatic influence on the evolution of the free surface. Such effects are particularly important during materials processing in the microgravity environment of space. Understanding the role of surface tension variations in interfacial evolution will hopefully lead to better control of free surface motion in engineering applications.
