Fractal Viscous Fingers

Abstract

Fluid motion or flow is generally uneventful. The fluid phase(s) is generally described by two main characteristics. One factor used to describe the flow is the viscosity. The second is the interfacial tension. As described elsewhere (Adamson, 1982; Chattoraj and Birdi, 1984; Birdi, 1989), when two fluid phases meet, the interfacial tension is proportional to the different forces that interact from one phase to the other. When the fluid flows, these two factors determine the characteristics of the system. However, the term viscosity, as used in the so-called Newtonian (as water) or non-Newtonian (such as toothpaste, cream, butter) case, requires some comments. The flow characteristics of fluid moving in any container or porous medium are quite common in everyday life (e.g., groundwater movement). However, the flow characteristics of two-phase fluid flow become much more interesting, and the latter type is also quite common and equally important. The flow phenomena concerning two phases (fluids) of different viscosity are somewhat special under certain conditions. The two fluids can be immiscible [e.g., oil—water (brine)] or miscible (groundwater; pollution). However, the investigation of such flow in three dimensions is obviously difficult because the motion will be quite complex, and the view of the interior parts will be obscured.