IV-3

Eric S. G. Shaqfeh

Stanford University

Abstract

Interfacial instabilities associated with the displacement of one fluid by another have received great attention in the literature after the seminal work by Saffman-Taylor. The mechanism by which an initially flat interface between two Newtonian fluids under slow viscous flow can develop "fingers" originates from the pressure profile that exists in the basic state. As described by Saffman-Taylor for Hele Shaw cell flows, a generically unstable pressure distribution occurs when displacing a more viscous fluid with a less viscous fluid. Similarly the reverse process is stable. The critical parameter for instability is either a Capillary number (CA) describing the ratio of the destabilizing viscous forces to the surface tension (if surface tension is the dominant stabilizing factor) or a Gravity number (Gr) as the ratio of the destabilizing viscous forces to gravity ( if gravity is the dominant stabilizing influence). The effect of this classical flow instability in coating flows (for example) has been the subject of numerous papers.

Recently there has been a growing body of evidence that fluid-fluid displacement involving highly elastic fluids can be very different. Most research demonstrates that the critical capillary (CA) or Gravity (Gr) number decreases rather sharply when the displaced fluid is highly elastic, although the literature is not uniform on this point. There have been no systematic studies where the levels of fluid elasticity are varied in order to distinguish elastic effects from other rheological influences. There has been no connection to theory and experiment in this area, and there are no firm mechanisms describing the elastic effects on displacement instabilities. In this presentation, we will briefly review the literature on this subject and then describe the results from a host of our recent experiments where flows of highly elastic polyisobutylene/polybutene Boger fluids were created in concentric and eccentric cylinder devices in which an air-fluid interface was present. The devices were mounted horizontally and only filled partially so that the interfacial deformation and instability was the focus of the experiment. In our flow configuration, the cylinders could be rotated such that the air was driven into the Boger fluids, or such that the fluid was driven into the air. In the former instance, the interface is unstable even for Newtonian fluids via the standard capillary driven fingering mechanisms. However, we show that the development of these instabilities is markedly changed by fluid elasticity, including: i) a dramatic change in the critical condition beyond a certain level of elasticity, ii) a large increase in the critical wavenumber (decrease in the wavelength) with increasing elasticity, iii) the transition (well above the critical condition) to new, purely elastic modes with highly different finger shapes (e. g. cusps). In the second case of viscous fluids displacing air, the interface is stable for Newtonian fluids. However, we demonstrate that there can be a purely elastic instability in this case that renders elastic displacement unstable even in classically sable flow parameter regimes. The form of this instability and proposals for the instability mechanism will be discussed in some detail. The talk will conclude with an initial theoretical prediction of the effects of elasticity on fluid-fluid displacement.