The Dynamics of Miscible Interfaces: Simulations

This research project focuses on the dynamics of interfacial regions between miscible fluids. While much attention has focused on immiscible interfaces in the past, miscible interfaces have been explored to a much lesser degree, so that there are many open questions regarding their dynamics at this time. Among the more pressing issues is the role that nonconventional stresses can play in such interfacial regions. Such stresses are typically not accounted for in efforts to model the dynamics of miscible flows. Our research aims to clarify under which circumstances these stresses do have to be taken into account, and what quantitative approaches are most suitable in this regard. In order to address these issues, we have focused on conducting linear stability analyses and nonlinear simulations for capillary tube and Hele-Shaw flows, and to compare the results with corresponding experiments performed in the labs of our co-investigators Prof. Maxworthy at USC, and Dr. Balasubramaniam at NASA. Over the duration of the project we have, among other things, focused on the effects of variable diffusion coefficients in such flows, and specifically on their influence in the growth of instabilities. Furthermore, our three-dimensional spectral element simulations have made good progress, so that we have come to a point where we can conduct more detailed comparisons with experimental observations. We are currently focusing our efforts on reproducing the tip-splitting instability observed by Maxworthy. Finally, we have discovered a new core-annular flow instability in the Stokes flow regime during the last year. This represents a significant finding, as this instability does not have an immiscible counterpart.