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Fluid Dynamics Seminar

Monday, April 26, 2010, 4:00 PM
Cullimore Hall 611
New Jersey Institute of Technology

Some recent results on multi-layered Hele-Shaw flows

Prabir Daripa

Department of Mathematics, Texas A & M University

Abstract

Motivated by applications and numerical simulation of fronts, multi-layered Hele-Shaw flow will be considered in this talk. Upper bound results on the growth rates will be discussed in the cases of constant viscosity layers and variable viscosity layers. The upper bound provides a way to assess cumulative effects of many layers and many interfaces on the growth rates of unstable waves. As an application of the bound, we obtain some sufficient conditions for suppressing instability of two-layer flows by introducing arbitrary number of constant viscosity fluid layers in between. This sufficient condition has very practical relevance because it narrows the choice of internal layer fluids based on surface tensions of all interfaces and viscosities of fluids. Importance of this condition which has been hitherto unknown is also discussed. Other consequences of these upper bounds and sufficient conditions are discussed. The case of internal fluid layers having unstable viscous profiles will be treated. The effect of diffusion on the instability will be also be discussed.