Universality Results for Multi-layer Radial Hele-Shaw Flows

Saffman-Taylor instability is a well known viscosity driven instability of an interface separating two immiscible fluids. We study linear stability of this displacement process in multi-layer radial Hele-Shaw geometry involving an arbitrary number of immiscible fluid phases. Universal stability results have been obtained and applied to design displacement processes that are considerably less unstable than the pure Saffman-Taylor case. In particular, we derive universal formula which gives specific values of the viscosities of the fluid layers corresponding to smallest unstable band. Other similar universal results will also be presented. The talk is based on ongoing work.