Interfacial Instabilities in a Hele-Shaw Cell

A Hele-Shaw cell consists of a thin gap between two parallel plates, along which fluid is forced to flow, providing a constrained geometry suitable for experimental and theoretical study. When one fluid is pumped through the cell to displace a second fluid, the interface between them can, in some cases, develop in an unstable fashion. The Newtonian Saffman-Taylor problem is one such example that has been well studied, predicting an instability driven by the viscosity difference between the two fluids. When the less viscous fluid displaces the more viscous one, the interface is unstable; but if the more viscous fluid displaces the less viscous one, the interface remains stable. The goal of the current study is to explore and analyse two other types of instabilities. The first one is the viscoplastic case of the Saffman-Taylor instability, replacing the displaced Newtonian fluid with a yield stress fluid. The second one is a fracturing instability that occurs when water is displaced by a yield stress fluid. In this case, the theory predicts no Saffman-Taylor instability and thus a stable interface, because the viscoplastic fluid has a higher effective viscosity than water. However, instead of growing asymmetrically, the interface cracks and leads the flow into flower-like shapes.