Ludwig Prandtl Memorial Lecture
Title: Some variants of classical multiphase flow problems
I will briefly discuss three problems that have classical roots and in each case seek to add one new feature to a modern version of the problem. In the first problem the Saffman-Taylor viscous fingering problem is discussed for the case that there are geometric variations in the flow directions – we show via experiments and theory that such changes can significantly modify the stability features of the flow. In the second problem we consider the low Reynolds number motion of a hot sphere in a fluid accounting for the variations of the viscosity with temperature – we show that the Lorentz Reciprocal Theorem provides a means to construct an analytical representation of the force and torque on the sphere for the case of small viscosity variations. Finally, we present experiments of unexpected dynamics in modest Reynolds number flows at a T-junction and rationalize the results by demonstrating the connections to vortex breakdown.