Two examples of mixing in fluid dynamics : a buoyancy driven flow and a time-periodic viscous flow
Flow problems involving mixing process are met in a wide variety of natural systems and industrial activities. Mixing span an enormous range of length an time scales and encompass Reynolds numbers varying over forty order of magnitude. We will present two examples of mixing in fluid dynamics, both were studied with an experimental approach.
First the buoyancy driven mixing of two fluids of different densities in the confined geometry of a tilted tube. The fluids are initially separted in an unstable configuration (the heavier fluid is above the lighter fluid) and the tilt angle is fixed for each experiment.Velocity and concentration measurements are performed in a vertical diametral plan. The flow displays a large variety of behaviors depending on the the tilt angle and the density contrast (which are the two control parameters), from a laminar counter-flow to a turbulent mixing thought a laminar flow with turbulent bursts. A secondary flow is identified and plays an important role for the momentum transport.
The second study is focused on periodically driven laminar flows (the Reynolds number is in order of 1e -3). Time-periodic viscous flow in a square cylindrical domain is considered. The flow is generated via translation of the top or bottom wall of the cylinder under specific forcing protocols. Each forcing protocol has a particular configuration consisting of n steps. The n-step flow (n = 3) is approximated as a piece-wise linear combination of n separate steady flows. Using 3D particle tracking velocimetry (3D PTV) we are interested in the formation and interaction of coherent structures due to fluid inertia, which play an important role in 3D mixing by geometrically determining the tracer transport. The disintegration of these structures by fluid inertia reflects an essentially 3D route to chaos.