Rate of chaotic mixing in localized flows

Jalila Boujlel (1) , Franck Pigeonneau (1) , Emmanuelle Gouillart (1) , Pierre Jop (1)

1 SVI - Surface du Verre et Interfaces

We experimentally study the rate of chaotic mixing in viscoplastic fluids, by using a rod-stirring protocol with a rotating vessel. Only a limited zone localized around the stirring rods is highly sheared at a given time. Using a dyed spot as initial condition, we measure the decay of concentration fluctuations of dye as mixing proceeds. The mixing rate is found to be proportional to the volume of highly-sheared fluid during a rotation period of the rods, and inversely proportional to the number of rotations of the rods over a rotation of the vessel. Thanks to numerical simulations and experimental measurements, we relate the volume of highly-sheared fluid to the parameters of the flow. We propose a quantitative two-zone model for the mixing rate taking into account the geometry of the highly-sheared zone, as well as the rate at which fluid is renewed inside this zone. For all experiments, the model predicts correctly the scaling of the exponential mixing rates during a first rapid stage, and a second slower one.

Mots clés: yield stress fluids; chaotic mixing

Domaines: Matière Molle [cond-mat.soft]; Mécanique des fluides [physics.class-ph]

Jalila Boujlel, Franck Pigeonneau, Emmanuelle Gouillart, Pierre Jop. Rate of chaotic mixing in localized flows. Physical Review Fluids, 2016, 1 (3), pp.031301(R). ⟨10.1103/PhysRevFluids.1.031301⟩. ⟨hal-01360390⟩