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Rate of chaotic mixing in localized flows

Rate of chaotic mixing in localized flows We study experimentally 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 the 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. Due 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Fluids American Physical Society (APS)

Rate of chaotic mixing in localized flows

Rate of chaotic mixing in localized flows

Physical Review Fluids , Volume 1 (3): 8 – Jul 28, 2016

Abstract

We study experimentally 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 the 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. Due 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.

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Publisher
American Physical Society (APS)
Copyright
©2016 American Physical Society
Subject
RAPID COMMUNICATIONS; Complex and non-Newtonian flows
ISSN
2469-990X
eISSN
2469-990X
DOI
10.1103/PhysRevFluids.1.031301
Publisher site
See Article on Publisher Site

Abstract

We study experimentally 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 the 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. Due 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.

Journal

Physical Review FluidsAmerican Physical Society (APS)

Published: Jul 28, 2016

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