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Impact of osmotic pressure on the stability of Taylor vortices

Published online by Cambridge University Press:  06 January 2022

Rouae Ben Dhia ,
Nils Tilton  and
Denis Martinand Open the ORCID record for Denis Martinand [Opens in a new window]
Rouae Ben Dhia
Affiliation:
Aix-Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
Nils Tilton
Affiliation:
Mechanical Engineering, Colorado School of Mines, Golden, CO 80401, USA
Denis Martinand*
Affiliation:
Aix-Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
*
†Email address for correspondence: denis.martinand@univ-amu.fr
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Abstract

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

JFM classification

Instability: Taylor-Couette flow Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A51
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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