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On the long-time transient formation of sink zones in near-critical fluids. A theoretical perspective

Published online by Cambridge University Press:  29 March 2021

Yash Kulkarni ,
Roger Khayat Open the ORCID record for Roger Khayat [Opens in a new window]  and
Sakir Amiroudine Open the ORCID record for Sakir Amiroudine [Opens in a new window]
Yash Kulkarni
Affiliation:
University of Bordeaux, CNRS, I2M Bordeaux, TalenceF-33400, France
Roger Khayat
Affiliation:
Mechanical and Materials Engineering, Western University, Canada
Sakir Amiroudine*
Affiliation:
University of Bordeaux, CNRS, I2M Bordeaux, TalenceF-33400, France
*
†Email address for correspondence: sakir.amiroudine@u-bordeaux.fr
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Abstract

Near-critical fluids subject to simultaneous thermal quench and an imposed external acceleration field are reported to develop ‘sink zones’, where the temperature in the bulk falls below the imposed boundary value. This anomalous cooling effect persists for a long period of time corresponding to the diffusive elimination of the cold boundary layer. The sink-zone phenomenon has been captured previously in numerical simulations (Zappoli et al., J. Fluid Mech, vol. 316, 1996, pp. 53–72; Sharma et al., Phys. Rev E, vol. 96, 2017, 063102; Sharma et al., Phys. Fluids, vol. 29, 2017, 126103) and was observed experimentally (Beysens et al., Phys. Rev. E, vol. 84, 2011, 051201). The present work provides a detailed and thorough theoretical analysis and interpretation based on matched asymptotic expansions. By examining the one-dimensional transient flow and temperature with a mean-field approach, we provide further insight into this striking phenomenon, showing that the behaviour involved is unique to highly compressible near-critical van der Waals gases. We also show that the sub-cooling phenomenon cannot be predicted in perfect gases unless very extreme conditions are applied.

JFM classification

Mathematical Foundations: General fluid mechanics Compressible Flows: Compressible boundary layers Boundary Layers: Boundary layer stability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A117
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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