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Spatio-temporal dynamics of a two-layer pressure-driven flow subjected to a wall-normal temperature gradient

Published online by Cambridge University Press:  15 February 2023

Ramkarn Patne Open the ORCID record for Ramkarn Patne [Opens in a new window]  and
Jaikishan Chandarana
Ramkarn Patne*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, India
Jaikishan Chandarana
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, India
*
†Email address for correspondence: [email protected]
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Abstract

The present study investigates the linear spatio-temporal and weakly nonlinear stability of a pressure-driven two-layer channel flow subjected to a wall-normal temperature gradient commonly encountered in industrial applications. The liquid–liquid interface tension is assumed to be a linearly decreasing function of temperature. The study employs both numerical (pseudo-spectral method) and long-wave approaches. The general linear stability analysis (GLSA) predicts shear-flow and thermocapillary modes that arise due to the imposed pressure and temperature gradients, respectively. The previous stability analyses of the same problem predicted a negligible effect of the pressure-driven flow on the linear stability of the system. However, the GLSA reveals stabilising and destabilising effects of the pressure-driven flow depending on the viscosity ratio ($\mu _r$), thermal conductivity ratio ($\kappa _r$), interface position ($H$) and the sign of the imposed temperature gradient ($\beta _1$). The analysis predicts a range of $H$ for given $\mu _r$ and $\kappa _r$, which can not be stabilised by the thermocapillarity. The numerically predicted long-wave instability is then captured using the long-wave asymptotic approach. The arguments based on the physical mechanism further successfully explain the role of $\mu _r$, $\kappa _r$, $H$, the sign of $\beta _1$ and the interaction between the velocity and temperature perturbations in stabilising/destabilising the flow. The spatio-temporal analysis reveals the dominance of the spanwise mode in causing the absolutely unstable flow. The weakly nonlinear analysis reveals a subcritical pitchfork bifurcation without shear flow. However, with the shear flow, the streamwise mode undergoes a supercritical Hopf bifurcation.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 957 , 25 February 2023 , A11
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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