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

Patne, Ramkarn (2023) Spatio-Temporal dynamics of a two-layer pressure-driven flow subjected to a wall-normal temperature gradient. Journal of Fluid Mechanics, 957. A11. ISSN 0022-1120

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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 , thermal conductivity ratio , interface position and the sign of the imposed temperature gradient . The analysis predicts a range of for given and, 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, the sign of 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.

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IITH Creators:

IITH Creators	ORCiD
Patne, Ramkarn	http://www.orcid.org/0000-0003-4052-1807

Item Type:

Article

Uncontrolled Keywords:

Marangoni convection; multiphase flow; bifurcation; channel flow; convection; flow stability; multiphase flow; nonlinear wave; P-T conditions; pressure field; shear flow; spatiotemporal analysis; temperature gradient; thermal conductivity; Decreasing functions; Liquid:liquid interface; Long waves; Marangoni convection; Pressure-driven; Pressure-driven flows; Spatio-temporal; Spatio-temporal dynamics; Two-layer; Weakly nonlinear stability; Heat convection; Hopf bifurcation; Linear stability analysis; Nonlinear analysis; Numerical methods; Shear flow; System stability; Thermal conductivity; Thermal Gradients

Subjects:

Chemical Engineering
Chemical Engineering > Technology of industrial chemicals

Divisions:

Department of Chemical Engineering

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

22 Aug 2023 05:26

Last Modified:

22 Aug 2023 05:26

URI:

http://raiithold.iith.ac.in/id/eprint/11583