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Role of finite extensibility on the centre-mode instability in viscoelastic channel flow

Published online by Cambridge University Press:  14 April 2025

Mohammad Khalid ,
Amit Badoni ,
Debanjan Dutta ,
Prajwal Naidu ,
Ganesh Subramanian Open the ORCID record for Ganesh Subramanian [Opens in a new window]  and
V. Shankar Open the ORCID record for V. Shankar [Opens in a new window]
Mohammad Khalid
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India Chemical Engineering Department, College of Engineering, Taibah University, Yanbu Al-Bahr 41911, Kingdom of Saudi Arabia
Amit Badoni
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
Debanjan Dutta
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
Prajwal Naidu
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
Ganesh Subramanian*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560064, India
V. Shankar*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
*
Corresponding authors: V. Shankar, [email protected]; Ganesh Subramanian, [email protected]
Corresponding authors: V. Shankar, [email protected]; Ganesh Subramanian, [email protected]
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Abstract

A purely elastic linear instability was recently reported for viscoelastic plane Poiseuille flow in the limit of ultra-dilute (solvent to solution viscosity ratio $\beta \gt 0.99$), highly elastic (Weissenberg number $W \sim 1000$) polymer solutions, within the framework of the Oldroyd-B model (Khalid et al., Phys. Rev. Lett., vol. 127, 2021, pp. 134–502). This is the first instance of a purely elastic instability in a strictly rectilinear shearing flow, with the phase speed of the unstable ‘centre mode’ being close to the base-state maximum velocity at the channel centreline. Subsequently, Buza, Page and Kerswell (J. Fluid Mech., vol. 940, 2022, A11) have shown, using the FENE-P model, that the centre-mode instability persists down to moderate elasticities ($W \sim O (100)$), the reduction in threshold evidently due to the finite extensibility of the polymer molecules. In this work, we augment this latter finding and provide a comprehensive account of the effect of finite extensibility on the centre-mode instability in viscoelastic channel flow, using the FENE-P and FENE-CR models, in both the absence and presence of fluid inertia. In both these models, finite extensibility causes a decrease in the polymer relaxation time at high shear rates, and the resulting weakening of elastic stresses would seem to indicate a stabilising effect. The latter trend has been demonstrated by earlier analyses of hoop-stress-driven instabilities in curvilinear flows, and is indeed borne out for the FENE-CR case, where finite extensibility has a largely stabilising influence on the centre-mode instability. In stark contrast, for the FENE-P model, finite extensibility plays a dual role – a stabilising one at lower values of the elasticity number $E$, but, surprisingly, a destabilising one at higher $E$ values. Further, the centre-mode instability is predicted over a significantly larger domain of the $Re$–$E$–$\beta$ parameter space, compared to the Oldroyd-B model, making it more amenable to experimental observations.

JFM classification

Instability: Shear-flow instability Non-Newtonian Flows: Viscoelasticity Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A28
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© The Author(s), 2025. Published by Cambridge University Press

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