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The center-mode instability of viscoelastic plane Poiseuille flow

M. Khalid,Indresh Chaudhary,P. Garg,V. Shankar,G. Subramanian

Published 2020 in arXiv: Fluid Dynamics

ABSTRACT

A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds number $Re = \rho U_{max} H/\eta$, the elasticity number $E = \lambda \eta/(H^2\rho)$, and the ratio of solvent to solution viscosity $\eta_s/\eta$; here, $\lambda$ is the polymer relaxation time, $H$ is the channel half-width, and $\rho$ is the fluid density. For experimentally relevant values (e.g., $E \sim 0.1$ and $\beta \sim 0.9$), the predicted critical Reynolds number, $Re_c$, for the center-mode instability is around $200$, with the associated eigenmodes being spread out across the channel. In the asymptotic limit of $E(1 -\beta) \ll 1$, with $E$ fixed, corresponding to strongly elastic dilute polymer solutions, $Re_c \propto (E(1-\beta))^{-\frac{3}{2}}$ and the critical wavenumber $k_c \propto (E(1-\beta))^{-\frac{1}{2}}$. The unstable eigenmode in this limit is confined in a thin layer near the channel centerline. The above features are largely analogous to the center-mode instability in viscoelastic pipe flow (Garg et al., Phys. Rev. Lett., 121, 024502 (2018)), and suggest a universal linear mechanism underlying the onset of turbulence in both channel and pipe flows of suffciently elastic dilute polymer solutions.

PUBLICATION RECORD

  • Publication year

    2020

  • Venue

    arXiv: Fluid Dynamics

  • Publication date

    2020-08-01

  • Fields of study

    Physics, Engineering

  • Identifiers
    arXiv 2008.00231
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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