Linear Rayleigh-Bénard stability of a transversely isotropic fluid

Craig Holloway, David Smith, Rosemary Dyson

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
169 Downloads (Pure)


Suspended fibres significantly alter fluid rheology, as exhibited in for example solutions of DNA, RNA and synthetic biological nanofibres. It is of interest to determine how this altered rheology affects flow stability. Motivated by the fact thermal gradients may occur in biomolecular analytic devices, and recent stability results, we examine the problem of Rayleigh-Bénard convection of the transversely isotropic fluid of Ericksen. A transversely isotropic fluid treats these suspensions as a continuum with an evolving preferred direction, through a modified stress tensor incorporating four viscosity-like parameters. We consider the linear stability of a stationary, passive, transversely isotropic fluid contained between two parallel boundaries, with the lower boundary at a higher temperature than the upper. To determine the marginal stability curves the Chebyshev collocation method is applied, and we consider a range of initially uniform preferred directions, from horizontal to vertical, and three orders of magnitude in the viscosity-like anisotropic parameters. Determining the critical wave and Rayleigh numbers, we find that transversely isotropic effects delay the onset of instability; this effect is felt most strongly through the incorporation of the anisotropic shear viscosity, although the anisotropic extensional viscosity also contributes. Our analysis confirms the importance of anisotropic rheology in the setting of convection.

Original languageEnglish
Pages (from-to)659-681
Number of pages23
JournalEuropean Journal of Applied Mathematics
Issue number4
Early online date25 Jun 2018
Publication statusPublished - Aug 2019


  • 76A05
  • 76D99
  • 76E06

ASJC Scopus subject areas

  • Applied Mathematics


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