Convective Stability of a General Viscoelastic Fluid Heated from Below

The stability problem for a plane layer of a general viscoelastic (simple) fluid heated from below is investigated. The nature of the problem suggests that linear viscoelasticity assumptions are sufficient to fully describe the phenomena. It is shown that under certain conditions the fluid is overstable; namely, an oscillating cell structure will be created before the classical (Bénard) steady secondary-flow instability appears. Stability criteria for the oscillatory modes have been found as well as wavenumber and oscillation periods for both rigid and free boundaries. The theoretical results have been applied to a Maxwell fluid and to some real viscoelastic solutions. The numerical results for the latter suggest that although oscillation of Bénard cells is theoretically possible, very high-temperature gradients or high gravitational fields would be required before the oscillating cells could be observed in common polymer solutions of moderate viscosity.