INERTIAL EFFECT ON THE STABILITY OF VISCOELASTIC CONE-AND-PLATE FLOW

摘要

The stability of axially symmetric cone-and-plate how of an Oldroyd-B fluid at non-zero Reynolds number is analysed. We show that stability is controlled by two parameters: E-1 = DeWe and E-2 = Re/We, where De, We, and Re are the Deborah, Weissenberg and Reynolds numbers respectively. The linear stability problem is solved by a perturbation method for E-2 small and by a Galerkin method when E-2 = O(1). Our results show that for all values of the retardation parameter beta and for all values of E-2 considered the base viscometric flow is stable if E-1 is sufficiently small. As E-1 increases past a critical value the flow becomes unstable as a pair of complex-conjugate eigenvalues crosses the imaginary axis into the right half-plane. The critical value of E-1 decreases as E-2 increases indicating that increasing inertia destabilizes the flow For the range of values considered the critical wavenumber k(c) first decreases and then increases as E-2 increases. The wave speed on the other hand decreases monotonically with E-2. The critical mode at the onset of instability corresponds to a travelling wave propagating inward towards the apex of the cone with infinitely many logarithmically spaced toroidal roll cells. [References: 18]