Linear stability of the flow of a second order fluid past a wedge

Abstract

The linear stability analysis of Rivlin-Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

Stability of the flow due to a linear stretching sheet

“…However, in order to be able to more accurately model industrial processes involving surface stretching a number of additional considerations should be taken in to account. Including the effects of a large temperature gradient on the flow of a polymeric fluid would result in a modification of not only the base flow profiles but also the governing perturbation equations (as evidenced in related studies by [20] and [26], for example). This, in turn, would affect the predictions for the critical Reynolds number for the onset of linear instability.…”