Shear-thickening elastic instability in inertialess pipe flow of White–Metzner fluid

Extensive rheological studies have shown that the non-Brownian particle suspensions in viscoelastic fluids, relevant in several applications, exhibit shear-thickening and elasticity. Previous theoretical and experimental analyses have demonstrated the existence of a shear-thinning elastic instability in the inertialess rectilinear flows of concentrated polymer solutions owing to the combined effect of shear-thinning and elasticity. These theoretical analyses employed the White–Metzner (WM) model, which modifies the upper convected Maxwell (UCM) model by allowing viscosity and relaxation time to be functions of the second invariant of the shear-rate tensor. Following previous studies, we consider the power-law model for the viscosity and relaxation time in the WM model, albeit with a power-law index greater than unity (n>1), implying shear-thickening. The present analysis predicts destabilization of the stable viscoelastic discrete modes due to shear-thickening in the inertialess pipe flow for n>1.64. The instability is termed shear-thickening elastic instability since both shear-thickening and elasticity are necessary ingredients for the existence of the predicted instability. The analysis reveals that the critical Weissenberg number (Wc) rapidly decreases as n increases beyond 1.64 and attains a constant value at sufficiently high n. In contrast, the critical wavenumber rapidly increases as n increases and plateaus off at high n. The wave speed of the perturbations at Wc is approximately 0.75 at sufficiently high n, indicating destabilization near the pipe center. Further analysis implicates the strengthening of the viscous part of the rz stress component perturbations due to the shear-thickening, leading to instability.