Inertial enhancement of the polymer diffusive instability

Abstract

Beneitez et al. (Phys. Rev. Fluids, 8, L101901, 2023) have recently discovered a new linear “polymer diffusive instability” (PDI) in inertialess rectilinear viscoelastic shear flow using the FENE-P model when polymer stress diffusion is present. Here, we examine the impact of inertia on the PDI for both plane Couette (PCF) and plane Poiseuille (PPF) flows under varying Weissenberg number W, polymer stress diffusivity 𝜀, solvent-to-total viscosity ratio 𝛽, and Reynolds number Re, considering the FENE-P and simpler Oldroyd-B constitutive relations. Both the prevalence of the instability in parameter space and the associated growth rates are found to significantly increase with Re. For instance, as 𝑅𝑒 increases with 𝛽 fixed, the instability emerges at progressively lower values of 𝑊 and 𝜀 than in the inertialess limit, and the associated growth rates increase linearly with 𝑅𝑒 when all other parameters are fixed. For finite 𝑅𝑒, it is also demonstrated that the Schmidt number 𝑆𝑐 = 1/(𝜀𝑅𝑒) collapses curves of neutral stability obtained across various 𝑅𝑒 and 𝜀. The observed strengthening of PDI with inertia and the fact that stress diffusion is always present in time-stepping algorithms, either implicitly as part of the scheme or explicitly as a stabiliser, implies that the instability is likely operative in computational work using the popular Oldroyd-B and FENE-P constitutive models. The fundamental question now is whether PDI is physical and observable in experiments, or is instead an artifact of the constitutive models that must be suppressed.