Beneitez et al. (2023b) have recently discovered a new linear "polymer
diffusive instability" (PDI) in inertialess viscoelastic rectilinear shear flow
of a FENE-P fluid with polymer stress diffusion. Here, we examine the impact of
inertia on the PDI, which we delineate for both plane Couette and channel
configurations under varying Weissenberg number W, polymer stress diffusivity
ε, solvent-to-total viscosity β and Reynolds number Re,
considering Oldroyd-B and FENE-P 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. This
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.Comment: 10 pages, 3 figure