Elastic Instabilities in Taylor-Couette flow: The Interplay of Hoop Stress and Polymer Diffusive Instability.

Viscoelastic fluids are known to exhibit purely elastic linear instabilities in curvilinear geometries such as Taylor–Couette and Dean flows, driven by hoop stresses, which are observed even in the absence of inertia. A recent direct numerical simulation (DNS) study of two-dimensional Taylor–Couette flow by Buel et. al. reveals a linear instability that differs from the classic hoop stress mode (HSM), which is inherently absent in the 2D regime. To investigate this, we introduce polymeric stress diffusion, akin to artificial viscosity in numerical simulations. We obtained the polymeric diffusive instability (PDI) for the curvilinear Taylor-Couette configuration. The PDI has been predicted in plane Couette flow by Beneitez et. al.. Our numerical results reveal that regardless of the polymer stress diffusivity (D) value, there is no significant change in critical Weissenberg number; only the value of the azimuthal wavenumber(n) at which the Weissenberg number becomes critical changes. The classical HSM is stabilized as diffusivity is increased. Till now, PDI has been reported only in 2D and was therefore considered a purely 2D instability. However, we demonstrate that PDI persists significantly in the 3D limit as well. As the axial wave number increases gradually, it tends to stabilize the PDI mode. However, the stabilization is not very prominent, as PDI persists even at axial wave numbers as high as 40.