Spatiotemporal linear stability of viscoelastic Saffman–Taylor flows

The temporal and spatiotemporal linear stability analyses of a displaced Oldroyd-B fluid with the mean flow in horizontally aligned, square, Hele–Shaw cell are reported to identify regions topological transition advancing interface. viscosity displacing is negligible comparison fluid. While all inertial terms model retained, interface assumed evolve on slow timescale compared perturbation (or so-called “quasi-stationary” approximation). parameters governing Reynolds number [Formula: see text], elasticity ratio solvent polymer solution where text] gap, length width), velocity, density driven fluid, relaxation time, respectively. Reasonably good agreement relative finger width data computed our experimental Stokes Newtonian regime found. In asymptotic limit critical number, Re c , diverges as wavenumber, α increases text]. confined domain, analysis indicates (a) destabilizing influence terms, (b) impact finite boundaries near wall, (c) stabilizing until number. Briggs idea analytic continuation deployed classify absolute convective instabilities well evanescent modes. phase diagram reveals presence an absolutely unstable region at high values confirming role inertia triggering pinch-off.