Radial flow of shear-thinning fluids between parallel plates

We analyze the pressure-driven radial flow of a shear-thinning fluid between parallel plates. Complex fluid rheology may significantly affect the hydrodynamic features of such non-Newtonian flows, which remain not fully understood, compared to Newtonian flows. We describe the shear-thinning rheology using the Ellis model and present a theoretical framework for calculating the pressure distribution and the flow rate-pressure drop relation. We first derive a closed-form expression for the pressure gradient, which allows us to obtain semi-analytical expressions for the pressure, velocity, and flow rate-pressure drop relation. We provide the corresponding asymptotic solutions for small and large values of the dimensionless flow rates. We further elucidate the entrance length required for the radial velocity of a shear-thinning fluid to reach its fully developed form, showing that this length approximates the Newtonian low-Reynolds-number value at low shear rates, but may strongly depend on the fluid’s shear-thinning rheology and exceed the Newtonian value at high shear rates. We validate our theoretical results with finite-element numerical simulations and find excellent agreement. Finally, we compare our theoretical and finite-element simulation results for the pressure distribution with the available experimental measurements, showing good agreement.