Squeeze-film flow of shear-thinning fluids

Abstract

Squeeze flows are common in a variety of applications, including engineering, biology, and rheometry. While the squeeze flow of Newtonian fluids has been extensively studied, the squeeze-flow dynamics of non-Newtonian fluids, which exhibit complex rheological properties, remain poorly understood. Here, we analyze the squeeze flow of a shear-thinning fluid between parallel plates under two scenarios: (i) a prescribed force applied to both plates and (ii) a prescribed squeeze velocity. We describe the shear-thinning rheology using the Ellis model and present a theory based on the lubrication approximation for calculating the time evolution of the gap between the plates and the force exerted on the plates. We first derive a closed-form governing equation relating the pressure gradient to the squeeze velocity. For the case of a prescribed squeeze velocity, this governing equation allows us to obtain the time-varying force exerted on the plates. For the case of a prescribed force, we solve the governing equation iteratively for the pressure and the time evolution of the gap. Furthermore, we provide asymptotic solutions for small and large values of shear rates, corresponding to Newtonian and power-law regimes. We validate our theoretical results with finite-element numerical simulations and find excellent agreement. Our theoretical findings using the Ellis model offer fundamental insights into the interplay between shear-thinning and zero-shear-rate effects in the dynamics of non-Newtonian squeeze-film flows.