Simulation of ratcheting non-Newtonian fluids using a geometric anisotropy

Abstract

In this work, we describe a simulation framework for fluid movement in a corrugated sawtooth channel whose walls are undergoing periodic repeated oscillations. The sawtooth geometry of the channel walls creates a fluid ratchet by generating an anisotropy in the fluid impedance. The simulations are developed using an immersed boundary method, and we present numerical results for both Newtonian and non-Newtonian fluids. These results are in agreement with physical studies of ratchets in the literature and with general flow behaviors expected for non-Newtonian fluids. In particular, we find enhanced mean flow rates for non-Newtonian fluids up to a critical value of the Weissenberg number. Existence of such a critical value has been shown for non-Newtonian flows in other environments, but has not been explored computationally for fluid ratchets. We also provide results which highlight the difference in movement of ratcheted non-Newtonian versus Newtonian fluids.