Generalized-Newtonian fluid transport by an instability-driven filament

Abstract

Cilia are micro-scale hair-like organelles. They can exhibit self-sustained oscillations which play crucial roles in flow transport or locomotion. Recent studies have shown that these oscillations can spontaneously emerge from dynamic instability triggered by internal stresses via a Hopf bifurcation. However, the flow transport induced by an instability-driven cilium still remains unclear, especially when the fluid is non-Newtonian. This study aims at bridging these gaps. Specifically, the cilium is modelled as an elastic filament, and its internal actuation is represented by a constant follower force imposed at its tip. Three generalized Newtonian behaviours are considered, i.e. the shear-thinning, Newtonian and shear-thickening behaviours. Effects of four key factors, including the filament zero-stress shape, Reynolds number ( $Re$ ), follower-force magnitude and fluid rheology, on the filament dynamics, fluid dynamics and flow transport are explored through direct numerical simulation at $Re$ of 0.04 to 5 and through a scaling analysis at $Re \approx 0$ . The results reveal that even though it is expected that inertia vanishes at $Re \ll 1$ , inertial forces do alter the filament dynamics and deteriorate the flow transport at $Re\ge 0.04$ . Regardless of $Re$ , the flow transport can be improved when the flow is shear thinning or when the follower force increases. Furthermore, a linear stability analysis is performed, and the variation of the filament beating frequency, which is closely correlated with the filament dynamics and flow transport, can be predicted.

Spontaneous oscillation of an active filament under viscosity gradients

“…More recently, motivated by the typically non-Newtonian bodily fluids hosting cilia and flagella, research has been conducted on a spontaneously oscillating filament in viscoelastic 28 or shear-thinning/thickening fluids. 29…”

“…More recently, motivated by the typically non-Newtonian bodily fluids hosting cilia and flagella, research has been conducted on a spontaneously oscillating filament in viscoelastic 28 or shearthinning/thickening fluids. 29 Besides these recognised rheological complexities, heterogeneity is also a notable characteristic in bodily fluids, often manifesting as spatially varying viscosity. A key question is how will the viscosity gradient affect ciliary oscillation?…”