Modelling the Fluid Mechanics of Cilia and Flagella in Reproduction and Development

TL;DR

This paper reviews the mechanics of cilia and flagella in microscale fluid flow, focusing on biological processes like embryonic symmetry breaking and microswimmer motility in non-Newtonian fluids, with computational models revealing effects of shear-thinning and shear-thickening.

Contribution

It provides a comprehensive analysis of viscous microscale flow mechanics and introduces models for embryonic flow and microswimmer propulsion in complex fluids, advancing understanding of biological fluid dynamics.

Findings

Cilium posterior tilt influences particle transport during embryogenesis.

Shear-thinning enhances microswimmer propulsion with optimal Deborah number around 0.8.

Shear-thickening impairs sperm motility.

Abstract

Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscous-dominated microscale flow, including time-reversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higher order multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: (1) left-right symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and (2) motility of microswimmers through non-Newtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a body-conforming finite element framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a three-sphere model swimmer and a model sperm are similarly affected by shear-thinning; in both cases swimming due to a prescribed beat is enhanced by shear-thinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shear-thickening hindering cell progress.