Effective viscosity of a suspension of flagellar beating microswimmers: Three-dimensional modeling

TL;DR

This paper presents a three-dimensional model of flagellar microswimmers, analyzing how their beating influences their motion and the suspension's viscosity, revealing increased viscosity and shear thinning behavior.

Contribution

It introduces a novel 3D model of microswimmers with flagellar beating and studies its effects on cell orbits and suspension rheology.

Findings

Unusual angular orbits in shear flow due to flagellar beating

Increased intrinsic viscosity in active suspensions

Shear thinning behavior consistent with experiments

Abstract

Micro-organisms usually can swim in their liquid environment by flagellar or ciliary beating. In this numerical work, we analyze the influence of flagellar beating on the orbits of a swimming cell in a shear flow. We also calculate the effect of the flagellar beating on the rheology of a dilute suspension of micro-swimmers. A three-dimensional model is proposed for Chlamydomonas Reinhardtii swimming with a breaststroke-like beating of two anterior flagella modeled by two counter-rotating fore beads. The active swimmer model reveals unusual angular orbits in a linear shear flow. Namely, the swimmer sustains orientations transiently across the flow. Such behavior is a result of the interplay between shear flow and swimmer's periodic beating motion of flagella which exert internal torques on the cell body. This peculiar behavior has some significant consequences on the rheological properties of the suspension. We calculate the Einstein's viscosity of the suspension composed of such isolated modeled microswimmers (dilute case) in a shear flow. We use numerical simulations based on a Rotne-Prager like approximation for hydrodynamic interaction between simplified flagella and the cell body. The results show an increased intrinsic viscosity for active swimmer suspensions in comparison to non-active ones as well as a shear thinning behavior in accordance with previous experimental measurements [Phys. Rev. Lett. 104 , 098102 (2010)].