title: Squirmers with swirl: a model forVolvoxswimming.
abstract: Colonies of the green algaVolvoxare spheres that swim through the beating of pairs of flagella on their surface somatic cells. The somatic cells themselves are mounted rigidly in a polymeric extracellular matrix, fixing the orientation of the flagella so that they beat approximately in a meridional plane, with axis of symmetry in the swimming direction, but with a roughly [Formula: see text] azimuthal offset which results in the eponymous rotation of the colonies about a body-fixed axis. Experiments on colonies ofVolvox carteriheld stationary on a micropipette show that the beating pattern takes the form of a symplectic metachronal wave (Brumleyet al.Phys. Rev. Lett., vol. 109, 2012, 268102). Here we extend the Lighthill/Blake axisymmetric, Stokes-flow model of a free-swimming spherical squirmer (LighthillCommun. Pure Appl. Maths, vol. 5, 1952, pp. 109-118; BlakeJ. Fluid Mech., vol. 46, 1971b, pp. 199-208) to include azimuthal swirl. The measured kinematics of the metachronal wave for 60 different colonies are used to calculate the coefficients in the eigenfunction expansions and hence predict the mean swimming speeds and rotation rates, proportional to the square of the beating amplitude, as functions of colony radius. As a test of the squirmer model, the results are compared with measurements (Drescheret al.Phys. Rev. Lett., vol. 102, 2009, 168101) of the mean swimming speeds and angular velocities of a different set of 220 colonies, also given as functions of colony radius. The predicted variation with radius is qualitatively correct, but the model underestimates both the mean swimming speed and the mean angular velocity unless the amplitude of the flagellar beat is taken to be larger than previously thought. The reasons for this discrepancy are discussed.
authors: Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Centre for Mathematical Sciences , Wilberforce Road , Cambridge CB3 0WA , UK.
authors: T J
authors: TJ
authors: Pedley
authors: Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093 Zurich, Switzerland.
authors: D R
authors: DR
authors: Brumley
authors: Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Centre for Mathematical Sciences , Wilberforce Road , Cambridge CB3 0WA , UK.
authors: R E
authors: RE
authors: Goldstein
keywords: biological fluid dynamics; micro-organism dynamics; swimming/flying