Biflagellate gyrotaxis in a shear flow

Abstract

A flagellated, bottom-heavy micro-organism's swimming direction in a shear flow is determined from a balance between the gravitational and viscous torques (gyrotaxis). Hitherto, the cell has been assumed to be a spheroid and the flagella have been neglected. Here we use resistive-force theory to calculate both the magnitude and the direction of a biflagellate cell's swimming velocity and angular velocity relative to the fluid when there is an arbitrary linear flow far from the cell. We present an idealized model for the flagellar beat but, in calculating the velocity of the fluid relative to an element of a flagellum, the presence of the cell body is not neglected. Results are given for the case of a spherical cell body whose flagella beat in a vertical plane, when the ambient linear flow is in the same vertical plane. Results show that resistive-force theory can be used for organisms where the cell body has significant effect on the flow past the flagella and that the viscous torque on the flagella is a significant term in the torque balance equations. A model is presented for the calculation of a cell's velocity and angular velocity in a shear flow which is valid up to high magnitudes of rate of strain or vorticity. The main application of the results will be to modify a recent continuum model for suspensions of gyrotactic micro-organisms (Pedley & Kessler 1990).