Fluid transport by cilia between parallel plates | Journal of Fluid Mechanics | Cambridge Core (original) (raw)

Abstract

The problem of fluid transport by cilia is investigated using the Green's function for a Stokeslet between two parallel plates. The discrete-cilia approach is used in building the model, and a readily usable expression for the velocities is obtained. Dependence on the direction of the metachronal wave and on time is not averaged out. Velocity fields, pressure fields and fluxes due to a single Stokeslet and to an infinite line of Stokeslets are discussed. It is found that the flux associated with Stokeslets in between two parallel plates is always zero, in contrast to a Stokeslet parallel to, and above, one plate. In the model one also has to add a plane Poiseuille flow, which incorporates non-zero flux. The flow due to the Stokeslet solution imposes a positive pressure gradient downstream, and the Poiseuille flow a negative pressure gradient. Calculated velocity profiles, in the pumping range, are seen to be time-independent in the centre of the channel and vary between a negative parabolic profile and a plug flow. The reason for these profiles and some possible biological applications are discussed.

Type

Research Article

References

Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary.Proc. Camb. Phil. Soc. 70,303–310.Google Scholar

Blake, J. R. 1972 A model for the micro-structure in ciliated organisms.J. Fluid Mech. 55,1–23.Google Scholar

Blake, J. R. 1973 Flow in tubules due to ciliary activity.Bull. Math. Biol. 35,513–523.Google Scholar

Blake, J. R. & Sleigh, M. A. 1974 Mechanics of ciliary locomotion.Biol. Rev. 49,85–125.Google Scholar

Blandau, R. J. 1969 Gamete transport – comparative aspects. In_The Mammalian Oviduct_ (ed. Hafez E. S. E. & R. J. Blandau).University of Chicago Press.

Blum, J. J. 1974 A note on fluid transport in ciliated tubules.J. Theor. Biol. 46,287–290.Google Scholar

Lardner, T. J. & Shack, W. J. 1972 Cilia transport.Bull. Math. Biophys. 34,325–335.Google Scholar

Liron, N. 1976 On peristaltic flow and its efficiency.Bull. Math. Biol. 38,573–596.Google Scholar

Liron, N. & Mochon, S. 1976a Stokes flow for a Stokeslet between two parallel flat plates.J. Engng Math. 10,287–303.Google Scholar

Liron, N. & Mochon, S. 1976b The discrete-cilia approach to propulsion of ciliated microorganisms.J. Fluid Mech. 75,593–607.Google Scholar