Since the Annual Review of Fluid Mechanics first published a review on microorganism locomotion by Jahn & Votta (1972) considerable progress has been made in the understanding of both the biological and the fluid-mechanical processes involved not only in microorganism locomotion but also in other fluid systems utilizing cilia. Much of this knowledge and research, which has been built on the solid foundation of the pioneering work of Sir James Gray (1928, 1968) and Sir Geoffrey Taylor (1951, 1952a,b), has been reported extensively elsewhere, particularly by Gray (1928, 1968), Sleigh (1962), Lighthill (1975), and Wu, Brokaw & Brennen (1975). The subject is now sufficiently broad that it precludes any exhaustive treatment in these few pages. Rather, we restrict this review primarily to a summary of present understanding of the low-Reynolds-number flows associated with microorganism propulsion and the hydromechanics of ciliary systems. In this introductory section we wish to put such fluid-mechanical studies in biological perspective. Section 2 outlines the present status of low-Reynolds-number slender-body theory, and we discuss the application of this theory to biological systems in the final sections.

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Fluid Mechanics of Propulsion by Cilia and Flagella

Peristaltic transport of blood: Casson model--II.

A study on peristaltic flow of nanofluids: Application in drug delivery systems

Mechanics of ciliary locomotion.

The classical lubrication-theory model of steady peristaltic transport of periodic sinusoidal waves in infinite-length tubes (Shapiro et al. 1969) is generalized to arbitrary wave shape and wavenumber in tubes of finite length. Whereas the classical model is steady in a frame of reference moving with the peristaltic waves, peristaltic transport in a finite-length tube is inherently non-steady. It may be shown, however, that pumping performance is independent of tube length if there exists an integral number of peristaltic waves in the tube. Three particularly interesting characteristics of non-steady peristalsis are described: (i) fluctuations in pressure and shear stress arise due to a non-integral number of waves in the finite-length tube; (ii) retrograde motion of fluid particles during peristaltic transport (reflux) has inherently different behaviour with single peristaltic waves as compared to multiple ‘train waves’, and (iii) finite tube length, the number of peristaltic waves and the degree of tube occlusion affect global pumping performance. We find that, whereas significant increases in pressure and shear stress result from the tube-to-wave length ratio being non-integral, global pumping performance is only slightly degraded by the existence of a non-integral number of waves in the tube during peristaltic transport. Furthermore, the extent of retrograde motion of fluid particles is much greater with single waves than with train waves. These results suggest that in the design and analysis of peristaltic pumps attention should be paid to the unsteady effects of finite tube length and to the differences between single and multiple peristaltic waves.

Non-steady peristaltic transport in finite-length tubes

Peristaltic flow in tubes.

Analytical investigation of cilia induced mucous flow.

The problem of small angle depressions in a liquid surface due to an impinging two-dimensional potential jet is considered. Using conformal mapping methods and finite Hilbert transforms, the problem is formulated as a non-linear singular integral equation. The integral equation is approximated by a set of non-linear algebraic equations which are solved numerically by a method of repeated linear corrections. In addition, an asymptotic solution (for low jet velocity) is derived.From the numerical solutions of the integral equation, the liquid-surface profiles and the free streamlines of the jet are calculated for four cases. These results verify the appearance of lips on the liquid surface which have been observed experimentally by others.

Depression of an infinite liquid surface by an incompressible gas jet

Transient radiation heating of a rotating cylindrical shell

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S. Raynor

Papers

Peristaltic flow in tubes.

Analytical investigation of cilia induced mucous flow.

Depression of an infinite liquid surface by an incompressible gas jet

Transient radiation heating of a rotating cylindrical shell

Solar heating of a rotating solid cylinder.