Mechanics of Swimming and Flying

Abstract

This book provides a clear and concise summary of the fluid dynamics of the locomotion of living organisms. The biological phenomena described in detail range from the swimming of bacteria and fish to the flying of insects and birds. The breadth of treatment requires the study of two basic fluid-dynamical regimes. In the first case, that of small organisms, the viscosity of the fluid is paramount in deciding the most effective swimming strategy. However, for larger insects, birds, and most fish, the viscosity of the air or water may be treated as if it were zero, and resulting mechanisms of propulsion are very different. Both these types are studied, with emphasis on the unsteady character of natural movements. Written for the advanced student, this volume assumes familiarity with basic fluid mechanics, although some elementary topics are included. It will be readily accessible to students of applied mathematics and biologists who have engineering or physics backgrounds.

On the self-propulsion of an -sphere micro-robot

“…At the same time our choice of slow time s = ε 2 t (3.5) agrees with the classical studies of self-propulsion for low Reynolds numbers, see Taylor (1951), Blake (1971) and Childress (1981), as well as geometric studies of Shapere & Wilczek (1989).…”

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

“…We represent the fluid mechanics by means of the three-dimensional time dependent Navier-Stokes equations for incompressible flow. Since the Reynolds number for bacterial swimming is on the order of 10 −5 [25], the Stokes equations could be used for this model.…”

“…Under the assumption that the ratio of the flagellar radius a to the flagellum length L is small [25], the flagellar velocity w can be represented in terms of the flagellar force distribution f approximately as…”

“…Most motile bacteria move by the use of one or more flagella and are able to swim in a viscous fluid environment [85]. Alternative forms of bacterial motility include gliding in myxobacteria [96,104,52,40] and the complex swimming mechanisms of spirochaetes [25,105]. Bacterial swarming on surfaces is also facilitated by flagella [58].…”

“…Lighthill [70,71] developed an alternative slender body theory, to be described later, and suggested more advanced modifications of the resistive force coefficients of Gray and Hancock. Childress [25] gave a formal proof of Lighthill's slender body theorem for an infinite flagellum. Johnson and Brokaw [67] investigated and compared the distinctions between (RFT) and (SBT) on forces, bending and shear moments.…”