Life at low Reynolds number

Abstract

E d i t o r’s note: This is a reprint (slightly edited) of a paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weisskopf, published by the American Institute of Physics (1976). The personal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced.

Artificial cilia fabricated using magnetic fiber drawing generate substantial fluid flow

“…Thus, a non-reciprocal motion needs to be adopted in order to generate a transportation effect, as concluded by Purcell in his ''scallop theorem'' (Purcell 1977). Indeed, for example, the motion of a paramecium's cilium can be divided into two parts: (1) an effective stroke during which they are straight and sweep widely in a plane perpendicular to the surface, thus maximizing their influence on the surrounding fluid; this effective stroke is followed by (2) a recovery stroke in which the cilia are bent and move close to the surface, thereby reducing their influence on the fluid.…”

Dynamics of bacterial flow: Emergence of spatiotemporal coherent structures

“…A population of live microorganisms, such as bacteria like E. coli, suspended in an aqueous environment can provide a particular interesting model system to study pattern formation and collective motion in biology since the dynamics of the individual bacteria can be directly observed and critical parameters such as density and activity may be brought under experimental control [4]. These microorganisms continuously consume nutrients and dissipate the energy through the process of propelling themselves against the frictional force exerted on them by the fluid [5]. With a typical size of a bacterium of the order of microns and a typical speed of the order of 10 µm/s, the Reynolds number R ≪ 1 is quite small.…”

Swimming at Low Reynolds Number: From Sheets to the African Trypanosome

“…A potential swimmer cannot move forward with a reciprocal actuation cycle, meaning a cycle which looks the same under time reversal. This is the content of Purcell's famous scallop theorem [26]. Swimming at low Reynolds number needs a nonreciprocal actuation cycle.…”

“…The physics governing swimming in the microscopic world is completely different from the macroscopic world. On a micron scale inertia is negligible and microorganisms have to resort to a propulsion mechanism where they are constantly in motion in order to translate forward [19,26]. These propulsion mechanisms are numerous and include the flagellar breast stroke of Chlamydomonas reinhardtii [9] and the planar flagellar beating of sperm cells [5,28].…”

“…To study various propulsion mechanism, simplified models have been introduced such as the Taylor sheet [32], the Purcell swimmer [26], and the squirming sphere [8,20]. They capture the basic physics of the different propulsion mechanisms.…”