Premium
On the squirming motion of nearly spherical deformable bodies through liquids at very small reynolds numbers
Author(s) -
Lighthill M. J.
Publication year - 1952
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160050201
Subject(s) - citation , reynolds number , motion (physics) , mathematics , mathematics education , computer science , calculus (dental) , combinatorics , physics , library science , artificial intelligence , mechanics , turbulence , medicine , dentistry
A spherical deformable body can swim, at very small Reynolds numbers, by performing small oscillations of shape. However, the mean velocity of translation is a t most of the order of the square of the amplitude of the deformations. Three examples of swimming motions, in &h of which the mapimum surface strain is 1/3, are illustrated in Figures 1, 2 and 3. Even in the moat efficient of the three (Fig. 2), the mean power required to obtaii a given mean velocity is twenty times that given by Stokes' formula for the uniform motion of a rigid sphere under an external force. This ratio varies as the inverse square of the maximum surface strain.