Theoretical modeling in microscale locomotion

• Published in: Microfluidics and nanofluidics 2016-07, Vol.20 (7), p.1, Article 98
• Main Authors: Koh, James B. Y., Shen, Xinhui, Marcos
• Format: Article
• Language: English
• Subjects: Analytical Chemistry; Biomedical Engineering and Bioengineering; Engineering; Engineering Fluid Dynamics; Nanotechnology and Microengineering; Review; Swimming
• ISSN: 1613-4982; 1613-4990
• DOI: 10.1007/s10404-016-1761-y

The validity of some commonly used models and approximations in theoretical studies of microscale locomotion are reviewed, by taking reference from conclusions drawn in experimental and numerical studies. The first model, resistive force theory, neglects interactions and results in vastly varying degrees of accuracy across different studies. The second, slender body theory, uses a series of force singularities to determine the velocity field and generally gives a single-digit percentage error. The method of regularized Stokeslet is the third model, which replaces each force singularity with a blob of distributed forces, and can be as accurate as 99.5 %. In the subsequent part of this review, we look into conditions under which some general assumptions are valid. The studies reviewed show unanimous agreement that wall effects and cell-to-cell interactions can be neglected when the cells are spaced an order of magnitude of their length scale away. In addition, the sedimentation velocity of motile spermatozoa as well as bacteria is concluded to be insignificant. Evidence is also presented to show that Brownian motion of particles larger than 10 µm is negligible. The effect of rheotaxis have to be considered when dealing with shear flow, as the velocity can be modified by over a tenth of a cell’s free-swimming velocity.