2134/36376
Arnold J.T.M. Mathijssen
Arnold J.T.M.
Mathijssen
Amin Doostmohammadi
Amin
Doostmohammadi
Julia M. Yeomans
Julia M.
Yeomans
Tyler Shendruk
Tyler
Shendruk
Hydrodynamics of micro-swimmers in films
Loughborough University
2018
Biological fluid dynamics
Low-Reynolds-number flows
Micro-organism dynamics
Mathematical Sciences not elsewhere classified
2018-12-10 13:46:17
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Hydrodynamics_of_micro-swimmers_in_films/9384800
One of the principal mechanisms by which surfaces and interfaces affect microbial
life is by perturbing the hydrodynamic flows generated by swimming. By summing
a recursive series of image systems, we derive a numerically tractable approximation
to the three-dimensional flow fields of a stokeslet (point force) within a viscous film
between a parallel no-slip surface and a no-shear interface and, from this Green’s
function, we compute the flows produced by a force- and torque-free micro-swimmer.
We also extend the exact solution of Liron & Mochon (J. Engng Maths, vol. 10 (4),
1976, pp. 287–303) to the film geometry, which demonstrates that the image series
gives a satisfactory approximation to the swimmer flow fields if the film is sufficiently
thick compared to the swimmer size, and we derive the swimmer flows in the
thin-film limit. Concentrating on the thick-film case, we find that the dipole moment
induces a bias towards swimmer accumulation at the no-slip wall rather than the
water–air interface, but that higher-order multipole moments can oppose this. Based
on the analytic predictions, we propose an experimental method to find the multipole
coefficient that induces circular swimming trajectories, allowing one to analytically
determine the swimmer’s three-dimensional position under a microscope.