  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
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 (1976) 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.
