  Confinement and wall effects are known to affect the kinematics and
propulsive characteristics of swimming microorganisms. When a solid body is
dragged through a viscous fluid at constant velocity, the presence of a wall
increases fluid drag, and thus the net force required to maintain speed has to
increase. In contrast, recent optical trapping experiments have revealed that
the propulsive force generated by human spermatozoa is decreased by the
presence of boundaries. Here, we use a series of simple models to analytically
elucidate the propulsive effects of a solid boundary on passively actuated
filaments and model flagella. For passive flexible filaments actuated
periodically at one end, the presence of the wall is shown to increase the
propulsive forces generated by the filaments in the case of displacement-driven
actuation, while it decreases the force in the case of force-driven actuation.
In the case of active filaments as models for eukaryotic flagella, we
demonstrate that the manner in which a solid wall affects propulsion cannot be
known a priori, but is instead a nontrivial function of the flagellum
frequency, wavelength, its material characteristics, the manner in which the
molecular motors self-organize to produce oscillations (prescribed activity
model or self-organized axonemal beating model), and the boundary conditions
applied experimentally to the tethered flagellum. In particular, we show that
in some cases, the increase in fluid friction induced by the wall can lead to a
change in the waveform expressed by the flagella which results in a decrease in
their propulsive force.
