  The effect of shape asymmetry of microswimmers on their adsorption capacity
at confining channel walls is studied by a simple dumbbell model. For a shape
polarity of a forward-swimming cone, like the stroke-averaged shape of a sperm,
extremely long wall retention times are found, caused by a non-vanishing
component of the propulsion force pointing steadily into the wall, which grows
exponentially with the self-propulsion velocity and the shape asymmetry. A
direct duality relation between shape asymmetry and wall curvature is proposed
and verified. Our results are relevant for the design microswimmer with
controlled wall-adhesion properties. In addition, we confirm that pressure in
active systems is strongly sensitive to the details of the particle-wall
interactions.
