A body immersed in a highly viscous fluid can locomote by drawing in and
expelling fluid through pores at its surface. We consider this mechanism of jet
propulsion without inertia in the case of spheroidal bodies, and derive both
the swimming velocity and the hydrodynamic efficiency. Elementary examples are
presented, and exact axisymmetric solutions for spherical, prolate spheroidal,
and oblate spheroidal body shapes are provided. In each case, entirely and
partially porous (i.e. jetting) surfaces are considered, and the optimal
jetting flow profiles at the surface for maximizing the hydrodynamic efficiency
are determined computationally. The maximal efficiency which may be achieved by
a sphere using such jet propulsion is 12.5%, a significant improvement upon
traditional flagella-based means of locomotion at zero Reynolds number. Unlike
other swimming mechanisms which rely on the presentation of a small cross
section in the direction of motion, the efficiency of a jetting body at low
Reynolds number increases as the body becomes more oblate, and limits to
approximately 162% in the case of a flat plate swimming along its axis of
symmetry. Our results are discussed in the light of slime extrusion mechanisms
occurring in many cyanobacteria
