  We analyse a simple 'Stokesian squirmer' model for the enhanced mixing due to
swimming micro-organisms. The model is based on a calculation of Thiffeault &
Childress [Physics Letters A, 374, 3487 (2010), arXiv:0911.5511], where fluid
particle displacements due to inviscid swimmers are added to produce an
effective diffusivity. Here we show that for the viscous case the swimmers
cannot be assumed to swim an infinite distance, even though their total mass
displacement is finite. Instead, the largest contributions to particle
displacement, and hence to mixing, arise from random changes of direction of
swimming and are dominated by the far-field stresslet term in our simple model.
We validate the results by numerical simulation. We also calculate nonzero
Reynolds number corrections to the effective diffusivity. Finally, we show that
displacements due to randomly-swimming squirmers exhibit PDFs with exponential
tails and a short-time superdiffusive regime, as found previously by several
authors. In our case, the exponential tails are due to 'sticking' near the
stagnation points on the squirmer's surface.

Fluid Dynamics;Soft Condensed Matter;Biological Physics