  We consider the tracer diffusion $D_{rr}$ that arises from the run-and-tumble
motion of low Reynolds number swimmers, such as bacteria. In unbounded dilute
suspensions, where the dipole swimmers move in uncorrelated runs of length
$\lambda$, an exact solution showed that $D_{rr}$ is independent of $\lambda$.
Here we verify this result in numerical simulations for a particular model
swimmer, the spherical squirmer. We also note that in confined
microenvironments, such as microscopic droplets, microfluidic devices and
bacterial microzones in marine ecosystems, the size of the system can be
comparable to $\lambda$. We show that this effect alone reduces the value of
$D_{rr}$ in comparison to its bulk value, and predict a scaling form for its
relative decrease.
