  The effect of crowding on the run-and-tumble dynamics of swimmers such as
bacteria is studied using a discrete lattice model of mutually excluding
particles that move with constant velocity along a direction that is randomized
at a rate $\alpha$. In stationary state, the system is found to break into
dense clusters in which particles are trapped or stopped from moving. The
characteristic size of these clusters predominantly scales as $\alpha^{-0.5}$
both in 1D and 2D. For a range of densities, due to cooperative effects, the
stopping time scales as ${\cal T}_{1d}^{0.85}$ and as ${\cal T}_{2d}^{0.8}$,
where ${\cal T}_d$ is the diffusive time associated with the motion of cluster
boundaries. Our findings might be helpful in understanding the early stages of
biofilm formation.
