``Casimir effect'' with active swimmers

In recent years, active matter has increasingly found applications in nanoengineering.\footnote{R. DiLeonardo et al, Proc. Natl. Acad. Sci. U.S.A. 107, 9541 (2010); B. Kaehr and J. B. Shear, Lab on a Chip, 9, 2632 (2009).} Here we show using molecular dynamics simulations that the natural motion of ``run-and-tumble'' bacteria will push together two parallel walls arranged in a Casimir geometry. This effect is robust as long as the wall separation is comparable to or smaller than the bacterial run-length, so that the bacterial motion is not Brownian on the length scale of the walls. The magnitude of the attractive force between the walls exhibits an unusual exponential dependence on the wall separation. The attraction arises from a depleted concentration of bacteria in the region between the plates; this is caused by the tendency of the bacteria to slide along the walls, which breaks time-reversal symmetry and allows a density difference to develop. The same mechanism was used recently to explain bacterial rectification.\footnote{M. B. Wan et al, Phys. Rev. Lett., 101, 018102 (2008); J. Tailleur and M. E. Cates, Europhys. Lett. 86, 60002 (2009).} The inclusion of steric interactions between the bacteria reduces the attraction between the plates but does not eliminate it.