  Cells swimming in confined environments are attracted by surfaces. We measure
the steady-state distribution of smooth-swimming bacteria (Escherichia coli)
between two glass plates. In agreement with earlier studies, we find a strong
increase of the cell concentration at the boundaries. We demonstrate
theoretically that hydrodynamic interactions of the swimming cells with solid
surfaces lead to their re-orientation in the direction parallel to the
surfaces, as well as their attraction by the closest wall. A model is derived
for the steady-state distribution of swimming cells, which compares favorably
with our measurements. We exploit our data to estimate the flagellar propulsive
force in swimming E. coli.
