Bacterial searching scope on a planar surface

The ability to explore a surface is biologically important for swimming bacteria. It has been demonstrated that a bacterium can swim near a planar surface for a prolonged period of time over a long distance. The eventual departure of the bacterium away from the surface has traditionally been interpreted as a classical one-dimensional Kramers problem about the angle made between bacterial orientation direction and the planar surface. In this work, we systematically study the near-wall dynamics of smooth-swimming Escherichia coli near a planar boundary through numerical simulations, from which we can extract the distance S the bacterium traveled during the period of time when it is near the surface. Our results demonstrate a characteristic travel distance [Formula: see text], as the probability [Formula: see text] decays exponentially with S. Furthermore, we demonstrate that the characteristic travel distance [Formula: see text] can be sensitively modulated by bacterial dimensions, i.e. the characteristic sizes of bacteria. Our results show that the diverse [Formula: see text] spans almost two orders of magnitude for bacteria with small variations in dimensions, where an exponential dependence is obtained.