Bacterial residence time near a plane for smooth swimmers

Bacterial dynamics near a boundary surface are biologically important. It has been demonstrated that bacteria can stay near the boundary surface for a prolonged time as if they are trapped. When the eventual escape of bacteria out of such entrapment is modeled as a classical one-dimensional Kramers problem concerning only the orientational degree of freedom, a simple but elegant formula can be obtained, but if/how the formula applies is unclear since the model totally neglects the contribution from the equally important translational degree of freedom characterized by the surface distance between the entrapped bacterium and the boundary surface. In this work, we systematically study the dynamics of smooth-swimming Escherichia coli near a planar boundary through numerical simulations, from which we can extract the bacterial residence time to compare with the analytical solution of the corresponding Kramers problem. It is demonstrated that two parameters, a characteristic pitch angle and a characteristic surface distance, are both needed for the correct parameterization of the analytical solution. Furthermore, we demonstrate that the characteristic pitch angle and surface distance can be modulated by bacterial dimensions, i.e., the characteristic sizes of bacteria, leading to diverse residence times (almost a factor of two orders of magnitude) for bacteria with small variations in dimensions.