The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is still not well understood. We demonstrate that it is crucial to include a commonly neglected entropic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: the ratio of thermal energy to self-propulsion, and an intrinsic shape factor. For an E. coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: the bacterial nose-down configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by the two dimensionless parameters.
Roberto Di Leonardo