An entropic effect essential for surface entrapment of bacteria

Abstract: 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 arising from the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: $\alpha_1$ the ratio of thermal energy to self-propulsion, and $\alpha_2$ an intrinsic shape factor. For $\alpha_1$ and $\alpha_2$ that match an {\it Escherichia 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 ${\alpha_1,\alpha_2}$.