An entropic effect essential for surface entrapment of bacteria

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 $\{\alpha_1,\alpha_2\}$.