  Adsorption to a surface, reversible-binding, and trapping are all prevalent
scenarios where particles exhibit "stickiness". Escape and first-passage times
are known to be drastically affected, but detailed understanding of this
phenomenon remains illusive. To tackle this problem, we develop an analytical
approach to the escape of a diffusing particle from a domain of arbitrary
shape, size, and surface reactivity. This is used to elucidate the effect of
stickiness on the escape time from a slab domain: revealing how adsorption and
desorption rates affect the mean and variance, and providing a novel approach
to infer these rates from measurements. Moreover, as any smooth boundary is
locally flat, slab results are leveraged to devise a numerically efficient
scheme for simulating sticky boundaries in arbitrary domains. Generalizing our
analysis to higher dimensions reveals that the mean escape time abides a
general structure that is independent of the dimensionality of the problem.
This letter thus offers a new starting point for analytical and numerical
studies of stickiness and its role in escape, first-passage, and
diffusion-controlled reactions.
