Escape of a sticky particle
Yuval Scher, Shlomi Reuveni, Denis S. Grebenkov
Abstract
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 a 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 an 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 paper thus offers a starting point for analytical and numerical studies of stickiness and its role in escape, first-passage, and diffusion-controlled reactions.