Escape of a Sticky Particle

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 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.

5 Pages + 13 appendices pages, 4 + 3 figures

References in corpus (7)

• Paradigm shift in diffusion-mediated surface phenomena
• Full distribution of first exit times in the narrow escape problem
• First passage time statistics for two-channel diffusion
• Exit time distribution in spherically symmetric two-dimensional domains
• First hitting times to intermittent targets
• An encounter-based approach to the escape problem
• Reversible reactions controlled by surface diffusion on a sphere

Cited by in corpus (6)

• Escape from textured adsorbing surfaces
• Continuous Gated First-Passage Processes
• Escape-from-a-layer approach for simulating the boundary local time in Euclidean domains
• Characterizing and quantifying weak chaos in fractional dynamics
• Adsorption and permeation events in molecular diffusion
• Universal Linear Response of First-Passage Kinetics: A Framework for Prediction and Inference