Escape from textured adsorbing surfaces
arxiv(2024)
摘要
The escape dynamics of sticky particles from textured surfaces is poorly
understood despite importance to various scientific and technological domains.
In this work, we address this challenge by investigating the escape time of
adsorbates from prevalent surface topographies, including holes/pits, pillars,
and grooves. Analytical expressions for the probability density function and
the mean of the escape time are derived. A particularly interesting scenario is
that of very deep and narrow confining spaces within the surface. In this case,
the joint effect of the entrapment and stickiness prolongs the escape time,
resulting in an effective desorption rate that is dramatically lower than that
of the untextured surface. This rate is shown to abide a universal scaling law,
which couples the equilibrium constants of adsorption with the relevant
confining length scales. While our results are analytical and exact, we also
present an approximation for deep and narrow cavities based on an effective
description of one dimensional diffusion that is punctuated by motionless
adsorption events. This simple and physically motivated approximation provides
high-accuracy predictions within its range of validity and works relatively
well even for cavities of intermediate depth. All theoretical results are
corroborated with extensive Monte-Carlo simulations.
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