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arXiv · 2507.11197

Improved boundary homogenization for a sphere with an absorbing cap of arbitrary size

Denis S. Grebenkov
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Abstract

Finding accurate approximations for the effective reactivity of a structured spherical target with a circular absorbing patch of arbitrary size is a long-standing problem in chemical physics. In this Communication, we reveal limitations of the empirical approximation proposed in [J. Chem. Phys. 145, 214101 (2016)]. We show that the original approximation fails at large patch surface fractions $\sigma$ and propose a simple amendment. The improved approximation is validated against a semi-analytical solution and is shown to be accurate over the entire range of $\sigma$ from $0$ to $1$. This approximation also determines the probability of reaction on the patch and the capacitance of such a structured target.

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Denis S. Grebenkov. 2025-07-15. Improved boundary homogenization for a sphere with an absorbing cap of arbitrary size. https://arxiv.org/abs/2507.11197

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