  We consider the classical problem of particle diffusion in $d$-dimensional
radially-symmetric systems with absorbing boundaries. A key quantity to
characterise such diffusive transport is the evolution of the proportion of
particles remaining in the system over time, which we denote by
$\mathcal{P}(t)$. Rather than work with analytical expressions for
$\mathcal{P}(t)$ obtained from solution of the corresponding continuum model,
which when available take the form of an infinite series of exponential terms,
single-term low-parameter models are commonly proposed to approximate
$\mathcal{P}(t)$ to ease the process of fitting, characterising and
interpreting experimental release data. Previous models of this form have
mainly been developed for circular and spherical systems with an absorbing
boundary. In this work, we consider circular, spherical, annular and
spherical-shell systems with absorbing, reflecting and/or semi-absorbing
boundaries. By proposing a moment matching approach, we develop several simple
one and two parameter exponential and Weibull models for $\mathcal{P}(t)$, each
involving parameters that depend explicitly on the system dimension,
diffusivity, geometry and boundary conditions. The developed models, despite
their simplicity, agree very well with values of $\mathcal{P}(t)$ obtained from
stochastic model simulations and continuum model solutions.

Computational Physics;Chemical Physics