= Diffusion-capacitance analogy
A quasi-static <chemical potential> outside a fixed-shape droplet solves the same <Laplace equation> as an <electrostatic potential> outside an equipotential conductor. If $\mu=\mu_s$ on the droplet and zero on the surrounding reservoirs, its outward diffusive current is
$$
I=-M\int_{\partial D}\partial_n\mu\,dS
=\frac M\epsilon C\mu_s,
$$
where $C$ is the corresponding electrostatic <capacitance> in a medium of <permittivity> $\epsilon$. The arbitrary $\epsilon$ cancels against the capacitance's proportionality to $\epsilon$. Thus electrostatic geometry directly determines evaporation rates.
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