= Solution
The flat interface is an equilibrium reservoir with $\mu=0$, while the droplet has the constant surface value $\mu_s=\gamma/(\phi_BR)$. The exterior <chemical potential> satisfies the <Laplace equation>, tends to zero far away, and obeys these two surface values. These are exactly the <electrostatic boundary conditions at a conductor> for a sphere held at potential $\mu_s$ above a grounded infinite plane.
Introduce an arbitrary <permittivity> $\epsilon$. In the electrostatic problem, $Q=-\epsilon\int_{S_R}\partial_n\mu\,dS=C(R,h)\mu_s$. Therefore the <diffusion-capacitance analogy> gives the outward current
$$
I(R,h)=-M\int_{S_R}\partial_n\mu\,dS=\frac M\epsilon C(R,h)\mu_s.
$$
For an isolated sphere, its <capacitance> is $C(R,\infty)=4\pi\epsilon R$, so $I(R,\infty)=4\pi MR\mu_s=4\pi M\gamma/\phi_B$. Dividing gives
$$
\boxed{I(R,h)=I(R,\infty)c(R/h),\qquad c(R/h)=\frac{C(R,h)}{C(R,\infty)}.}
$$
Thus <sphere-plane capacitance> determines the evaporation enhancement. The assumed spherical shape gives the corresponding law $\dot R=-M\gamma c(R/h)/(2\phi_B^2R^2)$ for <droplet evaporation near a planar reservoir>. The local surface current is generally nonuniform, even though its total is described by a single capacitance.
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