= Solution
The <Young–Laplace equation> gives a pressure excess $2\sigma/R$ inside a spherical droplet. Near coexistence, the common chemical-potential shift is $\mu\simeq\alpha\delta$, where $\alpha=f''(\phi_B)$, while changing phase changes the composition by approximately $2\phi_B$. Balancing the capillary pressure against this thermodynamic shift gives the <Gibbs--Thomson relation>
$$
2\phi_B\alpha\delta\simeq\frac{2\sigma}{R}.
$$
Hence the compositions immediately outside and inside are
$$
\phi(R^+)=-\phi_B+\delta(R),
\qquad
\phi(R^-)=+\phi_B+\delta(R),
$$
with
$$
\boxed{\delta(R)=\frac{\sigma}{\alpha\phi_BR}\propto\frac\sigma R.}
$$
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