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The far-field composition $-{\varphi }_B$ has chemical potential zero. Local curved-interface coexistence imposes $\mu (R)={\mu }_s=\gamma /({\varphi }_{B}R)$. The decaying spherically symmetric solution of the exterior Laplace equation isWith constant mobility, its outward current isThe linearized exterior composition is $\varphi (r)=-{\varphi }_B+\mu (r)/\alpha$, consistent with the surface shift in the previous part.

For diffusion-controlled droplet growth, the interior is uniform to leading order and has no diffusive current. Replacing exterior material by interior material requires the composition jump $2{\varphi }_B$, so conservation gives $2{\varphi }_B\dot{R}=-J_r(R)$. HenceThe negative sign represents evaporation. The total outward current is $4\pi R^2{J}_r(R)=4\pi M\gamma /{\varphi }_B$, independent of $R$ in this leading quasi-static capillary approximation.

Integrate the diffusion-controlled droplet growth equation: $d(R^3)/dt=-3M\gamma /(2{\varphi }_B^2)$. ThusSetting the radius to zero givesThis is the lifetime predicted by the sharp-interface quasi-static model. The final stage at a radius comparable to the interface width falls outside that approximation, while the leading lifetime for a large initial droplet is dominated by the larger radii.