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In Ostwald ripening, the higher interfacial chemical potential of small droplets drives diffusion toward larger droplets, increasing the characteristic domain size. The Gibbs--Thomson relation supplies the curvature-dependent surface value, while conserved order-parameter dynamics controls transport through the surrounding phase.

In the exterior write $\varphi =-{\varphi }_B+\tilde{\varphi }$. Linearization at the bulk minimum givesFor a large droplet, variations occur on scale $R$ much larger than the interfacial correlation length, so the second term is smaller by $O(\kappa /(\alpha R^2))$ and $\mu \simeq \alpha \tilde{\varphi }$. The conserved order-parameter dynamics then becomesDiffusion relaxes the exterior profile much faster than the droplet radius changes. In this quasistatic limit ${\partial }_t\tilde{\varphi }\simeq 0$, and therefore

TakeIts variational chemical potential isConservation gives $\dot{\varphi }=-\nabla \cdot \mathbf{J}$. Assuming an isotropic constant mobility $M>0$, local linear irreversible thermodynamics gives $\mathbf{J}=-M\nabla \mu$. Hence the noiseless conserved order-parameter dynamics isIt decreases the free energy because $\dot{F}=-\int M|\nabla \mu {|}^{2}d\mathbf{r}\le 0$ under closed or no-flux boundary conditions.

The functional derivatives areWith the stated Fourier convention,The first is conserved order-parameter dynamics; its deterministic rate and conserved-noise amplitude vanish at $q=0$. The second is nonconserved order-parameter dynamics.