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.
For a three-dimensional droplet with concentration jump , constant mobility , and quasi-static exterior chemical potential,The first formula solves the exterior Laplace equation. The second follows from conservation: the total outward flux removes excess composition at the rate . For a symmetric mixture, and the Gibbs--Thomson relation gives .
A quasi-static chemical potential outside a fixed-shape droplet solves the same Laplace equation as an electrostatic potential outside an equipotential conductor. If on the droplet and zero on the surrounding reservoirs, its outward diffusive current iswhere is the corresponding electrostatic capacitance in a medium of permittivity . The arbitrary cancels against the capacitance's proportionality to . Thus electrostatic geometry directly determines evaporation rates.
For a spherical droplet at fixed center height above a flat equilibrium reservoir, the diffusion-capacitance analogy and sphere-plane capacitance giveAt large separation, , soThe nearby reservoir increases the total flux and shortens the lifetime. The spherical-shape assumption controls the geometry; the local current density is not uniform over the surface.
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Ostwald ripening is a phenomenon that occurs in solid dispersions, emulsions, and other colloidal systems, where larger particles grow at the expense of smaller ones over time. This process is driven by differences in solubility and chemical potential between particles of different sizes. In a dispersed system, smaller particles tend to have a higher curvature (meaning they have a higher surface area relative to their volume) compared to larger particles.