Diffusion-Limited Growth of Wetting Layers

In binary liquid mixtures, the growth of wetting layers can be limited by diffusion. At complete wetting, the distance $l$ between the interfaces bounding the layer is shown to grow as $l\left(t\right)\mathrm{}\approx A_{*}{t}^{\theta }$ for large times $t$ where $A_{*}$ increases near the consolute point. In three dimensions where this growth behavior should be accessible to experiments, $\theta =\frac{1}{8} \mathrm{and} \frac{1}{10}$ for nonretarded and retarded van der Waals forces, respectively. The interfacial motion resulting from diffusion-limited growth is studied for general interactions, and a planar interface is found to be stable for $\theta <\frac{1}{2}$.