We have examined the growth with time t of the thickness l of wetting
layers from thin films of binary fluid mixtures, using real-space comp
osition-depth profiling based on nuclear reaction analysis. We find ov
er a wide range of parameters that the observed growth behavior has a
power law form l proportional to t(kappa) where kappa is the range 0.2
-0.3. Comparison with the predictions of a diffusion-limited wetting m
odel shows that growth of the wetting layers is driven primarily by lo
ng-ranged surface fields.