Coarsening and solidification via solvent-annealing in thin liquid films

We examine solidification in thin liquid films produced by annealing amorphous Alq(3) (tris-(8-hydroxyquinoline) aluminium) in methanol vapour. Micrographs acquired during annealing capture the evolution of the film: the initially-uniform film breaks up into drops that coarsen, and single crystals of Alq(3) nucleate randomly on the substrate and grow as slender 'needles'. The growth of these needles appears to follow power-law behaviour, where the growth exponent, gamma, depends on the thickness of the deposited Alq(3) film. The evolution of the thin film is modelled by a lubrication equation, and an advection-diffusion equation captures the transport of Alq(3) and methanol within the film. We define a dimensionless transport parameter, alpha, which is analogous to an inverse Sherwood number and quantifies the relative effects of diffusion- and coarsening-driven advection. For large alpha-values, the model recovers the theory of one-dimensional, diffusion-driven solidification, such that gamma -> 1/2. For low alpha-values, the collapse of drops, i.e. coarsening, drives flow and regulates the growth of needles. Within this regime, we identify two relevant limits: needles that are small compared to the typical drop size, and those that are large. Both scaling analysis and simulations of the full model reveal that gamma -> 2/5 for small needles and gamma -> 0.29 for large needles.