Coarsening and solidification via solvent-annealing in thin liquid films

• Published in: Journal of fluid mechanics 2013-05, Vol.723, p.69-90
• Main Authors: Yu, Tony S., Bulović, Vladimir, Hosoi, A. E.
• Format: Article
• Language: English
• Subjects: Advection; Advection-diffusion equation; Aluminum; Annealing; Coarsening; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Crystals; Diffusion; Diffusion; interface formation; Exact sciences and technology; Fluid mechanics; Liquids; Materials science; Mathematical models; Mechanical and acoustical properties; Methanol; Methods of deposition of films and coatings; film growth and epitaxy; Methyl alcohol; Needles; Physical properties of thin films, nonelectronic; Physics; Solid surfaces and solid-solid interfaces; Solidification; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Theory and models of film growth; Thin films
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.115

We examine solidification in thin liquid films produced by annealing amorphous ${\mathrm{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 ${\mathrm{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 ${\mathrm{Alq} }_{3} $ film. The evolution of the thin film is modelled by a lubrication equation, and an advection–diffusion equation captures the transport of ${\mathrm{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 $\gamma \rightarrow 1/ 2$ . 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 $\gamma \rightarrow 2/ 5$ for small needles and $\gamma \rightarrow 0. 29$ for large needles.