Structuring in thin films during meniscus-guided deposition

We theoretically study the evaporation-driven phase separation of a binary fluid mixture in a thin film deposited on a moving substrate, as occurs in meniscus-guided deposition for solution-processed materials. Our focus is on the limit of rapid substrate motion where phase separation takes place far away from the coating device. In this limit, demixing takes place under conditions mimicking those in a stationary film because substrate and film move at the same speed. We account for the hydrodynamic transport of the mixture within the lubrication approximation. In the early stages of demixing, diffusive and evaporative mass transport predominates, consistent with earlier studies on evaporation-driven spinodal decomposition. In the late-stage coarsening of the demixing process, the interplay of solvent evaporation, diffusive, and hydrodynamic mass transport results in several distinct coarsening mechanisms. The effective coarsening rate is dictated by the dominant mass transport mechanism and therefore depends on the material properties, evaporation rate, and time: slow solvent evaporation results in initially diffusive coarsening that for sufficiently strong hydrodynamic transport transitions to hydrodynamic coarsening, whereas rapid solvent evaporation can preempt and suppress hydrodynamic and diffusive coarsening. We identify a novel hydrodynamic coarsening regime for off-critical mixtures, arising from the interaction of the interfaces between solute-rich and solute-poor regions in the film with the solution-gas interface. This interaction induces a directional motion of solute-rich droplets along gradients in the film thickness, from regions where the film is relatively thick to where it is thinner. The solute-rich domains subsequently accumulate and coalesce in the thinner regions.