Spin casting of dilute solutions: Vertical composition profile during hydrodynamic-evaporative film thinning

We analyze the vertical composition profile during hydrodynamic-evaporative film thinning (spin casting) of mixtures of non-volatile solutes and volatile solvents. We present a generic approach based on ideal solution behavior. Our analysis complements more detailed (but more system specific) studies that are available in the literature. The hydrodynamic-evaporative film thinning is described analytically based on the solvent properties. We find a universal film thinning behavior as a function of the rotation speed, viscosity and evaporation rate. The thinning process is uniquely characterized by its transition height i.e., the film thickness where hydrodynamics and evaporation contribute equally to film thinning. The theoretically predicted film thinning is in agreement with experimental results. The evolution of the internal film composition is calculated numerically. The numerical description is tractable and offers quantitative insights into the influence of the experimental conditions on the evolution of the internal composition. A characteristic Sherwood Number is introduced as a fundamental process parameter. It characterizes the vertical solution profile and serves as a well-defined and experimentally accessible criterion for the regimes of quantitative validity of our analysis. We also present new power laws, which link the process control parameters to the composition evolution, process duration, and final solute coverage. Because the analysis is generic and tractable, it also yields valuable insights for solutions behaving non-ideally.