Internal flows in microscopic polymer solution droplets evaporating on flat surfaces

To control the formation process of polymer thin films from polymer solution droplets using inkjet printings, internal flows of the droplets on substrates are studied. In our previous study [1], internal flow of polymer solution droplets receding on a lyophobic surface was experimentally visualized. It was found that the direction of the circulation flow in the droplet depended on the solvent and the initial solute concentration. In particular, the flow direction of polystyrene-anisole solution was reversed as the initial solute concentration increased. In this study, to clarify this reason, the conservation equations of momentum, energy and mass on two-dimensional cylindrical coordinate are numerically solved using a finite element method. The mathematical model considers the free convections derived by the dependencies of the density and surface tension on the solute concentration. As a result, the dependences of the calculated velocities on the initial solute concentration agree qualitatively with the experiments. The mathematical model predicts that double circulation flows appear after a single flow develops at high initial solute concentrations, while double circulations do not develop at low concentrations. It is concluded that the difference between the flow directions investigated experimentally is due to such a change of the flow structure. The distribution of the surface tension on the free surface is also discussed. When a local minimum of the surface tension appears on the free surface, the double circulations develop. According to the result for a low contact angle, the local minimum point shifts toward the axis of symmetry with a lapse of time, and finally erases the double circulations.