Models for Marangoni drying

Abstract

Marangoni drying is a new ultra-clean drying process, which relies on surface-tension gradient forces, so-called Marangoni stresses. This method is of particular use in the semiconductor industry wherein obtaining ultra-clean surfaces is of paramount importance. The present work provides a mathematical description of this novel process involving four coupled partial differential equations, derived in the thin-layer approximation, for the film thickness, the concentration of chemicals in the air, at the air–liquid interface and in the bulk of the liquid film. Numerical solution of these equations yields prediction of typical profiles that accompany the spreading and drying processes. Particular attention is aimed at the prediction of the minimum film thickness as a function of system parameters with a view to optimizing the drying process.