Spreading of thin liquid droplets on rotating disks

In many industrial processes solids are coated to obtain specific surface properties, as e.g. corrosion resistance, mechanical, optical, or electrical properties. Even today many of such coating processes are not fully understood and the choice of parameters is mainly based on experience. Hence, a prediction of the complete hydrodynamic process in its dependency on the parameters appears highly desirable. This would e.g. allow for a precise prediction of the (liquid) layer thickness and shape and help to optimize the quality of the coating. A common coating technique is the so–called spin coating. The coating agent is dissolved or suspended in a liquid, brought onto the solid, spread by rotation, and the carrier liquid is finally removed by evaporation or by chemical reactions. In this article an evolution equation is derived from lubrication theory, valid for thin liquid layers. The model involves a dynamic contact angle, centrifugal, capillary, gravitational, and molecular (London–van–der–Waals) forces. The evolution equation without molecular forces can even be solved analytically, provided the capillary number is small. Otherwise a numerical integration of the governing equations is engaged. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)