NON-DIMENSIONAL ANALYSIS OF FILM INSTABILITY POINTS OF LIQUID FILM DEVELOPING OVER A ROTATING DISK VIA HIGHLY RESOLVED SIMULATIONS

Abstract

A liquid jet developing into a liquid film over a rotating disk is found in various industrial applications such as semiconductor manufacturing processes. The liquid film develops various instabilities such as the spiral wave and film break-up. This study performs a non-dimensional analysis on these film instability points. High-fidelity flow simulations are performed for a parametric study based on the rotation rate, flow rate, liquid viscosity, surface tension, and contact angle (CA). A non-dimensional model for the instability points is derived using the Buckingham‘s PI theorem. Parameter sensitivity analyses are performed using the simulation results for a reduced model. The spiral wave starting point is affected mainly by the Reynolds number and capillary number, but not by CA. Also, a reduced non-dimensional model using a single parameter can be derived by combining the non-dimensional parameters. On the break-up point, the surface tension and CA have primary effects, and the capillary number and CA are found to be the main non-dimensional parameters. Based on this finding, a reduced non-dimensional model that predicts the break-up point is derived.