Critical Marangoni Number for Disappearance of Striations during Spin-Coating

This study investigated the striations, which arise as spoke-like thickness undulations during the spin-coating process. It was found that the striations, which once appeared, then disappeared when a mixture of epoxy resin and diglyme solvent was used as the coating fluid. The time-dependent wavelength spectrum was obtained by applying short-time Fourier analysis to the optically measured spatiotemporal thickness variation. The wavelength components corresponding to the striations decreased by 3 orders of magnitude before and after the decay. Under the hypothesis that striations are generated by the type of solutal Marangoni-Bénard instability, the disappearance of the striations can be regarded as the result of the Marangoni number falling below the subcritical value for the occurrence of striations. To determine the critical Marangoni number for the disappearance of the instability, the transient Marangoni number <i>Ma</i> was predicted by a numerical simulation taking the thickness-thinning due to centrifugal force and solvent evaporation into account, together with the time evolution of the concentration distribution. The critical Marangoni numbers were determined as values of numerically predicted <i>Ma</i> corresponding to the time when the experimentally observed striations started to decay, and they were in the range of <i>Ma</i>_c = 90-160.