Spatio-temporal thickness variation and transient Marangoni number in striations during spin coating. (June 2020) - Shiratori, Suguru; Kato, Daiki; Sugasawa, Kyosuke; Nagano, Hideaki; Shimano, Kenjiro
Highlights: Real-time measurement of thickness variation in spin-coating of epoxy/xylene mixture. Transient Marangoni number is predicted by numerical simulation. Short-wavelength component suddenly disappears in the middle of the process. The disappearance may be related to the certain bifurcation of the flow regimes. The critical Marangoni number for this bifurcation is predicted from 1000 to 1800. Graphical abstract: Abstract: A formation process of striation, radial spoke-like thickness undulations arising during a spin coating, was experimentally investigated for mixtures of epoxy resin and xylene solvent. It was confirmed by optical measurement of thickness variations that the generation of striation started at a very early stage of spin coating. The spatio-temporal thickness variation exhibited a rather complex behavior that involved drastic changes to the wavelength spectrum. It is noteworthy that the short-wavelength components, which slowly grow during the early stage, suddenly vanished in the middle stage. The experimentally observed transient thickness variations are shown to correspond to changes in the flow regimes, under the hypothesis that striation is generated due to a derivative form of the solutal Marangoni-Bénard instability. The transient Marangoni number is predicted by a numerical simulation based on a simple mathematical model in which the thickness decreases due to centrifugal force and solvent evaporation is considered, together with the time evolution of the concentration distribution in the thickness direction. The Marangoni number Ma is predicted to increase as well as a decrease by some order of magnitude. The sudden disappearance of the short-wavelength component observed in the experiment might be associated with the falling of Ma down to the sub-critical value for a certain bifurcation of the flow regimes. The Marangoni number for the bifurcation is predicted to be in the range 1000 <  Ma  < 1800 when the rotation rate is small.