A numerical study for thermocapillary induced patterning of thin liquid films

The underlying mechanism of thermal induced patterning is investigated using a numerical phase-field model. Research on the subject has been mostly restricted to lubrication approximation, which is only valid for the cases that the initial film thickness is smaller than the characteristic wavelength of induced instabilities. Since the long-wave approximation is no longer valid in the later stages of pattern evolution, we employed the full governing equations of fluid flow and the thermally induced Marangoni effect to track the interface between the polymer film and the air bounding layer. Conducting a systematic study on the impact of influential parameters, we found that an increase in the temperature gradient, thermal conductivity ratio, and initial thickness of the thin film resulted in shorter processing time and faster pattern formation. Additionally, the contact angle between the polymer film and the bounding plates showed a significant effect on the shape of created features. Compared to the reported experimental observation by Dietzel and Troian [Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient, J. Appl. Phys. 108, 074308 (2010)], our numerical modeling provided a more accurate prediction of the characteristic wavelength against the linearized model currently used in the literature. The numerical findings in this study provide valuable insight into thermal-induced patterning, which can be a useful guide for future experimental works. Published under license by AIP Publishing.