Numerical study of the thermocapillary instability in a thin liquid–air film

It is well known that thermal field would cause instability on a two-fluid interface due to the Marangoni effect. This phenomenon is also referred to as thermocapillary flow. A thin liquid/air film experiences thermocapillary instability when it is confined between hot and cold plates. The periodic micro/nano-patterns can generally be observed in the film. Therefore, the thermocapillary instability can be used to fabricate micro/nano-polymeric structures. The present paper proposes a fully nonlinear numerical model based on the phase field method to study the dynamic process of thermocapillary instability. Interfacial evolution and nonlinear effects of the thin liquid film are especially investigated. The impact of the key parameters, e.g., the Marangoni and Reynolds numbers, on the stability are also explored. In addition to the single-mode analysis, the thermocapillary instability is also studied in the multi-mode condition. The conventional single-mode approach facilitates the stability analysis of different wavelengths, while the multi-mode method describes the experiments in a more practical way.