Thermocapillary effect on the dynamics of falling self-rewetting fluid films down a heated vertical cylinder

Abstract

Nonlinear dynamic analysis of a self-rewetting fluid (SRWF) film flowing down the surface of a vertical cylinder is performed in this paper. The effect of the Biot number, Marangoni number and the substrate curvature on the interfacial evolution patterns and flow stabilities are discussed by linear stability analysis and numerical simulations of the evolution equation of the film thickness. Starting from the characteristic temperature T0 relating to the minimum surface tension and the interfacial temperature Ti, the nonlinear dynamics of the liquid film is investigated numerically in the cases of either Ti>T0 or Ti<T0. Good agreement of linear stability analysis with numerical simulations proves that the LSA could predict the development of thin liquid film flows in the early-time evolution. Through the analysis, we demonstrate that the Marangoni number Ma and the Biot number Bi play contrary roles for the two cases. For Ti<T0, the fingering instability is enhanced by the Marangoni effect while the inverse Marangoni effect stabilizes the interface for Ti>T0. The growth rate changes linearly with the increase of Marangoni number while it changes in forms of arched shapes versus lg(Bi). The growth rate reaches a maximum/minimum value at Bi=1, corresponding to the most/least unstable state. The radius of the cylinder R plays a significant role in the long wavelength modes, showing a stabilizing effect. For perturbations of short waves, increment of R expands the instability region. Nonlinear oscillatory waves (Rayleigh–Plateau instability) appears when the radius is smaller than 1 and fingering pattern tends to occur if the cylinder has a large radius (R≥1).