Dynamics of thin liquid films flowing down the uniformly heated/cooled cylinder with wall slippage

Coating liquid films on cylinders occurs widely in nature, material sciences, and industrial processes. A typical example is the fabrication of thin solid films, which could be achieved by drawing the heated cylinder from the liquid pool and followed by a drying process. However, in some cases, the surface of the coated cylinder is actually not smooth and exhibits hydrophobicity where the slip effect may come into play. Therefore, in this paper, we study the dynamics of thin liquid films flowing down the uniformly heated or cooled cylinder in the presence of wall slippage. The thermocapillary and slip effects on the thin film flows are examined by a thin film model. Linear stability analysis (LSA) indicates that when the cylinder is heated, thermocapillary effect enhances the Rayleigh-Plateau instability, while when the cylinder is cooled, thermocapillary effect suppresses this instability. However, we find that wall slippage always promotes the capillary instability, and when M[Formula presented]<-[Formula presented], where M and β are the reduced Marangoni number and dimensionless slip length, the system are always linearly stable. The linear wave speed given by c_L=1+2β is promoted by the wall slippage but independent of the thermocapillary effect. In addition, nonlinear traveling-wave study shows that the size and moving speed of the sliding droplets are promoted for a heated cylinder and reduced for a cooled cylinder, respectively. The size and moving speed of the sliding droplets are enhanced by wall slippage. Finally, direct numerical simulations (DNS) of the full thin film model clearly demonstrate the role of thermocapillary and slip effects, agreeing well with the linear stability analysis and the nonlinear traveling-wave solutions. Our results offer insight into the influence of wall slippage on the dynamics of thin film flows coating on cylinders in non-isothermal environments.