Spreading of liquid films on a vertical rotational cylinder with different contact angles

Abstract This paper studies the flow dynamics of a thin liquid film falling down a vertical rotating cylinder. The influence of different contact angles, surface curvatures, and angular velocities on the flow and contact line characteristics of thin films is analyzed. To verify the results, numerical simulations based on a two-phase flow model are carried out, and a comparison with results by lubrication theory is presented. The results indicate significant numerical differences between the two models: the two-phase flow model reduces the diffusion distance by 15.5 mm and the capillary ridge height by 34.43% compared to the lubrication model. This disparity primarily originates from the lubrication theory’s neglect of the influence of the contact angle when applying boundary conditions in the precursor layer. It is worth noting that the flow profiles obtained by the two models agree well with each other, and the flow mechanism is well-explained. Numerical simulations indicate that wettability plays a crucial role in the diffusion process. A smaller contact angle (60°) significantly enhances capillary force, increasing the spreading distance by 143.38 mm compared to a larger contact angle (120°). Furthermore, the smaller cylindrical radius (20 mm) increases capillary force, resulting in a 7.18% increase in the diffusion distance of the liquid film compared to the cylindrical radius (60 mm). Meanwhile, the rotation velocity greatly affects the liquid membrane flow. The capillary ridge height increases by 10.96% at a rotation speed of 120 rpm compared to the stationary state. The curvature and rotational velocity of the substrate significantly influence the axial fluctuations of the free surface. Besides, we investigate the influence of time-varying speeds and find that periodic variations induce regular oscillations in the liquid film. These oscillations lead to a peak-to-valley height variation of 0.132 mm, suggesting potential applications in the creation of nanostructures and coating patterns.