Capillary and non-linear damping mechanisms on 3D wavy thin liquid films
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When they are deposited on solid substrates, coating flows are often subjected to disturbances while they are still in liquid phase. If those disturbances persist until solidification, they produce a wavy surface that affects the product quality. In this work, we investigate the evolution of three-dimensional non-uniformities on a thin liquid film dragged by a vertical substrate moving against gravity, a flow configuration typically encountered in coating processes. The receptivity of the liquid film to 3D disturbances is discussed with Direct Numerical Simulations, an in-house non-linear thin liquid film model, and linear stability analysis. The combination of these numerical tools allows for describing the mechanisms of non-linear and capillary damping, as well as for identifying the instability threshold of the system for the scales involved in coating processes. The results show in particular that transverse modulations can be beneficial for the damping of two-dimensional waves within the range of operational conditions considered in this study.