Damping of three-dimensional waves on coating films dragged by moving substrates

Abstract

[Abstract]: Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsens the product quality. In this article, we investigate the stability of a thin liquid film dragged by a vertical substrate moving against gravity, a fundamental flow configuration in various coating processes. The receptivity of the liquid film to three-dimensional disturbances is analyzed with Direct Numerical Simulations (DNS) and an in-house Integral Boundary Layer (IBL) film model. The latter was used for Linear Stability Analysis (LSA) and nonlinear wave propagation analysis. The numerical implementation of the IBL film model combines a finite volume formulation with a pseudo-spectral approach for the capillary terms that allows for investigating non-periodic surface tension-dominated flows. Both the model and the numerical solver were successfully validated with DNS computations. The combination of these numerical tools allows for describing the mechanisms of capillary and nonlinear damping and identifying the instability threshold of the coating processes. The results show that transverse modulations can be beneficial for damping two-dimensional waves within the range of operational conditions considered in this study, which are relevant to air-knife and slot-die coating.