  The jet wiping process is a cost-effective coating technique that uses
impinging gas jets to control the thickness of a liquid layer dragged along a
moving strip. This process is fundamental in various coating industries (mainly
in hot-dip galvanizing) and is characterized by an unstable interaction between
the gas jet and the liquid film that results in wavy final coating films. To
understand the dynamics of the wave formation, we extend classic laminar
boundary layer models for falling films to the jet wiping problem, including
the self-similar integral boundary layer (IBL) and the weighted integral
boundary layer (WIBL) models. Moreover, we propose a transition and turbulence
model (TTBL) to explore modelling extensions to larger Reynolds numbers and to
analyze the impact of the modelling strategy on the liquid film dynamics. The
validity of the long-wave formulation was first analyzed on a simpler problem,
consisting of a liquid film falling over an upward-moving wall, using Volume Of
Fluid (VOF) simulations. This validation proved the robustness of the integral
formulation in conditions that are well outside their theoretical limits of
validity. Finally, the three models were used to study the response of the
liquid coat to harmonic and non-harmonic oscillations and pulsations in the
impinging jet. The impact of these disturbances on the average coating
thickness and wave amplitude is analyzed, and the range of dimensionless
frequencies yielding maximum disturbance amplification is presented.
