Spatial–temporal evolution of entire layer thickness during dip coating with vertical withdrawal of Newtonian fluids

Abstract The present article addresses the layer thickness profile of Newtonian fluids upon dip coating with vertical withdrawal in the visco‐gravity regime. The past studies have been focusing on the thickness profile of the layer tip. However, the previous models have been unable to accurately predict this part, due to not realizing that the thickness has converged to the asymptotic thickness (the constant thickness) at the location far above the horizontal liquid surface. The present work shows that the layer thins along the withdrawal direction in the visco‐gravity regime and is self‐similar at dimensionless scales. By fully considering the characteristics of the thickness profile, a model is proposed to predict the thickness profile of the entire layer. The validity range of the model is investigated at different values of Reynolds number, showing that this model agrees well with experimental and simulated results over a wide range of Reynolds numbers.