Analytical prediction of roll coating with counter-rotating deformable rolls

Roll coating is a common technique for applying thin coating films on continuous substrates, e.g., papers and foils. Key advantages are the comparatively simple technology and the possibility of coating thin films using highly viscous fluids. Since roll coating is a self-metered process, the prediction of film thicknesses is of fundamental interest for industrial process control. In the present work, a new analytical approach for the prediction of the film thickness in roll coating with deformable rolls and negative gaps is developed. This method is based on the fluid dynamic theory of lubrication approximation. The film thickness is calculated depending on the geometry of the rolls (including the elasticity of the rubber), the fluid properties of the applied film and the roll velocities. This is gained by using boundary conditions for pressure and—in contrast to former literature—for force. The quality of the predicted results is validated with experimental data from literature. The comparison shows good agreement and thus the derived analytical model offers new possibilities for predicting film thickness and understanding of the associated influence parameters.