Analysis of influencing parameters in deformable roll coating of counter-rotating rolls

Roll coating is a comparatively simple and common technology for coating of continuous substrates like paper, coils, or foils, where the fluid is metered through the gap between two rolls. Rolls wrapped with a deformable rubber layer enable a precise metering for low fluid amounts and lead additionally to higher process stability. Many efforts have been made to investigate the influencing factors of deformable roll coating by experimental and numerical methods. Beside configurations with positive gaps, which are comparable to rigid roll setups, negative gaps, where only the elasticity of the rubber layer prevents overlapping of the rolls, are of interest as such configurations enable thin liquid layers. The main influencing factors on the volume flow rate through the gap are viscosity, average velocity, effective radius, Young’s modulus, load or pre-set gap height, and partly rubber thickness, when an influence of the layer height is assumed. The dependency is often given in empirically or numerically based power law relationships. In contrast to this, in the present study, an analytically based solution is used to investigate the influencing factors in deformable roll coating with negative gaps. This continues the authors' previous work, in which the analytical solution was derived. As a result, a general agreement with numerical and experimental results from literature is found. Additionally, the analytical approach allows for the first time the ability to quantify further trends. The proposed power law exponent for the dimensionless load and elasticity numbers from literature cannot be considered as constant in the whole common application range of roll coating but remarkable trends appear. Additionally, a new criterion for the critical rubber cover thickness is developed analytically which describes the limit value of the negligible influence of the rubber cover thickness on the volume flow rate. The present investigation enables the explanation of different literature results and offers a more general view in the understanding of roll coating processes.