The FEM based liquid transfer model in gravure offset printing using phase field method

The velocity control of a roller is crucial in gravure offset printing for determining the quality of the printed images such as width and thickness of an electric circuit. The velocity control also affects mass printability, especially when using micro-scale liquid of high conductivity ink. In this work, a liquid transfer model for gravure offset printing is developed using the phase field method to investigate interfacial dynamics. As a numerical scheme, the finite element method is used for discretization of the partial differential equation. The interfacial layer governed by the phase field variable is embodied by the Cahn–Hilliard equation for a convection–diffusion problem. The numerical results are compared with those from the literatures for their validation. The results were found to be in good agreement with both analytical and experimental results in the literatures. After the validation, the effects of several key factors in gravure offset printing, such as velocity, gravity, surface tension and viscosity on liquid transfer are studied with respect to the contact angle of the upper plate. The ranges of the velocity and contact angle are varied from 0.01 to 0.25?m/s and from 30° to 70°, respectively. Also, the values of the surface tension and viscosity are changed from 0.5 to 1.5?N/m and from 0.05 to 0.15 N?s/m², respectively. The simulation result showed that at α?=?β?=?60° regardless of gravity, the liquid transfer rate (R _%) is increased as the velocity of the upper plate is increased at velocities below 0.01?m/s for liquid with low density, whereas the liquid transfer rate is decreased as the velocity is increased for liquid with high density. Also, the liquid transfer rate is increased as the surface tension is increased until the contact angle (α?≤?β?=?60°) approached 60°. Whereas the liquid transfer rate is decreased as the surface tension is increased until the contact angle (α?≤?β?=?60°) is increased to 60°.