We considered the effect of the upper roller on plate-to-roll gravure offset printing. The x and y velocities of a liquid droplet due to cycloid movement are considered in a numerical model. The phase-field method is used for the interface dynamics of the two-phase fluids (gas and liquid). The liquid transfer ratio is simulated by changing the radius of the roller, the angular velocity of the roller, the contact angle between the liquid and contact surface, and the viscosity and surface tension, which primarily affect gravure offset printing. We developed a plate-to-roll model on basis of a cycloid motion. To validate the proposed model, simulation results of transfer ratio are compared with results reported in the literature for models based on the plate-to-plate configuration. The proposed plate-to-roll model shows good agreement with the plate-to-plate model. As one of our main results, we found that slip displacement occurs during plate-to-roll gravure offset printing. Effects of various parameters acting on the conventional plate to plate model are also studied in our plate-to-roll simulations.
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