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/m~2, 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°.
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机译：辊的速度控制在凹版胶印中对于确定印刷图像的质量（例如电路的宽度和厚度）至关重要。速度控制也会影响质量可打印性，尤其是在使用高导电性墨水的微型液体时。在这项工作中，使用相场方法开发了用于凹版胶印的液体转移模型，以研究界面动力学。作为数值方案，有限元方法用于偏微分方程的离散化。由相场变量控制的界面层由对流扩散问题的Cahn-Hilliard方程体现。将数值结果与文献中的结果进行比较以进行验证。结果被发现与文献中的分析结果和实验结果都非常吻合。验证后，相对于上板的接触角，研究了凹版胶印中几个关键因素的影响，例如速度，重力，表面张力和粘度对液体转移的影响。速度和接触角的范围分别从0.01到0.25 m / s和30°到70°。另外，表面张力和粘度的值分别从0.5N / m至1.5N / m和从0.05Ns / m至0.15Ns / m〜2变化。仿真结果表明，对于低密度液体，当α=β= 60°时，无论重力如何，当速度低于0.01 m / s时，随着上板速度的增加，液体传输速率（R_％）都会增加，而对于高密度液体，随着速度的增加，液体的传输速率会降低。同样，随着表面张力的增加，液体的传输速率也增加，直到接触角（α≤β= 60°）接近60°。然而，随着表面张力的增加，液体传输速率会降低，直到接触角（α≤β= 60°）增大至60°。
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