Computational study of viscoelastic effects on liquid transfer during gravure printing

Abstract

High speed roll-to-roll coating and printing are important in both classical and novel processes, e.g., in the emergent flexible electronics industry. Gravure in particular is attractive for its application to printing as well as its high quality and throughput in coating continuous thin films. Despite its long standing use, gravure is still poorly understood especially in the liquid transfer regime and when the coating liquid has a complex rheology. As with any coating flow, the dynamics are governed by many complex phenomena including free surfaces, (de)-wetting, and non-Newtonian rheology; these present observational, modeling, and computational challenges. Accordingly, modeling and computational work are usually limited by the level of detail in describing the physical phenomena. In this work, we compute the influence of viscoelasticity on the transfer of polymer solutions in an idealized gravure process: the liquid is held between a cavity and a flat disk that moves away at a constant velocity, with pinned contact lines on both the disk and cavity. Our computations show that when the disk separation velocity is sufficiently high as measured by the Weissenberg number—i.e., the consequent strain rate in the liquid bridge is high compared to the rate of polymer relaxation—large elastic stresses are activated at early times and induce an adverse drainage into the cavity. Gravity or other forces eventually overwhelm this elastic drainage at later times when stretching dynamics decay in importance. When gravitational and elastic drainage act in concert, they compete with the viscous forces that promote liquid transfer; this competition manifests as an optimum disk velocity for maximal liquid transfer. With the appropriate scaling, we find that the optimal disk velocities over a range of parameters reduce to an optimal Weissenberg number of about 0.1, which agrees well with experiments in the literature.