Scaling behavior of pattern formation in the flexographic ink splitting process

Abstract

We considered pattern formation, i.e. viscous fingering, in the ink splitting process between an elastic flexographic printing plate and the substrate. We observed an unexpected scaling behavior of the emerging pattern length scale (i.e., finger width) as a function of printing velocity, fluid viscosity, surface tension, and plate elasticity coefficients. Scaling exponents depended on the ratio of the capillary number of the fluid flow, and the elastocapillary number defined by plate elasticity and surface tension. The exponents significantly differed from rigid printing plates, which depend on the capillary number only. A dynamic model is proposed to predict the scaling exponents. The results indicate that flexo printing corresponded to a self-regulating dynamical equilibrium of viscous, capillary, and elastic forces. We argue that these forces stabilize the process conditions in a flexo printing unit over a wide range of printing velocities, ink viscosities, and mechanical process settings.