Emptying of gravure cavities containing shear-thinning and shear-thickening liquids

Roll-to-roll gravure is widely used for creating uniform coatings on a large scale and involves transfer of liquid from micron-scale cavities to a second surface.  To advance  fundamental understanding of the influence of rheology on liquid transfer, two-dimensional numerical simulations are used to study liquid emptying from a model configuration where liquid is confined between a stationary trapezoidal cavity and a horizontal substrate.  Liquid is driven out of the cavity by a combination of horizontal substrate motion and an imposed pressure gradient.  For Newtonian liquids, the fraction of liquid left in the cavity collapses onto a master curve with three distinct regimes.  The fraction of liquid left in the cavity is highly dependent on surface wettability in regime I, is characterized by a power-law relationship in regime II similar to that observed for liquid-film withdrawal, and approaches a plateau in regime III as the influence of surface wettability vanishes. Three distinct regimes are also observed for shear-thinning (shear-thickening) liquids.  Shear-thinning (shear-thickening) is found to improve (worsen) cavity emptying compared to the Newtonian case by aiding (hindering) contact-line motion through reduced (enhanced) viscosities near the dynamic contact line.