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

Jyun Ting Wu, Marcio S. Carvalho, Satish Kumar

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6 Scopus citations


One technology widely used for creating uniform coatings on a large scale is roll-to-roll gravure, which involves emptying of liquids from micron-scale cavities to a second surface. Although coating liquids containing functional additives usually exhibit non-Newtonian rheological behavior, fundamental understanding of the influence of liquid rheology on liquid transfer is still lacking. To address this issue, two-dimensional numerical simulations are used to study liquid emptying from a model configuration. In this configuration, liquid is confined between a stationary trapezoidal cavity and a horizontal substrate above the cavity. Liquid is driven out of the cavity by a combination of horizontal substrate motion and an imposed pressure gradient. Liquids exhibiting rate-dependent rheology described by Carreau-type expressions are considered, inertial and gravitational effects are neglected, and the nonlinear governing equations are solved using the Galerkin finite-element method. For Newtonian liquids, it is found that the fraction of liquid left in the cavity, Vr, collapses onto a master curve with three regimes distinguished by the relative strength of the driving forces aiding contact-line motion (surface-tension forces and imposed pressure gradient)and the resistance hindering contact-line motion (viscous forces). In the first regime, there is strong contact-line motion and Vr is highly dependent on surface wettability. In the second regime, Vr is characterized by a power-law relationship similar to that observed for liquid-film withdrawal. In the third regime, Vr approaches a plateau and the influence of surface wettability vanishes. Master curves with distinct regimes are also obtained for shear-thinning and shear-thickening liquids. Shear thinning is found to improve cavity emptying compared to the Newtonian case by aiding contact-line motion through reduced viscosities, whereas the opposite is observed for shear-thickening liquids.

Original languageEnglish (US)
Pages (from-to)46-55
Number of pages10
JournalJournal of Non-Newtonian Fluid Mechanics
StatePublished - Jun 2019

Bibliographical note

Funding Information:
This work was supported through the Industrial Partnership for Research in Interfacial and Materials Engineering of the University of Minnesota .

Publisher Copyright:
© 2019 Elsevier B.V.


  • cavities
  • coating
  • contact lines
  • gravure
  • printing
  • rheology
  • shear-thickening
  • shear-thinning


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