The filling of small cavities with liquids plays a central role in numerous settings including imprint lithography, gravure printing, microfluidics, lubricant-impregnated surfaces, and porous-media flow. Air entrapment resulting from incomplete filling may be detrimental for certain applications. Although wetting dynamics can be complicated by liquid rheology, the influence of non-Newtonian behavior is not well understood. To develop fundamental understanding, two-dimensional numerical simulations are used to study liquid filling in two model problems involving a stationary trapezoidal cavity and a horizontal plate above the cavity. In these model problems, liquid is driven into the cavity by (i) an imposed pressure gradient and (ii) a combination of horizontal plate motion and an imposed pressure gradient. Shear-thinning liquids described by a Carreau-type expression are considered, and the nonlinear governing equations with inertia and gravity neglected are solved using the Galerkin finite-element method. For both model problems, it is found that increasing cavity width and wettability, decreasing wall steepness, or lowering the capillary number generally improves filling by allowing the contact line on the cavity to slip more. Shear thinning enhances contact-line motion via reduced viscosities near the dynamic contact line and, as a consequence, leads to improved cavity filling.
Bibliographical noteFunding Information:
This work was supported through the Industrial Partnership for Research in Interfacial and Materials Engineering of the University of Minnesota.