(316z) Asymptotic Analysis of the Selective Dip-Coating of Power-Law Fluids Onto Chemically Micropatterned Surfaces

Free-surface microfluidic flow on chemically heterogeneous surfaces is used in such fields as nanotechnology, sol-gel processing, patterned colloidal deposition, microfluidic devices, sensors, and microelectronics processing, with applications ranging from selective material deposition to controlling the self-assembly of hierarchically organized nanostructures. One way to coat these patterned surfaces with fluid is the dip-coating process, which has been extensively investigated for chemically homogeneous plates, rods, and fibers. Microscopic surface heterogeneity can selectively confine liquids to particular regions on the substrate. Such confinement induces a significant lateral curvature of the liquid free surface, which can cause both quantitative and qualitative deviations from fluidic behavior on uniformly wetting surfaces.

The dip coating of a chemically micropatterned surface bearing alternating wetting and non-wetting vertical strips is analyzed for a non-Newtonian power-law fluid. Asymptotic matching of equations derived from the lubrication approximation is used to determine the thickness of the liquid films deposited on the O(10 micron) strips at small capillary numbers. A uniformly wetting surface is also considered using a consistent treatment of the governing equations for comparison. In the absence of an imposed length scale on uniform surfaces, the governing length scale in the dynamic meniscus is found from a balance of viscous and capillary forces. The power-law dependence of the viscosity can therefore have a considerable effect on the coating process. The effect of the power-law index on the thickness of the entrained liquid film is found to be greatly reduced for the micropatterned surfaces because of the dominant effect of the lateral fluid confinement by micropatterning, which imposes a geometric length scale that replaces the dynamic capillary length in the analysis. This diminished effect of power-law behavior is therefore also expected to hold for other non-Newtonian fluids coated onto micropatterned surfaces because the dominant geometric length scale is independent of fluid properties. Relative to uniform surfaces, the influence of non-Newtonian behavior on micropatterned surfaces is diminished more than the effects of Marangoni stresses induced by gradients in surfactant concentration, which were also shown to be less significant than on uniform surfaces because of the fluid confinement by micropatterning. The Newtonian limit is also discussed and compared to experimental results.