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Sliding droplets over an inclined substrate may deposit a residual liquid termed as pearling. This three-dimensional mechanism can be observed even on near-perfect surfaces and it is mainly affected by bond number, inclination angle and capillary number. However, specifically designed surfaces can alter the dynamic contact line and enforce droplets to deposit a pearl. We model three-dimensional droplet motion under long-wave assumption with a precursor film model for such substrates where the surface is designed as a continuous function and integrate the governing equations using quadratic Finite Element Method with adaptive mesh refinement. For various surface structures, energies, and inclination angles, we show the expedition/promotion of pearl formation alongside its mechanism, and how to periodically trap droplets inside the grooves. Finally, we discuss the volume control of entrapped droplets.

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During intaglio (gravure) printing, a blade wipes excess ink from the engraved plate with the object of leaving ink-filled cells defining the image to be printed. That objective is not completely attained. Capillarity draws some ink from the cell into a meniscus connecting the blade to the substrate, and the continuing motion of the engraved plate smears that ink over its surface. By examining the limit of vanishing capillary number ($Ca$, based on substrate speed), we reduce the problem of determining smear volume to one of hydrostatics. Using numerical solutions of the corresponding free-boundary problem for the Stokes equations of motion, we show that the hydrostatic theory provides an upper bound to smear volume for finite $Ca$. The theory explains why polishing to reduce the tip radius of the blade is an effective way to control smearing.