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We report the development and application of a refined version of the classical Cassie-Baxter wetting model for the prediction of surface topographies with superomniphobic traits. The sagging height defined through the capillary length was utilized to assess the relation between a curved liquid-air interface and the surface texture. The wettability, expressed in terms of the static apparent contact angle, was quantified for single- and double-scale surface topographies and for three representative liquids and the results were compared to those of the classical Cassie-Baxter model. Of the three single-scale topographies considered in this work, the fiber case exhibited the highest contact angle across length scales of surface topographies, whereas decreasing the length scale of surface patterns from a few hundreds of micrometers to a few hundreds of nanometers led to contact angle increase by 15%–20%. A generic expression for modeling multiscale hierarchical roughness of arbitrarily large multiplicity n was derived and applied. Multiscale hierarchical roughness was corroborated to be a promising way for achieving enhanced liquid repellency. Double-scale roughness was more efficient when the two length scales differed in size by at least one order of magnitude. The 'fiber on sinusoid' hierarchical topography exhibiting re-entrant geometry yielded contact angles over 150° for all considered wetting liquids.

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