Sebastian Zimmermann, Ellen Bold, Egbert Oesterschulze, Munehiro Chijiwa, Mareike Schäfer, Johannes L'huillier, Clarissa Schönecker

• Superhydrophobic (SHS) and liquid-infused surfaces (LIS) have shown great potential in various engineering applications. Due to their heterogeneous surface properties, a mathematical description of the flow behavior along such surfaces is challenging. Circular textured surfaces are of particular importance. They are modeled as either axially traversed tubes or annuli consisting of no-slip walls that are padded with rotationally symmetric finite-shear regions. The latter represents a viscous interaction zone with a second fluid, assumed with layer thickness zero. Zimmermann and Schönecker provide analytical equations that describe the flow field and effective slip length for such geometries. They are applicable to Newtonian fluids of arbitrary viscosity ratio. This article emphasizes the development of principles and guidelines for the design of SHS and LIS to enhance sliding effects, based on these analytical models. The approach presented here facilitates an geometric evaluation of slippery circular surfaces, aiming to offer insights for the design. Through this research, the potential for significant energy savings and enhanced fluid transport performance can be realized, contributing to the development of more efficient fluid engineering systems.