Analytical modeling of flow through circular geometries for optimizing superhydrophobic and liquid-infused surfaces

Superhydrophobic (SHS) and liquid-infused surfaces (LIS) have attracted significant interest for their potential to reduce drag and repel aqueous liquids, which is utilized in diverse engineering applications. However, understanding the intricate flow behaviour along such heterogenous surfaces is challenging. Circular textured surfaces, particularly, hold significance. Typically, they are represented as axially traversed tubes or annuli, featuring no-slip walls scattered with rotationally symmetric finite-shear regions. These regions represent viscous interaction zones with a second fluid. We provided analytical equations that capture the flow field and effective slip length for such circular geometries. The applicability of these equations extends to Newtonian fluids with arbitrary viscosity ratios between the main and lubricating fluid.

Based on these analytical models, we develop design principles and guidelines for SHS and LIS to optimize sliding effects. By employing this approach, comprehensive assessments and efficient optimizations of slippery circular surfaces become possible, paving the way for enhanced energy efficiency. The research offers insights into significant energy savings and improved fluid transport performance, thus contributing to the advancement of sustainable fluid engineering systems.