Equivalent slip length of flow around a super-hydrophobic cylinder

TL;DR

This study uses numerical simulations to determine an equivalent slip length for flow around a super-hydrophobic cylinder, providing a simplified model that accurately approximates complex slip-no-slip surface patterns.

Contribution

It introduces a quantitative relationship between the equivalent slip length and key flow parameters for super-hydrophobic cylinders, simplifying complex surface interactions.

Findings

The slip length model effectively approximates the slip-no-slip surface pattern.

A relationship between the Knudsen number and flow parameters is established.

The model is valid across a wide range of Reynolds numbers and surface patterns.

Abstract

In this research, a two-dimensional numerical simulation is conducted to determine the equivalent wall slip length for flow around a circular cylinder featuring a super-hydrophobic surface. The super-hydrophobic surface is modeled as an alternating distribution of slip and no-slip conditions along the cylinder's surface. The smallest unit of this alternating pattern is referred to as a monomer. The study takes into account the Reynolds number and two critical dimensionless parameters: the gas fraction (GF) and the ratio l/a. GF indicates the proportion of the slip length relative to the total length of the monomer, while l/a denotes the ratio of the monomer length (l) to the cylinder's radius (a). The ranges considered for the Reynolds number, GF, and l/a are from 0.2 to 180, 0.1 to 0.99, and $\pi$/80 to $\pi$/5, respectively. A dimensionless number, the Knudsen number (Kn), is introduced to measure the ratio between the equivalent slip length ($\lambda$) and the cylinder's diameter (D). By equating the integral wall friction resistance on the cylinder surface, a quantitative relationship between the equivalent Kn and the parameters (Re, GF, l/a) is established. A meticulous comparison of flow parameters between the equivalent slip length model and the slip-no-slip scenario reveals that the slip length model is an effective approximation for the slip-no-slip alternating model.