Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid infused tubes and annular pipes

TL;DR

This paper develops analytical models for pressure-driven Stokes flow in superhydrophobic and liquid-infused tubes, accounting for finite slip lengths and micro-geometry effects, validated by numerical simulations.

Contribution

It introduces new analytical expressions for velocity and slip length in slippery pipes with finite slip, extending beyond perfect slip assumptions.

Findings

Analytical solutions match numerical simulations accurately.

Models enable design optimization of slip surfaces in pipes.

Incorporates effects of fluid viscosity and slit micro-geometry.

Abstract

Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models incorporate a finite local slip length or shear stress along the slits and thus go beyond the assumption of perfect slip commonly employed for superhydrophobic surfaces. Thereby, they provide the possibility to assess the influence of both the viscosity of the air or other fluid that is modelled to fill the slits as well as the influence of the micro-geometry of these slits. Firstly, expressions for tubes and annular pipes with superhydrophobic or slippery walls are provided. Secondly, these solutions are combined to a tube-within-a circular pipe scenario, where one fluid domain provides a slip to the other. This scenario is interesting as an application to achieve stable fluid-fluid interfaces. With respect to modelling, it illustrates the specification of the local slip length depending on a linked flow field. The comparisons of the analytically calculated solutions with numerical simulations shows excellent agreement. The results of this article thus represent an important instrument for the design and optimization of slippage along surfaces in circular geometries.