2023/05/18 by Sebastian Zimmermann, Zimmermann, Sebastian, Clarissa Schönecker +1
Engineering · Materials Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Fluid Dynamics and Vibration Analysis #Surface Modification and Superhydrophobicity
paper · pdf · doi:10.48550/arxiv.2305.10777
openalex publication_date 2023/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.