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Analytical expressions for the velocity field and the effective slip lengthof pressure-driven Stokes flow through slippery pipes and annuli withrotationally symmetrical longitudinal slits are derived. Specifically, thedeveloped models incorporate a finite local slip length or shear stress alongthe slits and thus go beyond the assumption of perfect slip commonly employedfor superhydrophobic surfaces. Thereby, they provide the possibility to assessthe influence of both the viscosity of the air or other fluid that is modelledto fill the slits as well as the influence of the micro-geometry of theseslits. Firstly, expressions for tubes and annular pipes with superhydrophobicor slippery walls are provided. Secondly, these solutions are combined to atube-within-a circular pipe scenario, where one fluid domain provides a slip tothe other. This scenario is interesting as an application to achieve stablefluid-fluid interfaces. With respect to modelling, it illustrates thespecification of the local slip length depending on a linked flow field. Thecomparisons of the analytically calculated solutions with numerical simulationsshows excellent agreement. The results of this article thus represent animportant instrument for the design and optimization of slippage along surfacesin circular geometries.

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