Annular Newtonian Poiseuille flow with pressure-dependent wall slip

TL;DR

This paper analytically investigates how pressure-dependent wall slip influences steady Newtonian annular Poiseuille flow, revealing that slip effects are significant at weak slip and small gaps, with minimal impact at high slip or large gaps.

Contribution

It provides an analytical solution incorporating pressure-dependent slip effects in annular flow, including an explicit formula for pressure drop and analysis of slip influence under various conditions.

Findings

Pressure-dependent slip effects are more pronounced with weak slip.

Effects diminish as slip coefficient increases, approaching perfect slip.

Flow phenomena are amplified in narrower annular gaps.

Abstract

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier's slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.