Asymptotic solution of Newtonian fluid with linear Navier slip boundary condition

The analysis of boundary conditions at solid-fluid interfaces remains a formidable challenge, necessitating the integration of classical continuum mechanics with microscopic molecular effects. While the no-slip boundary condition has historically been the standard in Navier-Stokes frameworks, its universality is increasingly questioned. Empirical evidence frequently contradicts this assumption in specialized regimes, most notably in non-Newtonian dynamics, rarefied gas flows, and moving contact line problems.
To address these discrepancies, contemporary research has pivoted toward slip-flow models, leveraging advanced computational and mathematical frameworks such as spectral methods and fractional calculus.
However, applying these models to singular geometries remains a complex task requiring specific analytical treatments.
In this study, we address this challenge by revisiting the construction of an asymptotic solution for corner flow singularities.
We employ the Evans-Navier-slip condition—a refined modification of the classical Navier-slip model—to characterize the flow field near the singularity. Finally, the proposed asymptotic solution is validated against numerical simulations of a Newtonian L-shaped flow across three distinct aspect ratios.