# Stability Analysis of Navier–Stokes–Voigt Fluids in Porous Media with Slippery Effect

## TL;DR

This study examines how slip conditions and porous media affect the stability of fluid flow, showing that symmetric slip and strong damping can prevent instability.

## Contribution

The paper introduces a stability analysis of NSV fluids in porous media with asymmetric slip, revealing how symmetry breaking and material properties influence flow stability.

## Key findings

- Symmetric slip conditions lead to optimal flow stability, while asymmetric slip causes significant destabilization.
- Increasing porous medium permeability or Voigt regularization can counteract slip-induced instability.
- Manufacturing defects in slip conditions can be mitigated by optimizing the porous medium matrix.

## Abstract

This paper investigates the linear stability of Navier–Stokes–Voigt (NSV) fluid flow in a channel filled with a homogeneous porous medium under general asymmetric slip boundary conditions. This study bridges the research gap between idealized theoretical models (uniform coating) and realistic engineering surfaces in superhydrophobic channels. In practice, manufacturing defects often lead to non-uniform slip distributions. By solving the generalized eigenvalue problem using the Chebyshev spectral collocation method, we quantify the sensitivity of the critical Reynolds number to symmetry breaking. The results reveal that symmetric slip achieves optimal stability, whereas symmetry breaking causes a significant destabilizing effect. Energy analysis clarifies the physical origin of this instability. Furthermore, we find that increasing the porous medium permeability parameter or the Voigt regularization parameter effectively counteracts the slip-induced instability. Specifically, flow stability can be restored even under highly asymmetric slip conditions if the porous damping or the viscoelastic regularization effect is sufficiently strong. This implies that inevitable manufacturing defects in engineering can be compensated for by optimizing the porous medium matrix.