Dual Role of Wall Slip on Linear Stability of Plane Poiseuille Flow

The linear stability of plane Poiseuille flow is extended to the cases of two wall boundaries maintaining different slip coefficients β₁ and β₂. We determine the slip coefficient pairs, β_1c and β_2c, which yield the same critical Reynolds number as the classical no-slip case. It is found that the wall slip may stabilize the flow for β₁>β_1c and β₂>β_2c, whereas slightly destabilize the flow for β₁<β_1c and β₂<β_2c.