Stability and sensitivity analysis of a t-shaped micro-mixer with superhydrophobic surfaces

Superhydrophobic surfaces (SHSs) are characterized by a stable layer of gas trapped in micro- or nano- grooves, with a consequently reduction of the solid-fluid contact area and of the corresponding skin-friction drag. SHSs have been largely studied and applied for drag-reduction of turbulent flows in macro-channels, while as concern transition to turbu- lence, they result to be effective only in micro-channels with dimensions of few millimeters. In this context, this work aims at investigating the stability properties of the flow in a 2D T- mixer employing anisotropic SHSs in the outlet channel. Global stability analyses of the res- ulting flow fields have been carried out varying the characteristics of the SHSs, i.e. the slip equivalent length Λ and the orientation angle θ of the grooves to the main pressure gradient direction. Starting from a steady and symmetric flow solution at low Reynolds numbers, the transition scenario is first characterized by a pitchfork supercritical bifurcation that drives the system towards a new asymmetric steady state. The use of SHSs always leads to a reduction of the critical Reynolds number for the onset of this first bifurcation, compared to the T-mixer with solid walls. The neutral stability curves of this bifurcation together with the destabilising global modes will be discussed. In addition, the existence of a 3D bifurcation on the nominal 2D flow configuration has been investigated. Finally, using the properties of the adjoint operator, a structural sensitivity analysis is performed in order to localise the core of the instability and to better understand its nature.