Stability of the flow over superhydrophobic micro roughnesses: The influence of the interface

Superhydrophobic surfaces are known for their drag reduction properties. However, the interface between the lubricant and the overlying flow may easily become unstable, leading to the depletion of the superhydrophobic layer and to a consequent drag increase. In this paper, we investigate the modal and non-modal instability of the flow over longitudinal trapezoidal superhydrophobic riblets, including, for the first time, the gas/liquid interface dynamics in the stability analyses. A two-dimensional stability problem, obtained with a domain transform technique and interface modelling using a linearised Young–Laplace equation, is coupled with the n−periodic stability framework introduced by Schmid et al. (2017). The latter technique, using a Bloch wave formalism, allows the computation of the stability of an array of n riblet units of given periodicity at a reasonable numerical cost. For small periodicities, the most unstable mode is a fundamental instability stemming from the three-dimensionalisation of a Tollmien–Schlichting wave. Conversely, in the case of large riblet periodicities, a subharmonic mode linked to capillarity effects becomes the most unstable. Nonmodal transient growth analysis shows that the superhydrophobic riblets have a weak effect on the overall growth. However, riblets having small periodicities induce a slight stabilisation of the flow, while large ones induce an increase of the energy growth on detuned perturbations. The resulting energy growth mechanism induces interface deformations encompassing more than one subunit.