  Liquid-infused surfaces (LIS) are a promising technique for reducing
friction, fouling and icing in both laminar and turbulent flows. Previous work
has demonstrated that these surfaces are susceptible to shear-driven drainage.
Here, we report a different failure mode using direct numerical simulations of
a turbulent channel flow with liquid-infused longitudinal grooves. When the
liquid-liquid surface tension is small and/or grooves are wide, we observe
traveling-wave perturbations on the interface with amplitudes larger than the
viscous sublayer of the turbulent flow. These capillary waves induce a
roughness effect that increases drag. The generation mechanism of these waves
is explained using the theory developed by Miles for gravity waves. Energy is
transferred from the turbulent flow to the LIS provided that there is a
negative curvature of the mean flow at the critical layer. Given the groove
width, the Weber number and an estimate of the friction Reynolds number, we
provide relations to determine whether a LIS behaves as a smooth or rough
surface in a turbulent flow.
