Effect of the Cassie state in grooved channels on one-dimensional sound waves

Previous experiments and analyses have demonstrated that elastic boundaries reduce the speed of sound and alter the acoustic waves in fluid-filled tubes. Similar effects will occur in any configuration with deformable boundaries and fluid-fluid interfaces. In this work, we study the propagation of nonlinear acoustic waves in 1D liquid-filled tubes with superhydrophobic longitudinal grooved boundaries. Recently, grooved channels have attracted significant interest because of their reduced friction to flow, but such configurations also allow for a new kind of sound wave behavior due to the dependence of the pressure on the triple-phase contact line. We derive a model which contains an interplay between the pressure and the shape of the liquid-gas interface, subject to the hysteresis of the contact line, which is a dominant mechanism for energy dissipation. Our results present front propagation, showing an order of magnitude reduction in the speed of sound, as well as oscillation patterns in which the liquid is pinned in one part of the channel yet oscillating in the rest of the channel.