Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

It is known that an increased flow rate can be achieved in channel flows when smooth walls are replaced by superhydrophobic surfaces. This reduces friction and increases the flux for a given driving force. Applications include thermal management microelectronics, where competition between convective conductive resistance must accounted order to evaluate any advantages of these Of particular interest hydrodynamic stability underlying basic flows, something has been largely overlooked literature, but key relevance applications typically base design on steady states or apparent-slip models approximate them. We consider global problem case longitudinal grooves periodic spanwise direction. The driven along either motion upper lid constant pressure gradient. In walls, former (plane Couette flow) linearly stable at all Reynolds numbers whereas latter Poiseuille becomes unstable above relatively large number. When present our work shows additional instabilities arise both cases, with critical small enough achievable applications. Generally, lid-driven one mode found neutral as number increases, indicating inviscidly stable. For pressure-driven two modes coexist exchange depending height slip fraction. first remains corresponds two-dimensional Rayleigh equation, while second neutrally infinite numbers. Comparisons experimental observations Daniello et al. ( Phys. Fluids , vol. 21, issue 8, 2009, p. 085103) encouraging.