Analytic solutions for unsteady flows over a superhydrophobic surface

A class of unsteady analytic solutions for the evolution of viscous Newtonian fluids over a superhydrophobic surface is derived. The surface is represented by regular rectilinear riblets and the fluid is assumed to flow along the grooves' direction. A mixed boundary condition is imposed on the surface, consisting in homogeneous Neumann conditions over the riblet voids and homogeneous Dirichlet conditions on the wall intervals. The transition between the above conditions is modelled through a Robin condition with non-constant smooth coefficients in a completely general manner. A global solution is derived and relevant examples, that can be fruitfully adopted as benchmark solutions for testing numerical solvers, are discussed.