On three simple experiments to determine slip lengths

It is now well established that for fluid flow at the micro- and nano-scales the standard no-slip boundary condition of fluid mechanics at fluid-solid interfaces is not applicable and must be replaced by a boundary condition that allows some degree of tangential fluid slip. Although molecular dynamics studies support this notion, an experimental verification of a slip boundary condition remains lacking, primarily due to the difficulty of performing accurate experimental observations at small scales. In this article, three simple fluid problems are studied in detail, namely a fluid near a solid wall that is suddenly set in motion (Stokes' first problem), the long-time behavior of a fluid near an oscillating solid wall (Stokes' second problem), and the long-time behavior of a fluid between two parallel walls one of which is oscillating (oscillatory Couette flow). The no-slip boundary condition is replaced with the Navier boundary condition, which allows a certain degree of tangential fluid slip via a constant slip length. The aim is to obtain analytical expressions, which may be used in an experimental determination of the constant slip length for any fluid-solid combination.