Analysis of laminar jet impingement and hydraulic jump on a horizontal surface with slip

This paper explores the influence surface slip, uniform in all directions with constant slip length, exerts on the physics of laminar jet impingement on a flat horizontal surface. Slip exists on superhydrophobic surfaces, and due to the relatively thin film dynamics associated with the growth of the laminar jet after impingement, its influence on the fluid physics is significant. An analysis based on momentum considerations is presented that allows prediction of the relevant thin film parameters as a function of radial position from the impingement point, jet Reynolds number, and constant relative slip length of the surface. Further, the analysis allows determination of the hydraulic jump location in terms of laminar jet characteristics and imposed downstream liquid depth. The results reveal that at a given radial location, the boundary layer growth and thin film thickness decrease, while the surface velocity of the thin film increases with increasing slip at the surface. The departure from classical no-slip behavior is quantified over a range of realizable slip conditions. Increasing slip length also leads to formation of hydraulic jumps at increasing radial location. An expression based on the results is presented that allows prediction of the hydraulic jump location as a function of the magnitude of the slip and all other influencing variables.