Jet impingement and the hydraulic jump on horizontal surfaces with anisotropic slip

Abstract

This paper presents an analysis that describes the dynamics of laminar liquid jet impingement on horizontal surfaces with anisotropic slip. Due to slip at the surface and the anisotropy of its magnitude, the overall behavior departs notably from classical results. For the scenario considered the slip length varies as a function of the azimuthal coordinate and describes superhydrophobic surfaces micropatterned with alternating ribs and cavities. The thin film dynamics are modeled by a radial momentum analysis for a given jet Reynolds number and specified slip length and the influence of slip on the entire flow field is significant. In an average sense the thin film dynamics exhibit similarities to behavior that exists for a surface with isotropic slip. However, there are also important deviations that are a direct result of the azimuthally varying slip and these become more pronounced at higher Reynolds numbers and at greater slip lengths. The analysis also allows determination of the azimuthally varying radial location of the hydraulic jump that forms due to an imposed downstream depth. Departure from the no slip case and from the scenario of isotropic slip is characterized over a range of jet Reynolds numbers and realistic slip length values. The results show that for all cases the hydraulic jump is elliptical, with eccentricity increasing as the Reynolds number or slip length increases, or as the downstream depth decreases. The radial location of the hydraulic jump is greatest in the direction of greatest slip (parallel to the microribs), while it is a minimum in the direction transverse to the rib/cavity structures. The model results for the hydraulic jump radial position are compared to experimental measurements with good agreement.