When a vertical laminar jet impinges on a horizontal surface, it will spread out in a thin film. If the surface is hydrophobic and a downstream depth is not maintained, the film will radially expand until it breaks up into filaments or droplets. We present the first analysis and model that describes the location of this transition for both isotropic and anisotropic structured superhydrophobic (SH) surfaces. All surfaces explored are hydrophobic or SH, where the SH surfaces exhibit an apparent slip at the plane of the surface due to a shear free condition above the air filled cavities between the structures. The influence of apparent slip on the entire flow field is significant and yields behavior that deviates notably from classical behavior for a smooth hydrophilic surface where a hydraulic jump would form. Instead, break up into droplets occurs where the jet’s outward radial momentum is balanced by the inward surface tension force of the advancing film. For hydrophobic surfaces, or SH surfaces with random micropatterning, the apparent slip on the surface is uniform in all directions and droplet breakup occurs in a circular pattern. When alternating rib/cavity microstructures are used to create the SH surface, the apparent slip varies as a function of the azimuthal coordinate, and thus, the breakup location is elliptically shaped. The thin film dynamics are modeled by a radial momentum analysis for a given jet Weber number and specified slip length and the location of breakup for multiple surfaces over a range of jet Weber numbers and realistic slip length values is quantified. The results of the analysis show that the breakup radius increases with increasing Weber number and slip length. The eccentricity of the breakup ellipse for the rib/cavity SH structures increases with increasing Weber number and slip length as well. A generalized model that allows prediction of the transition (break-up) location as a function of all influencing parameters is presented. Model results are compared to experimental measurements with very good agreement.

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.

The Influence of Superhydrophobicity on Laminar Jet Impingement and Turbulent Flow in a Channel with Walls Exhibiting Riblets Joseph F. Prince Department of Mechanical Engineering, BYU Doctor of Philosophy The object of this work is to explore the influence superhydrophobic (SH) surfaces exert in laminar jet impingement and when they are combined with riblets in turbulent channel flow. A SH surface generates an apparent slip due to the combination of micropatterning and chemical hydrophobicity. Because of surface tension, water does not enter the cavities between the features, increasing the contact angle of a water droplet on the surface and reducing the liquid-solid contact area. An analysis based on the integral momentum approach of Karman and Pohlhausen is presented that predicts jet impingement behavior on SH surfaces. The model is first applied to the scenario where the slip at the surface is isotropic and a downstream depth is imposed such that a circular hydraulic jump occurs. The model predicts the thin film parameters downstream of the jet and the radial location of the hydraulic jump. An increase in the hydraulic jump radius occurs as slip increases, momentum of the jet increases, or the downstream depth decreases. Modifications to the model are made for the scenario where the slip at the surface varies azimuthally, as would be the case for a surface patterned with microribs. The average behavior is similar, although now an elliptically shaped jump forms with the major axis aligned parallel to the rib/cavity structures. The ellipse eccentricity increases as the slip increases, the jet momentum increases, or the downstream depth decreases. Where there is no downstream depth imposed on SH surfaces, the thin film breaks up into droplets instead of forming a hydraulic jump. Further changes are made to the model to incorporate this behavior for isotropic and anisotropic surfaces resulting in circular and elliptically shaped breakups respectively. This work also explores SH surfaces with riblets in turbulent channel flow. Pressure drop measurements across surfaces exhibiting superhydrophobicity, riblets, and surfaces with both drag reducing mechanisms are presented. The SH surface reduces drag because the effective surface area is reduced and riblets are able to reduce drag by dampening the spanwise turbulence. Photolithography was used to fabricate all surface types. An aluminum channel with a control and a test section was used for testing. Pressure transducers recorded the pressure drop across smooth silicon wafers and patterned test surfaces simultaneously allowing for computation of the friction factors.

In this paper we consider the combined drag reducing mechanisms of superhydrophobicity with riblets. Pressure drop measurements were acquired for turbulent flow in a channel with superhydrophobic walls, riblet walls, and walls with both drag reducing mechanisms. The superhydrophobic structuring was composed of alternating microribs (15 microns tall and 8 microns wide) and cavities (32 microns wide), aligned parallel to the flow. Superhydrophobic surfaces function to reduce drag by minimizing the effective liquid-solid contact area as water will not penetrate the cavities between microribs due to surface tension. The riblets were nominally 80 microns tall, 18 microns wide, spaced with a period of 160 microns and were also aligned parallel to the flow. Riblets function by damping out spanwise turbulent motions. Since turbulence is a three-dimensional phenomenon, this destruction of turbulent motions acts to reduce the average friction at the surface. Fabrication of the drag reducing surfaces was completed with photolithographic techniques on silicon wafers. The wafers were inserted into a channel consisting of a control section with smooth wafers and a test section with patterned wafers. In all cases, the test section walls were structured on top and bottom while the side walls were left smooth. The channel had a hydraulic diameter of 7.3 mm and an aspect ratio of 10:1. Tests were obtained over a Reynolds number range of 5 × 103 to 1.5 × 104. The superhydrophobic surfaces with riblets showed a maximum drag reduction of 7.0% which was a higher reduction than either the surfaces patterned with riblets or the superhydrophobic surfaces.

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.