Julie Crockett

Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux

This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) walls. The superhydrophobic walls considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie–Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results, the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

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-s...

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

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 r...

Effects of isotropic and anisotropic slip on droplet impingement on a superhydrophobic surface

The dynamics of single droplet impingement on micro-textured superhydrophobicsurfaces with isotropic and anisotropic slip are investigated. While several analytical models exist to predict droplet impact on superhydrophobicsurfaces, no previous model has rigorously considered the effect of the shear-free region above the gas cavities resulting in an apparent slip that is inherent for many of these surfaces. This paper presents a model that accounts for slip during spreading and recoiling. A broad range of Weber numbers and slip length values were investigated at low Ohnesorge numbers. The results show that surface slip exerts negligible influence throughout the impingement process for low Weber numbers but can exert significant influence for high Weber numbers (on the order of 102). When anisotropic slip prevails, the droplet exhibits an elliptical shape at the point of maximum spread, with greater eccentricity for increasing slip and increasing Weber number. Experiments were performed on isotropic and anisotropic micro-structured superhydrophobicsurfaces and the agreement between the experimental results and the model is very good.

Pressure Drop Measurements in Turbulent Channel Flow Over Superhydrophobic Surfaces With Riblets

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.Copyright

Thermal Transport to Sessile Droplets on Superhydrophobic Surfaces With Rib and Cavity Features

This paper reports on measurements of thermal transport to solitary sessile water drops placed on heated superhydrophobic substrates at constant temperature. Data was obtained by heating the surfaces to specified constant temperatures and gently placing a single water droplet of nominally 3 mm diameter on the surface. The droplet was allowed to evaporate completely while two video cameras and one infrared camera imaged it during the evaporation process. The images were post-processed to yield transient geometric and thermal information, including droplet volume, projected droplet-substrate contact area, and droplet temperature. The total evaporation time and Nusselt and Grashof numbers were determined from the measurements. For all scenarios, the substrate temperature was maintained below the saturation temperature of water and was varied from 60 to 100 °C. Three different rib-patterned superhydrophobic substrates were investigated of 0.5, 0.8, and 0.95 cavity fraction, respectively. The rib features ranged in width from 2 to 30 μm and in height from 15 to 20 μm, while the cavities between the ribs ranged in width from 30 to 38 μm. Results were also obtained for a smooth hydrophobic substrate for comparison purposes. Droplet evaporation times increase with substrate cavity fraction and decrease with increasing substrate temperature. Heat transfer rates decrease with increasing substrate cavity fraction and increase with substrate temperature. The Nusselt number generally increases with the Grashof number raised to the 1/4 power, and Nusselt number is larger for lower cavity fraction substrates.© 2013 ASME

On jet impingement and thin film breakup on a horizontal superhydrophobic surface

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 rand...

Effective Temperature Jump Length and Influence of Axial Conduction for Thermal Transport Through Channels With Superhydrophobic Walls

This paper presents a numerical investigation of thermal transport in a parallel-plate channel comprised of superhydrophobic walls. The scenario analyzed in this paper is laminar, fully developed, steady flow with constant properties. The superhydrophobic walls considered here have alternating micro-ribs and cavities aligned perpendicular to the flow direction. The cavities are assumed to be non-wetting and contain air. The thermal transport through the ribs is considered to have a constant heat flux while the thermal transport through the air/fluid interface over the cavity is considered to be negligible. Numerical results have been obtained over a range a Peclet numbers, cavity fractions, and relative rib/cavity widths. Results were also obtained where axial conduction was neglected and these results are compared to previous analytical work with excellent agreement. When the influence of axial conduction is not neglected, however, the results for local wall temperatures and Nusselt numbers show departure from the previous analytical results. The departure is more pronounced at low Peclet numbers and at large relative channel diameters. This paper provides a comparison over a wide range of parameters that characterize the overall influence of axial conduction. In general, the results show that the relative size of the cavity compared to the total rib/cavity module width (cavity fraction) and the flow Peclet number have a significant impact on the total thermal transport properties. Also, the rib/cavity module width compared to the hydraulic diameter affects the overall thermal transport behavior. Lastly, this paper explores the concept of a temperature jump length which is analogous to the hydrodynamic slip length. The ratio of temperature jump length to hydrodynamic slip length is presented in terms of cavity fraction, Peclet number, and relative size of the rib cavity module.Copyright

Analytical Model of Post-Impact Droplet Spreading on a Micro-Patterned Superhydrophobic Surface With Surface Slip

Several analytical models exist to predict droplet impact behavior on superhydrophobic surfaces. However, no previous model has rigorously considered the effect of surface slip on droplet spreading and recoiling that is inherent in many superhydrophobic surfaces. This paper presents an analytical model that takes into account surface slip at the solid-fluid interface during droplet deformation. The effects of slip are captured in terms that model the kinetic energy and viscous dissipation and are compared to a classical energy conservation model given by Attane et al. and experimental data from Pearson et al. A range of slip lengths, Weber numbers, Ohnesorge numbers, and contact angles are investigated to characterize the effects of slip over the entire range of realizable conditions. We find that surface slip does not influence normalized maximum spread diameter for low We but can cause a significant increase for We > 100. Surface slip affects dynamical parameters more profoundly for low Oh numbers (0.002–0.01). Normalized residence time and rebound velocity increase as slip increases for the same range of We and Oh. The influence of slip is more significantly manifested on normalized rebound velocity than normalized maximum spread diameter. Contact angles in the range of 150°–180° do not affect impact dynamics significantly.Copyright