Julie Vanderhoff

The trapping and detrapping of short internal waves by an inertia wave

The refraction of a spectrum of short internal waves by a packet of inertia waves is considered. It is found that a short inertia-wave packet produces a larger net change in a spectrum of short waves than a long inertia-wave packet, provided the short waves are trapped at some time during the interaction. Specifically, an incident narrow-banded short-wave spectrum broadens more quickly and more fully when refracted by the short inertia-wave packet. The results are explained in terms of a frequency conservation law, which constrains short-wave change in the limit of a long inertia-wave packet.

Hydraulic Jump due to Jet Impingement on Micro-Patterned Surfaces Exhibiting Ribs and Cavities

This paper reports experimental results characterizing the hydraulic jumps that form due to liquid jet impingement on micro-patterned surfaces with alternating micro-ribs and cavities. The surfaces are characterized by the cavity fraction, which is defined as the width of a cavity divided by the combined width of a cavity and an adjoining rib. The surfaces are all hydrophilic and thus the cavity regions are wetted during the impingement process. Four different surface designs were studied, with respective cavity fractions of 0 (smooth surface), 0.5, 0.8, and 0.93. The experimental data spans a Weber number range (based on the jet velocity and diameter) of 600 to 2100 and a corresponding Reynolds number range of 11500 to 21400. As with jet impingement on a smooth surface, when a liquid jet strikes a ribbed surface it then moves radially outward in a thin film and eventually experiences a hydraulic jump, where the thickness of the film increases by an order of magnitude, and the velocity decreases accordingly. However, the anisotropy of the patterned surface causes a disparity in frictional resistance dependent upon the direction of the flow relative to the orientation of the ribs. This results in a hydraulic jump which is elliptical rather than circular in shape, where the major axis of the ellipse is aligned parallel to the ribs, concomitant with the frictional resistance being smallest parallel to the ribs and greatest perpendicular to the ribs. When the water depth downstream of the jump was imposed at a predetermined value, the major and minor axis of the jump decreased with increasing water depth, following classical hydraulic jump behavior. The experimental results indicate that for a given cavity fraction and downstream depth, the radius of the jump increases with increasing Reynolds number. At a specified Reynolds number and downstream depth, the hydraulic jump radius in the direction parallel to the ribs of a patterned surface is nominally equal to the jump radius for a smooth surface, regardless of cavity fraction. The jump radius perpendicular to the ribs is notably less than that for a smooth surface, and this radius decreases with increasing cavity fraction.Copyright

Fully-Developed Thermal Transport in Microchannels With Streamwise Grooved 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 walls. The superhydrophobic walls considered here exhibit micro-ribs and cavities aligned in the streamwise direction. The cavities are assumed to be non-wetting 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.Copyright

Influence of Superhydrophobic Walls on the Thermal Transport to Liquid Droplets

This paper presents an experimental investigation of the thermal transport to liquid droplets resting on heated horizontal superhydrophobic surfaces. The superhydrophobic surfaces considered here exhibit alternating micro-ribs and cavities. Specifically, we consider the transient thermal response to water droplets as they are placed on heated superhydrophobic surfaces. For comparative purpose we also consider the same scenario with smooth hydrophobic and smooth hydrophilic surfaces. Experiments were conducted over a range of surface temperatures varying from 60 to 165 °C. The results show radically different behavior in the transient thermal transport for the three surface types considered. At all temperatures the total droplet evaporation time on the superhydrophobic surfaces was nearly an order of magnitude greater than on the smooth hydrophilic surface. At temperatures elevated above the saturation temperature, where vigorous boiling was evident on the hydrophilic surface, the droplets on the superhydrophobic surfaces remained at bulk temperatures significantly lower than the saturation temperature. Further, the droplets on the superhydrophobic surfaces exhibited Leidenfrost-like behavior at surface temperatures far below the typical Leidenfrost point. Analysis of the data reveals overall heat transfer coefficients that are much lower on the superhydrophobic surfaces than on the other surfaces, over the entire range of temperatures explored.Copyright