Justin A. Weibel

Assessment of Water Droplet Evaporation Mechanisms on Hydrophobic and Superhydrophobic Substrates

Evaporation rates are predicted and important transport mechanisms identified for evaporation of water droplets on hydrophobic (contact angle ~110°) and superhydrophobic (contact angle ~160°) substrates. Analytical models for droplet evaporation in the literature are usually simplified to include only vapor diffusion in the gas domain, and the system is assumed to be isothermal. In the comprehensive model developed in this study, evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Conjugate heat and mass transfer are solved in the solid substrate, liquid droplet, and surrounding gas. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. The influences of evaporative cooling and convection on the evaporation characteristics are determined quantitatively. The liquid-vapor interface temperature drop induced by evaporative cooling suppresses evaporation, while gas-phase natural convection acts to enhance evaporation. While the effects of these competing transport mechanisms are observed to counterbalance for evaporation on a hydrophobic surface, the stronger influence of evaporative cooling on a superhydrophobic surface accounts for an overprediction of experimental evaporation rates by ~20% with vapor diffusion-based models. The local evaporation fluxes along the liquid-vapor interface for both hydrophobic and superhydrophobic substrates are investigated. The highest local evaporation flux occurs at the three-phase contact line region due to proximity to the higher temperature substrate, rather than at the relatively colder droplet top; vapor diffusion-based models predict the opposite. The numerically calculated evaporation rates agree with experimental results to within 2% for superhydrophobic substrates and 3% for hydrophobic substrates. The large deviations between past analytical models and the experimental data are therefore reconciled with the comprehensive model developed here.

Carbon Nanotube Coatings for Enhanced Capillary-Fed Boiling from Porous Microstructures

Due to their high intrinsic thermal conductivity, carbon nanotubes (CNTs) have previously been incorporated into a variety of thermal management applications to improve cooling performance. Implementation of controlled CNT growth techniques and functionalization methods are applied herein to enhance boiling heat transfer from the porous capillary wicking surfaces widely used in high heat flux thermal management devices. A microwave plasma-enhanced chemical vapor deposition (MPCVD) synthesis process resulted in growth of a permeable CNT coating, and physical vapor deposition of copper over these nanotubes yielded the requisite hydrophilic wicking surface. An array of test samples was fabricated and then evaluated using an experimental test facility to determine the reduction in surface temperature resulting from CNT coating and micropatterning of the porous surfaces under two-phase heat transfer conditions with water as the working fluid. Both CNT coating and micropatterning techniques were able to provide significant performance enhancements, reducing the surface superheat up to 72% compared to baseline tests and eliminating disadvantageous temperature overshoot corresponding to boiling incipience. Such performance gains are attributable to the formation of nanoporous cavities that increase nucleation site density and high permeability vents through which vapor can readily depart the surface under vigorous boiling conditions. The synthesis procedures developed that result in the observed enhancement can be readily incorporated into currently employed devices.

Design of Integrated Nanostructured Wicks for High-Performance Vapor Chambers

The performance of passive phase-change cooling devices, such as vapor chambers or heat pipes, may be significantly enhanced by exploiting the superior thermal properties of carbon nanotube (CNT) arrays. The potential for large reductions in overall package resistance with the use of high-conductivity wick materials enhanced with CNT nanostructures is investigated. While such nanostructured wicks feature very small pore sizes that support high capillary pressures, it is shown that the high fluid flow resistance through these dense arrays prevents their use as the lone fluid transport mechanism. It is proposed that evaporator surfaces comprised of nanostructured wicks fed by interspersed conventional wick materials (such as sintered powders) can provide the required permeability for fluid flow while simultaneously decreasing the effective evaporator thermal resistance. Optimization of wicks with integrated sintered and nanostructured areas requires a study of the trade-offs between the greater permeability of the sintered materials and the greater capillary pressure and thin-film evaporation area offered by the nanostructures. A numerical model is developed to estimate the thermal resistance of the evaporator region compared to that of a homogeneous sintered powder wick. The inputs needed for this model include the permeability and the capillary pressure in the two regions. A parametric study is conducted as a function of the ratio of conduction and evaporative resistances for the nanostructured and sintered regions. For a given heat input, the optimal liquid-feeding geometry that minimizes thermal resistance is obtained. In the best cases, the thermal resistance is reduced by a factor of thirteen through the use of the integrated nanostructured wicks compared to the resistance of a homogeneous sintered powder wick.

Coalescence-Induced Jumping of Multiple Condensate Droplets on Hierarchical Superhydrophobic Surfaces

Coalescence-induced jumping of condensate droplets from a superhydrophobic surface with hierarchical micro/nanoscale roughness is quantitatively characterized. Experimental observations show that the condensate droplet jumping is induced by coalescence of multiple droplets of different sizes, and that the coalesced droplet trajectories typically deviate from the surface normal. A depth-from-defocus image processing technique is developed to track the out-of-plane displacement of the jumping droplets, so as to accurately measure the droplet size and velocity. The results demonstrate that the highest jumping velocity is achieved when two droplets coalesce. The jumping velocity decreases gradually with an increase in the number of coalescing droplets, despite the greater potential surface energy released upon coalescence. A general theoretical model that accounts for viscous dissipation, surface adhesion, line tension, the initial droplet wetting states, and the number and sizes of the coalescing droplets is developed to explain the trends of droplet jumping velocity observed in the experiments.

Thermal Performance of Carbon Nanotube Enhanced Vapor Chamber Wicks

Vapor chambers are often used as spreaders to dissipate high heat fluxes by taking advantage of liquid-vapor phase change. Wicking of the working fluid in vapor chambers is accomplished through capillary action, which is strongly affected by the wick structure. Traditionally, copper meshes with micrometer-scale pore sizes have been used as wicking structures, but it is expected that heat fluxes in the next generation of high-power electronic devices will cause boiling in these devices and lead to dryout with conventional wick materials. With a goal of increasing maximum heat dissipation and reducing thermal resistance, a wick structure composed of both conventional copper mesh and carbon nanotubes has been developed and characterized. The high-permeability mesh provides for a low-resistance bulk flow path while the carbon nanotubes, with their high thermal conductivity and high surface area, modify the wick surface for enhanced capillary action. CNT-enhanced integrated wicks were fabricated by sintering a copper mesh on Cu-Mo-Cu substrates, on which CNTs were grown. A thin layer of copper was evaporated onto the CNTs to improve wicking and wettability with water, the working fluid of interest. Samples grown under varying degrees of positive bias voltage and varying thicknesses of post-CNT-growth copper evaporation were fabricated, so that the surface morphology of the samples could be varied. The resultant boiling curves and associated wick thermal resistances indicate that micro/nano integrated wicks fabricated with higher positive bias voltages during CNT synthesis, and thicker copper coatings, lead to improved thermal performance and lower wick thermal resistance. Notably, heat fluxes at the heater surface of greater than 500 W/cm2 were observed without reaching a critical heat flux condition.© 2010 ASME

Effect of Superhydrophobic Surface Morphology on Evaporative Deposition Patterns

Prediction and active control of the spatial distribution of particulate deposits obtained from sessile droplet evaporation are vital in printing, nanostructure assembly, biotechnology, and other applications that require localized deposits. This Letter presents surface wettability-based localization of evaporation-driven particulate deposition and the effect of superhydrophobic surface morphology on the distribution of deposits. Sessile water droplets containing suspended latex particles are evaporated on non-wetting textured surfaces with varying microstructure geometry at ambient conditions. The droplets are visualized throughout the evaporation process to track the temporal evolution of contact radius and apparent contact angle. The resulting particle deposits on the substrates are quantitatively characterized. The experimental results show that superhydrophobic surfaces suppress contact-line deposition during droplet evaporation, thereby providing an effective means of localizing the deposition of su...

Water and Ethanol Droplet Wetting Transition during Evaporation on Omniphobic Surfaces

Omniphobic surfaces with reentrant microstructures have been investigated for a range of applications, but the evaporation of high- and low-surface-tension liquid droplets placed on such surfaces has not been rigorously studied. In this work, we develop a technique to fabricate omniphobic surfaces on copper substrates to allow for a systematic examination of the effects of surface topography on the evaporation dynamics of water and ethanol droplets. Compared to a water droplet, the ethanol droplet not only evaporates faster, but also inhibits Cassie-to-Wenzel wetting transitions on surfaces with certain geometries. We use an interfacial energy-based description of the system, including the transition energy barrier and triple line energy, to explain the underlying transition mechanism and behaviour observed. Suppression of the wetting transition during evaporation of droplets provides an important metric for evaluating the robustness of omniphobic surfaces requiring such functionality.

NANO-STRUCTURED TWO-PHASE HEAT SPREADER FOR COOLING ULTRA-HIGH HEAT FLUX SOURCES

A two-phase heat spreader has been developed for cooling high heat flux sources in high-power lasers, high-intensity light-emitting diodes, and semiconductor power devices. The heat spreader targets the passive cooling of heat sources with fluxes greater than 5 W/mm2 without requiring any active power consumption for the thermal solution. The prototype vapor chamber consists of an evaporator plate, a condenser plate and an adiabatic section, with water as the phase-change fluid. The custom-designed high heat flux source is composed of a platinum resistive heating pattern and a temperature sensor on an aluminum nitride substrate which is soldered to the outside of the evaporator. Experiments were performed with several different microstructures as evaporator surfaces under varying heat loads. The first microstructure investigated, a screen mesh, dissipated 2 W/mm2 of heat load but with an unacceptably high evaporator temperature. A sintered copper powder microstructure with particles of 50 μm mean diameter supported 8.5 W/mm2 without dryout. Four sets of particle diameters and different thicknesses for the sintered copper powder evaporators were tested. Additionally, some of the sintered structures were coated with multi-walled carbon nanotubes (CNT) that were rendered hydrophilic. Such nano-structured evaporators successfully showed a further reduction in thermal resistance of the vapor chamber.Copyright

Marangoni Convection in Evaporating Organic Liquid Droplets on a Nonwetting Substrate

We quantitatively characterize the flow field inside organic liquid droplets evaporating on a nonwetting substrate. A mushroom-structured surface yields the desired nonwetting behavior with methanol droplets, while use of a cooled substrate (5-15 °C) slows the rate of evaporation to allow quasi-static particle image velocimetry. Visualization reveals a toroidal vortex within the droplet that is characteristic of surface tension-driven flow; we demonstrate by means of a scaling analysis that this recirculating flow is Marangoni convection. The velocities in the droplet are on the order of 10-45 mm/s. Thus, unlike in the case of evaporation on wetting substrates where Marangoni convection can be ignored for the purpose of estimating the evaporation rate, advection due to the surface tension-driven flow plays a dominant role in the heat transfer within an evaporating droplet on a nonwetting substrate because of the large height-to-radius aspect ratio of the droplet. We formulate a reduced-order model that includes advective transport within the droplet for prediction of organic liquid droplet evaporation on a nonwetting substrate and confirm that the predicted temperature differential across the height of the droplet matches experiments.

Spurious Current Suppression in VOF-CSF Simulation of Slug Flow through Small Channels

A numerical treatment is proposed to minimize the creation of unphysical, spurious currents in modeling liquid–gas slug flow using the volume of fluid-continuum surface force (VOF-CSF) method. An elongated gas slug drawn into a small circular channel initially filled with liquid is considered. To suppress spurious currents formed by numerical errors in calculation of the surface tension force at small capillary numbers (Ca < 0.01), an artificial relative reference frame is specified with motion in a direction opposite to the flow. An increase in the local relative velocity magnitude near the interface is demonstrated to be the key mechanism for spurious current suppression. A comparison of simulations performed with and without this treatment shows that spurious currents are eliminated at Ca = 0.0029; liquid film thickness, gas slug velocity, and liquid-phase circulation near the leading slug interface are preserved and the computed values agree with the literature. This demonstrates that the proposed moving reference frame method does not influence the computed physical phenomena of interest while suppressing unphysical spurious velocities.