Electrostatic charging of jumping droplets

With the broad interest in and development of superhydrophobic surfaces for self-cleaning, condensation heat transfer enhancement and anti-icing applications, more detailed insights on droplet interactions on these surfaces have emerged. Specifically, when two droplets coalesce, they can spontaneously jump away from a superhydrophobic surface due to the release of excess surface energy. Here we show that jumping droplets gain a net positive charge that causes them to repel each other mid-flight. We used electric fields to quantify the charge on the droplets and identified the mechanism for the charge accumulation, which is associated with the formation of the electric double layer at the droplet–surface interface. The observation of droplet charge accumulation provides insight into jumping droplet physics as well as processes involving charged liquid droplets. Furthermore, this work is a starting point for more advanced approaches for enhancing jumping droplet surface performance by using external electric fields to control droplet jumping.United States. Dept. of Energy. Office of Basic Energy Sciences (Solid-State Solar-Thermal Energy Conversion Center Award DE-FG02-09ER46577)United States. Office of Naval ResearchNational Science Foundation (U.S.) (Major Research Instrumentation Grant for Rapid Response Research (MRI- RAPID))National Science Foundation (U.S.) (Award ECS-0335765)National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 1122374

Thermal Transport in Micro- and Nanoscale Systems

Small-scale (micro-/nanoscale) heat transfer has broad and exciting range of applications. Heat transfer at small scale quite naturally is influenced – sometimes dramatically – with high surface area-to-volume ratios. This in effect means that heat transfer in small-scale devices and systems is influenced by surface treatment and surface morphology. Importantly, interfacial dynamic effects are at least non-negligible, and there is a strong potential to engineer the performance of such devices using the progress in micro- and nanomanufacturing technologies. With this motivation, the emphasis here is on heat conduction and convection. The chapter starts with a broad introduction to Boltzmann transport equation which captures the physics of small-scale heat transport, while also outlining the differences between small-scale transport and classical macroscale heat transport. Among applications, examples are thermoelectric and thermal interface materials where micro- and nanofabrication have led to impressive figure of merits and thermal management performance. Basic of phonon transport and its manipulation through nanostructuring materials are discussed in detail. Small-scale single-phase convection and the crucial role it has played in developing the thermal management solutions for the next generation of electronics and energy-harvesting devices are discussed as the next topic. Features of microcooling platforms and physics of optimized thermal transport using microchannel manifold heat sinks are discussed in detail along with a discussion of how such systems also facilitate use of low-grade, waste heat from data centers and photovoltaic modules. Phase change process and their control using surface micro-/nanostructure are discussed next. Among the feature considered, the first are microscale heat pipes where capillary effects play an important role. Next the role of nanostructures in controlling nucleation and mobility of the discrete phase in two-phase processes, such as boiling, condensation, and icing is explained in great detail. Special emphasis is placed on the limitations of current surface and device manufacture technologies while also outlining the potential ways to overcome them. Lastly, the chapter is concluded with a summary and perspective on future trends and, more importantly, the opportunities for new research and applications in this exciting field

Water condensation on a super-hydrophobic spike surface

Condensation-induced water drop growth was studied on a super-hydrophobic spike surface. The dynamics are described by three main stages depending on the size of the drop with respect to the different spike pattern length scales. The initial stage is characterized by nucleation of the drops at the bottom (cavities) of the spikes. During the intermediate stage, large drops are surrounded by smaller drops within the neighboring cavities in what is described as a “bright ring”. This ring persists until coalescence occurs with the central drop. The last stage is characterized by Wenzel-type drops growing with scaling laws similar to that on a planar surface but with contact angle $\theta^\ast \approx 111^\circ$, lower than for deposited drops ($\theta = 164^\circ$). Condensation on spike surfaces does not retain anything of super-hydrophobicity, in contrast to super-hydrophobic square and strip patterns

Dynamics of Drop Coalescence on a Surface: The Role of Initial Conditions and Surface Properties

An investigation of the coalescence of two water drops on a surface is presented and compared with drop spreading. The associated capillary numbers are very low (< 10-5). The drops relax exponentially towards equilibrium. The typical relaxation time tc decreases with contact angle. tc is proportional to the drop size R, thus defining a characteristic velocity U* =R/tc. The corresponding U* values are smaller by many orders of magnitude than the bulk hydrodynamic velocity (U = /, with the gas-liquid surface tension and the viscosity). The dynamics of receding (coalescence) and spreading motion is found of the same order when coalescence or spreading is induced by a syringe. The dynamics of coalescence induced with the syringe deposition is systematically faster by an order of magnitude than condensation-induced coalescence. This disparity is explained by the coupling of the contact line motion with the oscillation of the drop observed for syringe deposition but absent for condensation-induced coalescence

Dynamic drying in the early-stage coalescence of droplets sitting on a plate

The early-stage coalescence of two sessile drops is investigated theoretically and experimentally. The coalescence of small sessile drops of diethylene glycol on silicon wafer is induced either by condensation or syringe deposition. The bridge geometry in directions parallel and perpendicular to the substrate, the bridge contact angle and the direct fluid velocity are simultaneously analyzed. The process is characterized by the nucleation and growth of a bridge between the two drops. Three stages are identified. i) An initial stage of dynamic drying where the capillary number $Ca > 0.02$ and the contact line does not move appreciably. The bridge does not wet the solid and its size grows as time t perpendicularly to the substrate and as $t^{1/2}$ parallel to the substrate. ii) A late stage where the contact line starts to move and where the bridge relaxes exponentially, making eventually the composite drop to be ellipsis like. This stage is followed by iii) a very slow evolution limited by the contact line motion where the drop relaxes to a circular shape with a dynamics that is 6 to 7 orders larger than bulk hydrodynamics predicts

Numerical simulations of growth dynamics of breath figures on phase change materials: The effect of accelerated coalescence due to droplet motion

We present the growth dynamics of breath figures on phase change materials using numerical simulations. We propose a numerical model which accounts for both growth due to condensation and random motion of droplets on the substrate. We call this model as growth and random motion (GRM) model. Our analysis shows that for dynamics of droplet growth without droplet motion, simulation results are in good agreement with well-established theories of growth laws and self-similarity in surface coverage. We report the emergence of a growth law in the coalescence-dominated regime for the droplets growing simultaneously by condensation and droplet motion. The overall growth of breath figures (BF) exhibits four growth regions, namely, initial $\langle R \rangle \sim t^{\alpha_1 }$ , intermediate or crossover $\langle R \rangle \sim t^{\alpha_2 }$ , coalescence-dominated regime $\langle R \rangle \sim t^{\alpha_3 }$ , and no coalescence regime in late time $\langle R \rangle \sim t^{\alpha_4 }$ , where $\langle R \rangle$ and t are the average droplet radius and time, respectively. The power law exponents are $\alpha_1 \approx 1/2$ , $\alpha_2 \approx 1.0$ , $\alpha_3 \approx 3.0$ , and $\alpha_4 \approx 1/3$ . Moreover, the surface coverage reaches a maximum value $\varepsilon^2 \approx 0.35$ where the third growth regime $t^{\alpha_3 }$ starts. We also demonstrate that during the growth dynamics of BF, the random motion amplitude δ and its probability p(R) linked to the power exponent γ of droplet radius R have a specific limiting range within which its effect is more predominant

Difference in the Dynamic Scaling Behavior of Droplet Size Distribution for Coalescence under Pulsed and Continuous Vapor Delivery

Dynamic scaling behavior of the droplet size distribution in the coalescence regime for growth by pulsed laser deposition is studied experimentally and by computer simulation, and the same is compared with that for continuous vapor deposition. The scaling exponent for pulsed deposition is found to be (1.2±0.1), which is significantly lower as compared to that for continuous deposition (1.6±0.1). Simulations reveal that this dramatic difference can be traced to the large fraction of multiple droplet coalescence under pulsed vapor delivery. A possible role of the differing diffusion fields in the two cases is also suggested