An Exploration of Transport Within Micro and Nano Droplet Clusters During Dropwise Condensation of Water on Nanostructured Surfaces

Abstract

Experimental studies of dropwise condensation have generally indicated that higher heat transfer coefficients correspond to smaller mean sizes for droplets growing through condensation on the surface. Recent investigations of dropwise condensation on nanostructured surfaces suggest that optimizing the design of such surfaces can push mean droplet sizes down to smaller values and significantly enhance heat transfer. This paper summarizes a theoretical exploration of the limits of heat transfer enhancement that can be achieved by pushing mean droplet size to progressively smaller sizes. A model analysis is developed that predicts transport near clusters of water droplets undergoing dropwise condensation. The model accounts for interfacial tension effects on thermodynamic equilibrium and noncontinuum transport effects, which become increasingly important as droplet size becomes progressively smaller. In this investigation, the variation of condensing heat transfer coefficient for droplet clusters of different size was explored for droplet diameters ranging from hundreds of microns to tens of nanometers. The model predictions indicate that the larger droplet transport trend of increasing heat transfer coefficient with decreasing mean droplet size breaks down as droplet size becomes smaller. The model further predicts that as drop size becomes smaller, a peak heat transfer coefficient is reached, beyond which the coefficient drops as the size continues to diminish. This maximum heat transfer coefficient results from the increasing importance of surface tension effects and non-continuum effects as droplet size becomes smaller. The impact of these predictions on the interpretation of dropwise condensation heat transfer data, and the implications for design of nanostructured surfaces to enhance dropwise condensation are discussed in detail.

On Localized Vapor Pressure Gradients Governing Condensation and Frost Phenomena

“…In an all-liquid condensing system, these dry zones are driven solely by the difference in supersaturation degree (SSD) between droplets of disparate sizes. There exist some rigorous computational studies that have solved for the heat transfer coefficients and droplet growth by numerically solving the transport equations. , Here, we show by simple scaling arguments how we can estimate the dry zone length between droplets over a wide parameter space. Consider a mother droplet exhibiting a radius of curvature r m = 10 μm and a temperature T d at its liquid–vapor interface.…”

“…However, the model is based on simple scaling arguments and more importantly on the continuum limit where fluxes are governed by eqs and . A computational model in this regard , can help shed more light on the noncontinuum transport effects on dry zones in the very early stages of nucleation when r ∼ 1–10 nm.…”

“…Homogeneous nucleation has been addressed in considerable depth in the fields of cloud physics and atmospheric sciences. , For this reason and also because the phenomena of dry zones, ice bridging, and frost halos are generally intrinsic to substrates, we limit ourselves here to the case of heterogeneous nucleation. Note that in the present discussion we have not considered the noncontinuum transport effects that have been studied in previous works, − which if considered would not change the formulation but use a different value of surface tension. We will first consider the case of new water/ice embryos nucleating on a dry portion of the substrate.…”

“…It can be seen that the supersaturation is quite significant for nanometric droplets (for example, SSD > 1 when r ∼ 1 nm) but becomes insignificant (<0.1% supersaturation) for micrometric droplets whose vapor pressure can be approximated as saturated. Note that in order to obtain better estimates of SSD, curvature-induced changes in surface tension − should be considered when the droplet curvature becomes comparable to the thickness of the liquid–vapor interface.…”