Droplet | 液滴群聚效应改写经典冷凝传热模型

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The case of the coarsening-induced disappearing droplets

Nenad Miljkovic

The progress of mankind has depended on incremental technological advancements over the past centuries. One of these was the development of the steam engine and steam power cycle. Currently, the steam power cycle is the most prevalent method used to convert thermal energy (coal, natural gas, oil, nuclear) into electrical energy. As of summer 2022, more than 70% of the global electrical power production uses a steam cycle. As Xianming Dai and his co-workers note, increasing the overall efficiency of the cycle, even by a fraction of a percent, represents an immense opportunity to reduce the adverse effects of global climate.

The past century has seen a number of innovations, which have the potential to enhance the efficiency of the steam cycle. Among these, the most straightforward is to maximize the steam condensation heat transfer inside the condenser (Figure 1a). Doing so can increase the overall efficiency by up to 2%. The current state-of-the-art steam power cycle condensers are made of metals such as steel, titanium, and copper–nickel. These materials are water wetting, resulting in the formation of a thin liquid film once steam condenses on their surface. This filmwise condensation results in a condensation heat transfer coefficient on the order of 10–100 kW/(m²K), which sets the coolant to steam saturation temperature difference. Many decades ago, researchers in Europe noted that coating these metal surfaces with a thin layer of a hydrophobic fatty acid can result in a 10× increase in condensation heat transfer coefficient (Figure 1b). This in turn can reduce the steam to coolant temperature difference and condenser pressure, and increase the overall efficiency.

Figure 1

Opportunities and value of dropwise condensation of steam. (a) Suggested improvements to a steam plant to enhance efficiency. The red box highlights the opportunity for improvement by designing a condenser to decrease turbine back-pressure. 1 (b) Steam condensation heat flux as a function of subcooling for a fixed vapor temperature of 100°C. Dropwise condensation experiments conducted on flat hydrophobic surfaces before 2000 are plotted in the dark gray lines grouped within a shaded “dropwise regime” region; other condensation experiments with surface modification via roughening and coatings are plotted in color; and the Nusselt filmwise condensation model is plotted as a dashed gray line for comparison. 

In an effort to predict dropwise condensation performance, a number of seminal works have developed detailed models of condensation by combining individual droplet growth dynamics with droplet population theory. Dropwise condensation heat transfer has been successfully predicted by using analytical approaches, numerical simulations, or deep learning methods. More recently, researchers have discovered that dropwise condensation can be promoted on hydrophilic liquid or solid surfaces. In this issue of Droplet, Xianming Dai and his co-workers report a novel approach to address the challenges facing these classical models when applied to liquid-infused hydrophilic surfaces. Specifically, the authors note that the effect of coarsening-induced disappearance of droplets cannot be captured using past modeling approaches.

When droplets form on a hydrophilic lubricant-infused surface, meniscus-mediated coarsening of droplets occurs. Classical models, which rely on time-averaging of droplet distributions, fail to capture this coarsening effect. The authors propose a dynamic model to account for coarsening effects. To achieve high-frequency droplet disappearance, the authors use a lubricant-infused surface, sometimes termed as a slippery liquid-infused porous surface (SLIPS), which has the unique characteristics of enabling exceptional topographical (smoothness) and chemical homogeneity. Using detailed experiments, the authors show that the classical models break down when applied to dropwise condensation on the SLIPS where a low (<30%) water coverage ratio occurs. Using a host of optical experiments and data analysis, the authors chose to elegantly modify the classical approach (as opposed to radically changing the method) by modifying the precoalescence droplet number density (n(R)) via the addition of a second-order term, which accounts for droplet-coarsening. The modified number density is experimentally determined via power law fitting and verified by comparing the calculated results with measured heat flux (a quantity that utilizes the integrated number density).

Although coalescence-induced droplet jumping shows similar droplet disappearance phenomena due to surface-to-kinetic energy release and out-of-plane droplet jumping, the droplets jump away from the surface. Coarsening results in droplet liquid accumulation at larger droplets, and hence can be perceived as additional droplets growth when not properly resolving the microscale droplets. This fact reminds me of recent work looking at the effect of droplet growth due to coarsening from shaded droplets residing beneath the contact line, which is a similar phenomenon but does not occur on SLIPS. I would be interested if the developed dynamic model could be applied to shaded droplets to account for the discrepancy in apparent droplet distribution. Furthermore, I note that if an imaging system was indeed able to resolve the full droplet distribution (down to approximately 1 µm diameter length scale), the classical models would indeed work well for predicting the overall physical phenomena. Where the work by Xianming Dai and co-workers succeeds is in the ability to modify conventional analysis techniques, which cannot be used to predict the full droplet distribution, and enable them to account for coarsening effects and enable the understanding of condensation heat transfer physics. We hope that Droplet will publish a range of experimental, computational, and theoretical contributions from the scientific community in this broad area in our future issues.