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Register a new userVapor flux on bumpy surfaces: condensation and transpiration on leaves
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Sunghwan Jung
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Drop condensation and evaportation as a result of the gradient in vapor concentration are important in both engineering and natural systems. One of the interesting natural examples is transpiration on plant leaves. Most of water in the inner space of the leaves escapes through stomata, whose rate depends on the surface topography and a difference in vapor concentrations inside and just outside of the leaves. Previous research on the vapor flux on various surfaces has focused on numerically solving the vapor diffusion equation or using scaling arguments based on a simple solution with a flat surface. In this present work, we present and discuss simple analytical solutions on various 2D surface shapes (e.g., semicylinder, semi-ellipse, hair). The method of solving the diffusion equation is to use the complex potential theory, which provides analytical solutions for vapor concentration and flux. We find that a high mass flux of vapor is formed near the top of the microstructures while a low mass flux is developed near the stomata at the leaf surface. Such a low vapor flux near the stomata may affect transpiration in two ways. First, condensed droplets on the stomata will not grow due to a low mass flux of vapor, which will not inhibit the gas exchange through the stomatal opening. Second, the low mass flux from the atmosphere will facilitate the release of high concentrated vapor from the substomatal space.
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Water vapor condensation is common in nature and widely used in industrial applications, including water harvesting, power generation, and desalination. As compared to traditional filmwise condensation, dropwise condensation on lubricant-infused surfaces (LIS) can lead to an order-of-magnitude increase in heat transfer rates. Small droplets (with the diameter below 100 $mu$m) account for nearly 85 percent of the total heat transfer and droplet sweeping plays a crucial role in clearing nucleation sites, allowing for frequent re-nucleation. Here, we focus on the dynamic interplay of microdroplets with the thin lubricant film during water vapor condensation on LIS. Coupling high-speed imaging, optical microscopy, and interferometry, we show that the initially uniform lubricant film re-distributes during condensation. Governed by lubricant height gradients, microdroplets as small as 2 $mu$m in diameter undergo rigorous and gravity-independent self-propulsion, travelling distances multiples of their diameters at velocities up to 1100 $mu$m/s. Although macroscopically the movement appears to be random, we show that on a microscopic level capillary attraction due to asymmetrical lubricant menisci causes this gravity-independent droplet motion. Based on a lateral force balance analysis, we quantitatively find that the sliding velocity initially increases during movement, but decreases sharply at shorter inter-droplet spacing. The maximum sliding velocity is inversely proportional to the oil viscosity and is strongly dependent of the droplet size, which is in excellent agreement with the experimental observations. This novel and non-traditional droplet movement is expected to significantly enhance the sweeping efficiency during dropwise condensation, leading to higher nucleation and heat transfer rates.
Gaseous thermal transpiration flows through a rectangular micro-channel are simulated by the direct simulation BGK (DSBGK) method. These flows are rarefied, within the slip and transitional flow regimes, which are beyond many traditional computational fluid dynamic simulation schemes, such as those based on the continuum flow assumption. The flows are very slow and thus many traditional particle simulation methods suffer large statistical noises. The adopted method is a combination of particle and gas kinetic methods and it can simulate micro-flows properly. The simulation results of mass flow rates have excellent agreement with experimental measurements. In another case of 2D channel, the DSBGK comparisons with the DSMC result and the solution of Shakhov equation are also in very good agreement. Another finding from this study is that numerical simulations by including two reservoirs at the channel ends lead to appreciable differences in simulation results of velocity and pressure distributions within the micro-channel. This is due to the inhaling and exhaling effects of reservoirs at the channel ends. Even though excluding those reservoirs may accelerate the simulations significantly by using a single channel in simulations, special attentions are needed because this treatment may over-simplify the problem, and some procedures and results may be questionable. One example is to determine the surface momentum accommodation coefficient by using analytical solution of the mass flow rate obtained in a single-channel problem without the confinement effect of reservoirs at the two ends.
Transport phenomena involving condensate liquids generated from the phase change heat transfer in microchannels and in engineered superhydrophobic surfaces require consideration of slip effects. In this study, the laminar film condensation over upward facing flat slabs and circular disks of finite sizes with free edges in the presence of wall slip effects is investigated. By considering the Navier slip model and extending the classical Nusselt analysis, the mass, momentum, and energy of the liquid film in two-dimensional and axisymmetric coordinates are solved for the film thickness and the heat transfer rate in non-dimensional form. Numerical solution yields the local structure of the condensate film profile and the Nusselt number for different values of the slip coefficient. Investigation of the results reveals that the condensate film on horizontal surfaces becomes thinner and the overall heat transfer rate is enhanced with an increase in the slip coefficient. In particular, a regression analysis of the results indicates a power law dependence of the Nusselt number on the non-dimensional slip coefficient with an exponent close to 0.5. Significant enhancement in phase change heat transfer follow from the modification of the local velocity profiles within the condensate film, especially in resulting from the additional momentum gain near the wall surfaces due to increases in slip effects.
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