Analysis of drop size distribution as a function of surface roughness properties and operating condition - Balbarona, Juvy A.
Heat transfer between a fluid and a surface via condensation is dependent on the rate and manner of how the liquid forms on the surface. Previous studies have reported that smaller droplets have better heat transfer than large drops. This has prompted increased exploration into various surface fabrication techniques that can result to smaller and sustained droplets over the past decade. The frequency distribution of the size of these drops is a direct measure of how well the surface performs as a non-wetting material. During dropwise condensation, drop size distribution is used directly to quantify heat transfer. Growth rate of drops and size distribution during this phase change process are both due to the interaction between the solid surface and the liquid condensate. Intuitively, these parameters should vary with surface characteristics as well as operating condition during condensation. In this study, the effect of surface roughness on drop size distribution during dropwise condensation on copper is explored. The topography of the copper surface is varied by oxygen plasma treatment which resulted to the formation of surface microstructures with distinct roughness features. This is followed by post functionalization to create superhydrophobic copper surfaces, ensuring that only dropwise condensation will occur. The resulting static water contact angle on the samples range from 150° to 160° indicating superhydrophobicity. Actual condensation experiments are carried out on the treated samples at different cooling water temperatures, and sequential images of drops are recorded. Drop size distributions extracted from these images are found to vary significantly with time, as well as with cooling water temperature. Surface plot of drop surface coverage against time reveals the growth rate of distinct generation of drops. This pattern is also seen in the plot of drop count against time. To characterize the varying dropwise condensation behaviors on the different surfaces, a drop size distribution model is developed combining a power law growth model, an exponentially decaying population model, and a Gaussian probability model growth variations. The developed models are found to agree well with the experiment data with correlations ranging from 88% to 94%. The growth model can sufficiently describe the growth of drops from 0.02 mm to 0.1 mm but may be extrapolated to describe the growth of even smaller drops. The study then compared the growth rate and the frequency of the generational turnover versus operating conditions and surface properties. Drop growth rate is found to decrease with increasing cooling water temperature primarily due to the reduction of temperature difference that drives condensation. Drop growth rate however increases as surface roughness is decreased. Specifically, drop growth increases as core roughness Sk, developed area Sdr, and root means square gradient Sdq decrease. Sweep interval is also found to vary with surface roughness expressed as a measure of roughness porosity. As surface roughness becomes more porous, contact area between the drop and the solid surface is increased. Consequently, adhesive force at the solid-liquid interface is also increased, which delays the detachment of the drop from the surface resulting to a large sweep interval. Sweep interval, however, does not affect the drop growth rate, but affects significantly the distribution of drops of different sizes. Given the growth model, population model, and the average sweep interval, the condensation rate may be determined for one generation of drops, which is proportional to the heat transfer rate due to dropwise condensation. More importantly, the developed mathematical model and sweep interval can be used to sufficiently model the time-varying drop size distribution, from which total condensation heat transfer may be determined for a given time interval