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1. Investigating the origin of the far-field reflection interference fringe (RIF) of microdroplets

   https://doi.org/10.1063/5.0211245  

   Kim, Iltai_Isaac; Lie, Yang; Park, Jaesung; Kim, Hyun-Joong; Kim, Hong-Chul; Yoon, Hongkyu (May 2024, Journal of Applied Physics)

   We show that the reflection interference fringe (RIF) is formed on a screen far away from the microdroplets placed on a prism-based substrate, which have low contact angles and thin droplet heights, caused by the dual convex–concave profile of the droplet, not a pure convex profile. The geometric formulation shows that the interference fringes are caused by the optical path difference when the reflected rays from the upper convex profile at the droplet–air interface interfere with reflection from the lower concave profile at oblique angles lower than the critical angle. Analytic solutions are obtained for the droplet height and the contact angle out of the fringe number and the fringe radius in RIF from the geometric formulation. Furthermore, the ray tracing simulation is conducted using the custom-designed code. The geometric formulation and the ray tracing show excellent agreement with the experimental observation in the relation between the droplet height and the fringe number and the relation between the contact angle and the fringe radius. This study is remarkable as the droplet's dual profile cannot be easily observed with the existing techniques. However, the RIF technique can effectively verify the existence of a dual profile of the microdroplets in a simple setup. In this work, the RIF technique is successfully developed as a new optical diagnostic technique to determine the microdroplet features, such as the dual profile, the height, the contact angle, the inflection point, and the precursor film thickness, by simply measuring the RIF patterns on the far-field screen. 

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2. Interference fringe (IF) technique for droplet contact angle and thickness measurements: Ultralow contact angle and nanoscale thickness measurement

   https://doi.org/10.1063/5.0273187  

   Kim, Iltai Isaac; Lie, Yang (July 2025, Journal of Applied Physics)

   Recently, reflection interference fringe (RIF) and transmission fringe (TIF) techniques have been introduced to investigate the origin of far-field interference fringe (IF) formation and to determine a droplet's contact angle and thickness by measuring the fringe radius. In this study, characteristics of the IF technique are analyzed based on the RIF and TIF by varying the schematics, such as configuration (transmission/reflection), the droplet's side (left-hand side/right-hand side), and the substrate types (flat/prism). The analysis also investigates the refraction effect at the droplet edge and the maximum incidence and contact angles. The schematic variation shows that the widest contact angle range can be measured in a transmission configuration with droplet's right-hand side, and that the fringe radius decreases with incidence angles on a prism substrate, consistent with the recent observation. Refraction at the droplet edge causes the fringe radius to increase or decrease depending on the degree of refraction. Based on the characteristics study, it is revealed that the IF technique can determine nanometer-scale thicknesses below 100 nm on droplets, corresponding to ultra-small contact angles of less than 0.01°, with an extended working distance of 3000 mm and an optimized incidence angle, assuming a spherical profile. This finding is significant, as it demonstrates that the nanoscale thickness can be determined in situ under ambient conditions using a simple optical configuration, without requiring a sophisticated setup, such as a microscope. It is anticipated that the IF technique can be combined with other nanoscale thickness measurement techniques to enhance its measurement reliability. 

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3. Investigation of sessile droplet evaporation using a transient two-step moving mesh model

   https://doi.org/10.1016/j.ijheatmasstransfer.2023.124151  

   Li, Xue; Murray, Brandon; Narayan, Shankar (August 2023, International Journal of Heat and Mass Transfer)

   The evaporation of droplets on surfaces is a ubiquitous phenomenon essential in nature and industrial applications ranging from thermal management of electronics to self-assembly-based fabrication. In this study, water droplet evaporation on a thin quartz substrate is analyzed using an unsteady two-step arbitrary Lagrangian-Eulerian (ALE) moving mesh model, wherein the evaporation process is simulated during the constant contact radius (CCR) and contact angle (CCA) modes. The numerical model considers mass transfer in the gas domain, flow in the liquid and gas domains, and heat transfer in the solid, liquid, and gas domains. Besides, the model also accounts for interfacial force balance, including thermocapillary stresses, to obtain the instantaneous droplet shape. Experiments involving droplet evaporation on unheated quartz substrates agree with model predictions of contact radius, contact angle, and droplet volume. Model results indicating temperature and velocity distribution across an evaporating water droplet show that the lowest temperatures are at the liquid-gas interface, and a single vortex exists for the predominant duration of the droplet's lifetime. The temperature of the unheated substrate is also significantly reduced due to evaporative cooling. The interfacial evaporation flux distribution, which depends on heat transfer across the droplet and advection in the surrounding medium, shows the highest values near the three-phase contact line. In addition, the model also predicts evaporation dynamics when the substrate is heated and exposed to different advection conditions. Generally, higher evaporation rates result from higher substrate heating and advection rates. However, substrate heating and advection in the surrounding gas have minimal effects on the relative durations of CCR and CCA modes for a given receding contact angle. Specifically, in this case, a 40× increase in substrate heating rate or 7.5× increase in gas velocity can only change these relative durations by 3%. This study also highlights the importance of surface wettability, which affects evaporation dynamics for all the conditions explored by the numerical model. 

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4. Analyzing interfacial transport for water evaporating into dry nitrogen

   https://doi.org/10.1016/j.applthermaleng.2021.117910  

   Murray, B.; Fox, M. J.; Narayan, S. (December 2021, Applied thermal engineering)

   Markides, C. N. (Ed.)

   Designing air-water systems for industrial applications requires a fundamental understanding of mass accommodation at the liquid-vapor interface, which depends on many factors, including temperature, vapor concentration, and impurities that vary with time. Hence, understanding how mass accommodation changes over a droplet’s lifespan is critical for predicting the performance of applications leveraging evaporation. In this study, experimental data of water droplets on a gold-coated surface evaporating into dry nitrogen is coupled with a computational model to measure the accommodation coefficient at the liquid-vapor interface. We conduct this measurement by combining macroscopic observations with the microscopic kinetic theory of gasses. The experiments utilize a sensitive piezoelectric device to determine the droplet radius with high accuracy and imaging to measure the droplet contact angle. This setup also quantifies the trace amounts of non-volatile impurities in the droplet. For water droplets evaporating in a pure nitrogen stream, the accommodation coefficient directly relates to vapor flux over the droplet’s surface and is affected by the presence of impurities. We obtained a surface-averaged accommodation coefficient close to 0.001 across multiple water droplets evaporating close to room temperature. This quantification can aid in conducting a more accurate analysis of evaporation, which can assist in the improved design of evaporation-based applications. We believe the modeling approach presented in this work, which integrates the kinetic theory of gases to the macroscale flow behavior, can provide a basis for predicting evaporation kinetics in the presence of extremely dry non-condensable gas streams. 

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5. Impact of Dropwise Condensation on the Biomass Production Rate in Covered Raceway Ponds

   https://doi.org/10.3390/en14020268  

   Hoeniges, Jack; Zhu, Keyong; Pruvost, Jeremy; Legrand, Jack; Si-Ahmed, El-khider; Pilon, Laurent (January 2021, Energies)

   null (Ed.)

   This study investigates the effect of condensed water droplets on the areal biomass productivity of outdoor culture systems with a free surface, protected by a transparent window or cover to prevent contamination and to control the growth conditions. Under solar radiation, evaporation from the culture causes droplets to condense on the interior surface of the cover. To quantify the effect of droplets on the system’s performance, the bidirectional transmittance of a droplet-covered window was predicted using the Monte Carlo ray-tracing method. It was combined with a growth kinetics model of Chlorella vulgaris to predict the temporal evolution of the biomass concentration on 21 June and 23 September in Los Angeles, CA. A droplet contact angle of 30∘ or 90∘ and a surface area coverage of 50% or 90% were considered. Light scattering by the condensed droplets changed the direction of the incident sunlight while reducing the amount of light reaching the culture by up to 37%. The combined effect decreased the daily areal biomass productivity with increasing droplet contact angle and surface area coverage by as much as 18%. Furthermore, the areal biomass productivity of the system was found to scale with the ratio X0/a of the initial biomass concentration X0 and the specific illuminated area a, as previously established for different photobioreactor geometries, but even in the presence of droplets. Finally, for a given day of the year, the optical thickness of the culture that yielded the maximum productivity was independent of the window condition. Thus, the design and operation of such a system should focus on maintaining a small droplet contact angle and surface area coverage and an optimum optical thickness to maximize productivity. 

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