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1. Surface tension and evaporation behavior of liquid fuel droplets at transcritical conditions: Towards bridging the gap between molecular dynamics and continuum simulations

   https://doi.org/10.1016/j.fuel.2023.130187  

   Jangale, Prajesh; Hosseini, Ehsan; Zakertabrizi, Mohammad; Jarrahbashi, Dorrin (November 2023, Fuel)

   The phase transition from subcritical to supercritical conditions, referred to as transcritical behavior, significantly impacts the evaporation and fuel–air mixing in high-pressure liquid-fuel propulsion systems. Transcritical behavior is characterized as a transition from classical two-phase evaporation to a single-phase gas-like diffusion regime as surface tension and latent heat of vaporization reduce. However, the interfacial behavior represented by the surface tension coefficient and evaporation rate during this transition which are crucial inputs for Computational Fluid Dynamics (CFD) simulations of practical transcritical fuel spray is still missing. This study aims at developing new evaporation rate and surface tension models for transcritical n-dodecane droplets using molecular dynamics (MD) simulations irrespective of the droplet size. As MD simulations are primarily limited to the nanoscale, the new models can bridge the gap between MD and continuum simulations and enable the direct application of these findings to microscopic droplets. A new characteristic timescale, i.e., “undroplet time,” is defined which marks the transition from classical two-phase evaporation to single-phase gas-like diffusion behavior. The undroplet time indicates the onset of droplet core disintegration and penetration of nitrogen molecules into the droplet, which occurs after the vanishment of the surface tension. By normalizing the time with respect to the undroplet time, the rate of surface tension decay, evaporation rate, and the rate of droplet mass depletion become independent of the droplet size. Calculation of pairwise correlation coefficients for the entire MD results shows that both surface tension coefficient and evaporation rate are strongly correlated with the background temperature, while pressure and droplet size play a less significant role past the critical point. Therefore, new models for surface tension coefficient and evaporation rate spanning from sub- to supercritical conditions are developed as a function of background pressure and temperature, which can be used in continuum simulations. The identified phase change behavior based on the undroplet time shows a good agreement with the phase change regime maps obtained using microscale experiments and nanoscale MD predictions. 

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2. Benchmarking surface tension measurement method using two oscillation modes in levitated liquid metals

   https://doi.org/10.1038/s41526-021-00137-9  

   Brosius, Nevin; Ward, Kevin; Wilson, Evan; Karpinsky, Zachary; SanSoucie, Michael; Ishikawa, Takehiko; Matsumoto, Satoshi; Narayanan, Ranga (December 2021, npj Microgravity)

   null (Ed.)

   Abstract The Faraday forcing method in levitated liquid droplets has recently been introduced as a method for measuring surface tension using resonance. By subjecting an electrostatically levitated liquid metal droplet to a continuous, oscillatory, electric field, at a frequency nearing that of the droplet’s first principal mode of oscillation (known as mode 2), the method was previously shown to determine surface tension of materials that would be particularly difficult to process by other means, e.g., liquid metals and alloys. It also offers distinct advantages in future work involving high viscosity samples because of the continuous forcing approach. This work presents (1) a benchmarking experimental method to measure surface tension by excitation of the second principal mode of oscillation (known as mode 3) in a levitated liquid droplet and (2) a more rigorous quantification of droplet excitation using a projection method. Surface tension measurements compare favorably to literature values for Zirconium, Inconel 625, and Rhodium, using both modes 2 and 3. Thus, this new method serves as a credible, self-consistent benchmarking technique for the measurement of surface tension. 

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3. Computational Analysis of Secondary Droplet Breakup at Transcritical Conditions with Surface Tension Effects

   https://doi.org/10.2514/6.2024-2380  

   Jangale, Prajesh A; Boyd, Bradley; Jarrahbashi, Dorrin (January 2024, American Institute of Aeronautics and Astronautics)

   In the pursuit of enhanced engine performance and reduced emissions, the design of liquid-fueled propulsion systems is shifting towards much higher combustor pressures, surpassing the nominal critical pressure of the fuel and air. This trend leads to the adoption of supercritical conditions, wherein the liquid fuel is injected into the ambient air at supercritical pressure and temperature, causing the fuel temperature to exceed its nominal critical point. This transition from a liquid-like to a gas-like behavior, known as "transcritical behavior," is a crucial aspect governing the operation of modern high-pressure propulsion and energy conversion systems. In these systems, the primary liquid jet breakup and the subsequent break-up of the resulting droplets into smaller droplets, namely secondary breakup, significantly impact mixing and combustion processes. Despite its importance, there has been a limited focus on droplet breakup at supercritical conditions, particularly at higher flow speeds relevant to high-speed liquid-fuel propulsion systems. Surface tension effects are often neglected in the simulation of transcritical flow, assuming surface tension vanishes beyond the critical point, while recent experiments and molecular dynamics simulations suggest that surface tension effects persist at transcritical conditions. To gain insight into the effects of surface tension on transcritical flows, we have developed a fully compressible multiphaseDirect Numerical Simulation (DNS) approach that accounts for decaying surface effects. The diffuse interface method is employed to represent transcritical interfaces, accounting for surface tension effects calculated using molecular dynamics simulations. This approach is employed to investigate the behavior of subcritical n-dodecane droplets in a supercritical nitrogen environment interacting with a shockwave, aiming to identify the governing breakup regimes at transcritical conditions. The development of quantitative measures enables the generalization of droplet breakup modes for transcritical droplets. The insights gained from this study contribute to advancing the understanding of transcritical liquid breakup, providing valuable knowledge for designing and optimizing high-speed propulsion systems 

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4. Prediction of the Atomization Process in Respimat® Soft MistTM Inhalers Using a Volume of Fluid-to-Discrete Phase Model

   https://doi.org/10.3390/bioengineering12030264  

   Sperry, Ted; Feng, Yu (March 2025, Bioengineering)

   This study investigates the atomization process in Respimat® Soft MistTM Inhalers (SMIs) using a validated Volume of Fluid (VOF)-to-Discrete Phase Model (DPM) to simulate the transition from colliding liquid jets to aerosolized droplets. Key parameters, including colliding jet inlet velocity, surface tension, and liquid viscosity, were systematically varied to analyze their impact on the atomization, i.e., aerosolized droplet size distributions. The VOF-to-DPM simulation results indicate that higher jet inlet velocities enhance ligament fragmentation, producing finer and more uniform droplets while reducing total atomized droplet mass. The relationship between surface tension and atomization performance in colliding jet atomization is not monotonic. Reducing surface tension plays a complex dual role in the atomization process. On the one hand, lower surface tension enhances the likelihood of liquid jet breakup into a liquid sheet, leading to the formation of smaller ligaments under the same airflow conditions and shear forces. This increases the probability of generating more secondary droplets. On the other hand, reduced surface tension also destabilizes the liquid surface shape, decreasing the formation of fine, high-sphericity droplets in regimes where surface tension is a dominant force. Viscosity also influences atomization through complex mechanisms, i.e., lower viscosity reduces resistance to ligament breakup but promotes droplet interactions and coalescence, while higher viscosity suppresses ligament fragmentation, generating larger droplets and reducing atomization efficiency. The validated VOF-to-DPM framework provides critical insights for enhancing the performance and efficiency of inhalation therapies. Future work will incorporate nozzle geometry, jet impingement angles, and surfactant effects to better understand and optimize the atomization process in SMIs, focusing on achieving preferred droplet size distributions and emitted doses for enhanced drug delivery efficiency in human respiratory systems. 

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5. Analytical theory for a droplet squeezing through a circular pore in creeping flows under constant pressures

   https://doi.org/10.1063/5.0156349  

   Tang, Zhengxin; Yaya, François; Sun, Ethan; Shah, Lubna; Xu, Jie; Viallat, Annie; Helfer, Emmanuèle; Peng, Zhangli (August 2023, Physics of Fluids)

   We derived equations and closed-form solutions of transit time for a viscous droplet squeezing through a small circular pore with a finite length at microscale under constant pressures. Our analyses were motivated by the vital processes of biological cells squeezing through small pores in blood vessels and sinusoids and droplets squeezing through pores in microfluidics. First, we derived ordinary differential equations (ODEs) of a droplet squeezing through a circular pore by combining Sampson flow, Poiseuille flow, and Young–Laplace equations and took into account the lubrication layer between the droplet and the pore wall. Second, for droplets wetting the wall with small surface tension, we derived the closed-form solutions of transit time. For droplets with finite surface tension, we solved the original ODEs numerically to predict the transit time. After validations against experiments and finite element simulations, we studied the effects of pressure, viscosity, pore/droplet dimensions, and surface tension on the transit time. We found that the transit time is inversely linearly proportional to pressure when the surface tension is low compared to the critical surface tension for preventing the droplet to pass and becomes nonlinear when it approaches the critical tension. Remarkably, we showed that when a fixed percentage of surface tension to critical tension is applied, the transit time is always inversely linearly proportional to pressure, and the dependence of transit time on surface tension is nonmonotonic. Our results provided a quick way of quantitative calculations of transit time for designing droplet microfluidics and understanding cells passing through constrictions. 

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