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1. Spreading dynamics of droplets impacting on oscillating hydrophobic substrates

   https://doi.org/10.1017/jfm.2024.414  

   Potnis, Aditya; Saha, Abhishek (June 2024, Journal of Fluid Mechanics)

   Droplet impact on oscillating substrates is important for both natural and industrial processes. Recognizing the importance of the dynamics that arises from the interplay between droplet transport and substrate motion, in this work, we present an experimental investigation of the spreading of a droplet impacting a sinusoidally oscillating hydrophobic substrate. We focus particularly on the maximum spread of droplets as a function of various parameters of substrate oscillation. We first quantify the maximum spreading diameter attained by the droplets as a function of frequency, amplitude of vibration, and phase at the impact for various impact velocities. We highlight that there can be two stages of spreading. Stage I, which is observed at all impact conditions, is controlled by the droplet inertia and affected by the substrate oscillation. For certain conditions, a Stage II spreading is also observed, which occurs during the retraction process of Stage I due to additional energies imparted by the substrate oscillation. Subsequently, we derive scaling analyses to predict the maximum spreading diameters and the time for this maximum spread for both Stage I and Stage II. Furthermore, we identify the necessary condition for Stage II spreading to be greater than Stage I spreading. The results will enable optimization of the parameters in applications where substrate oscillation is used to control the droplet spread, and thus heat and mass transfer between the droplet and the substrate. 

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2. 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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3. On the rheology and magnetization of dilute magnetic emulsions under small amplitude oscillatory shear

   https://doi.org/10.1017/jfm.2022.1019  

   Abdo, Rodrigo F.; Abicalil, Victor G.; Cunha, Lucas H.P.; Oliveira, Taygoara F. (January 2023, Journal of Fluid Mechanics)

   A dilute magnetic emulsion under the combined action of a uniform external magnetic field and a small amplitude oscillatory shear is studied using numerical simulations. We consider a three-dimensional domain with a single ferrofluid droplet suspended in a non-magnetizable Newtonian fluid. We present results of droplet shape and orientation, viscoelastic functions and bulk emulsion magnetization as functions of the shear oscillation frequency, magnetic field intensity and orientation. We also investigate how the magnetic field induces mechanical anisotropy by producing internal torques in oscillatory conditions. We found that, when the magnetic field is parallel to the shear plane, the droplet shape is mostly independent of the shear oscillation frequency. Regarding the viscometric functions, we show how the external magnetic field modifies the storage and loss moduli, especially for a field aligned to the main velocity gradient. The bulk emulsion magnetization is studied in the same fashion as the viscoelastic functions of the oscillatory shear. We show that the in-phase component of the magnetization with respect to the shear rate reaches a saturation magnetization, at the high frequencies limit, dependent on the magnetic field intensity and orientation. On the other hand, we found a non-zero out-of-phase response, which indicates a finite emulsion magnetization relaxation time. Our results indicate that the magnetization relaxation is closely related to the mechanical relaxation for dilute magnetic emulsions under oscillatory shear. 

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4. 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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5. 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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