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1. urfactant Spreading on a Deep Subphase: Coupling of Marangoni Flow and Capillary Waves

   https://doi.org/doi.org/10.1016/j.jcis.2022.01.142  

   Sauleda, ML; Hsieh, T-L; Xu, W; Tilton, RD; Garoff, S (January 2022, Journal of colloid and interface science)

   Unknown (Ed.)

   Abstract Hypothesis Surfactant-driven Marangoni spreading generates a fluid flow characterized by an outwardly moving “Marangoni ridge”. Spreading on thin and/or high viscosity subphases, as most of the prior literature emphasizes, does not allow the formation of capillary waves. On deep, low viscosity subphases, Marangoni stresses may launch capillary waves coupled with the Marangoni ridge, and new dependencies emerge for key spreading characteristics on surfactant thermodynamic and kinetic properties. Experiments and modeling Computational and physical experiments were performed using a broad range of surfactants to report the post-deposition motion of the surfactant front and the deformation of the subphase surface. Modeling coupled the Navier-Stokes and advective diffusion equations with an adsorption model. Separate experiments employed tracer particles or an optical density method to track surfactant front motion or surface deformation, respectively. Findings Marangoni stresses on thick subphases induce capillary waves, the slowest of which is co-mingled with the Marangoni ridge. Changing Marangoni stresses by varying the surfactant system alters the surfactant front velocity and the amplitude – but not the velocity – of the slowest capillary wave. As spreading progresses, the surfactant front and its associated surface deformation separate from the slowest moving capillary wave. 

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2. Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows

   https://doi.org/10.1017/jfm.2022.856  

   Jia, Leroy L.; Irvine, William T.M.; Shelley, Michael J. (November 2022, Journal of Fluid Mechanics)

   Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension. 

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3. The effects of Surfactin on sprayed droplets in flat fan, full cone, and low energy precision application bubbler nozzles: droplet formation and spray breakup

   https://doi.org/10.3389/fmech.2024.1354664  

   Stallbaumer-Cyr, Emily M; Aguilar, Jonathan; Betz, Amy R; Derby, Melanie M (January 2024, Frontiers in Mechanical Engineering)

   Introduction:Agriculture is the largest user of water globally (i.e., 70% of freshwater use) and within the United States (i.e., 42% of freshwater use); irrigation ensures crops receive adequate water, thereby increasing crop yields. Surfactants have been used in various agricultural spray products to increase spray stability and alter droplet sizes. Methods:The effects of the addition of surfactant (0.1 wt% Surfactin; surface tension of 29.2 mN/m) to distilled water (72.79 mN/m) on spray dynamics and droplet formation were investigated in four flat fan (206.8–413.7 kPa), one full cone (137.9–413.7 kPa), and three LEPA bubbler (41.4–103.4 kPa) nozzles via imaging. Results and discussion:The flat fan and cone nozzles experienced second wind-induced breakup (i.e., unstable wavelengths drive breakup) of the liquid sheets exiting the nozzle; the addition of surfactant resulted in an increased breakup length and a decreased droplet size. The fan nozzles volumetric median droplet diameter decreased with the addition of surfactant (e.g., decreased by 26.3–65.6 μm in one nozzle). The full cone nozzle volumetric median droplet diameter decreased initially with the addition of surfactant (27.8, 14.3, and 13.4 μm at 137.9, 206.8, and 310.3 kPa respectively), but increased at 413.7 kPa (24.3 μm). Sprays from the bubbler nozzles were measured and observed to experience Rayleigh (i.e., the droplets form via capillary pinching at the end of the jet) and first wind-induced breakup (i.e., air impacts breakup along with capillary pinching). The effect of Surfactin on droplet size was minimal for the 41.4 kPa bubbler nozzle. The addition of surfactant increased the diameter of the jet or ligament formed from the bubbler plate, thereby increasing the breakup length and the droplet size at 68.9 and 103.4 kPa (droplet size increased by 750.6 and 4,462.7 μm, respectively). 

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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. In-process monitoring and prediction of droplet quality in droplet-on-demand liquid metal jetting additive manufacturing using machine learning

   https://doi.org/10.1007/s10845-022-01977-2  

   Gaikwad, Aniruddha; Chang, Tammy; Giera, Brian; Watkins, Nicholas; Mukherjee, Saptarshi; Pascall, Andrew; Stobbe, David; Rao, Prahalada (June 2022, Journal of Intelligent Manufacturing)

   Abstract In droplet-on-demand liquid metal jetting (DoD-LMJ) additive manufacturing, complex physical interactions govern the droplet characteristics, such as size, velocity, and shape. These droplet characteristics, in turn, determine the functional quality of the printed parts. Hence, to ensure repeatable and reliable part quality it is necessary to monitor and control the droplet characteristics. Existing approaches for in-situ monitoring of droplet behavior in DoD-LMJ rely on high-speed imaging sensors. The resulting high volume of droplet images acquired is computationally demanding to analyze and hinders real-time control of the process. To overcome this challenge, the objective of this work is to use time series data acquired from an in-process millimeter-wave sensor for predicting the size, velocity, and shape characteristics of droplets in DoD-LMJ process. As opposed to high-speed imaging, this sensor produces data-efficient time series signatures that allows rapid, real-time process monitoring. We devise machine learning models that use the millimeter-wave sensor data to predict the droplet characteristics. Specifically, we developed multilayer perceptron-based non-linear autoregressive models to predict the size and velocity of droplets. Likewise, a supervised machine learning model was trained to classify the droplet shape using the frequency spectrum information contained in the millimeter-wave sensor signatures. High-speed imaging data served as ground truth for model training and validation. These models captured the droplet characteristics with a statistical fidelity exceeding 90%, and vastly outperformed conventional statistical modeling approaches. Thus, this work achieves a practically viable sensing approach for real-time quality monitoring of the DoD-LMJ process, in lieu of the existing data-intensive image-based techniques. 

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