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1. 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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2. The obstacle problem in no-tension structures and cable nets

   https://doi.org/10.1098/rspa.2022.0229  

   Amendola, Ada; Mattei, Ornella; Milton, Graeme W.; Seppecher, Pierre (January 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We consider the problem of finding a net that supports prescribed point forces, yet avoids certain obstacles, with all the elements of the net being under compression (or all being under tension), and being confined within a suitable bounding box. In the case of masonry structures, when described through the simple, no-tension constitutive model, this consists, for instance, in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region Γ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region Γ ′ available to the obstacle with Γ ⊂ Γ ′ . The case where some of the forces are reactive is also treated. 

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3. 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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4. Inertio-Capillary Impacts

   Alventosa, Luke FL (May 2023, Brown Digital Repository)

   Droplet impacts are of fundamental importance to the natural water cycle as collision and coalescence of droplets are the primary mechanism by which warm rain forms. Additionally, droplet impacts are of paramount significance in a variety of industrial processes, including spray cooling, wet scrubbing, and even play a role in cooling nuclear reactors. Throughout this work, we utilize a combination of theoretical mod- eling and experiments to elucidate the dynamics of these common phenomena. The first problem we analyze is a droplet impacting a deep fluid bath. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. The limit where capillarity and fluid inertia dominate the interfacial dynamics is investigated. This so-called inertio-capillary limit is shown to define an upper bound on the possible coefficient of restitution for droplet–bath im- pact. We then consider the scenario where the substrate is no longer deformable, and study the dynamics of non-wetting droplets impacting on stationary and vibrating substrates, with deterministic chaos emerging in the latter case. Extending beyond axisymmetric impacts, we then analyze droplet impact scenarios where there is some relative tangential velocity between the substrate and droplet. We determine the thresholds for coalescence, and our results suggest that substrate deformability plays an important role in transitions between the bouncing and merging regimes. Finally, we consider an analogous solid case to the normal droplet impact studies, where a small rigid sphere impacts and rebounds from a deformable elastic membrane. We perform experiments and identify new previously unreported behaviors in this simple system which are attributed to the non-negligible inertia of the membrane. Overall, the dynamics of these impact scenarios are extremely rich, producing physical phe- nomena that are inherently multi-scale, requiring information and knowledge from micron to centimeter scales. As showcased here, reduced-order modeling and con- trolled experiments are essential in distilling some simplicity out of the complexity. 

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5. 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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