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1. Capillary wave-assisted collapse of non-Newtonian droplets

   https://doi.org/10.1063/5.0231029  

   He, Ziwen; Tran, Huy; Pack, Min Y (September 2024, Physics of Fluids)

   Understanding the peripheral capillary wave propagation during droplet impact is crucial for comprehending the physics of wetting onset and droplet fragmentation. Although Newtonian droplets have been extensively studied, we show how capillary waves deform non-Newtonian droplets in such a way that rheological features, such as the critical concentrations for the overlap (c*) and entangled polymer molecules (c**), may be directly obtained from the deformation history. Determining these critical concentrations is essential as they mark transitions in the rheological behavior of aqueous polymeric solutions, influencing viscosity, elasticity, and associated fluid dynamics. We have also compared capillary waves among Newtonian, shear-thinning, and Boger fluid droplets and found that although the fluid kinematics appear to be purely biaxial extensional flow, the infinite-shear properties of the droplets dominate the physics of capillary wave formation and propagation. 

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2. A Regime Diagram for Internal Lee Waves in Coastal Plain Estuaries

   https://doi.org/10.1175/JPO-D-21-0261.1  

   Li, Renjian; Li, Ming (December 2022, Journal of Physical Oceanography)

   Abstract Using an idealized channel representative of a coastal plain estuary, we conducted numerical simulations to investigate the generation of internal lee waves by lateral circulation. It is shown that the lee waves can be generated across all salinity regimes in an estuary. Since the lateral currents are usually subcritical with respect to the lowest mode, mode-2 lee waves are most prevalent but a hydraulic jump may develop during the transition to subcritical flows in the deep channel, producing high energy dissipation and strong mixing. Unlike flows over a sill, stratified water in the deep channel may become stagnant such that a mode-1 depression wave can form higher up in the water column. With the lee wave Froude number above 1 and the intrinsic wave frequency between the inertial and buoyancy frequency, the lee waves generated in coastal plain estuaries are nonlinear waves with the wave amplitude Δ h scaling approximately with , where V is the maximum lateral flow velocity and is the buoyancy frequency. The model results are summarized using the estuarine classification diagram based on the freshwater Froude number Fr f and the mixing parameter M . The Δ h decreases with increasing Fr f as stronger stratification suppresses waves, and no internal waves are generated at large Fr f . The Δ h initially increases with increasing M as the lateral flows become stronger with stronger tidal currents, but decreases or saturates to a certain amplitude as M further increases. This modeling study suggests that lee waves can be generated over a wide range of estuarine conditions. 

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3. High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

   https://doi.org/10.1017/jfm.2022.330  

   Mostert, W.; Popinet, S.; Deike, L. (July 2022, Journal of Fluid Mechanics)

   We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number ( Re , wave inertia relative to viscous effects) and Bond number ( Bo , wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo , and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value $$Re_\lambda \sim 100$$ , consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. ( J. Fluid Mech. , vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale, $$r_H$$ . We confirm two regimes in the bubble size distribution, $$N(r/r_H)\propto (r/r_H)^{-10/3}$$ for $$r>r_H$$ , and $$\propto (r/r_H)^{-3/2}$$ for $$r 

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4. Drag force in granular shear flows: regimes, scaling laws and implications for segregation

   https://doi.org/10.1017/jfm.2022.706  

   Jing, Lu; Ottino, Julio M.; Umbanhowar, Paul B.; Lueptow, Richard M. (October 2022, Journal of Fluid Mechanics)

   The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations. 

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5. 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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