# gst: anomalous oscillation modes of (superfluid) pendant droplets; horizontal translation on a flat surface, bouncing off at the corner and vertical oscillations at the edge.

<< Droplets should exhibit various dynamical phenomena when adhered to a surface; not all of them are realized in classical fluids. Visualization of superfluid  4^He (helium-4) pendant droplets revealed that the droplets were horizontally translated on a flat surface, bouncing off at the corner, known as the Noether mode that reflects the translation symmetry. >>️

<< The droplets exhibited another mode in vertical oscillations with high amplitude that included oscillation of the droplet edge. The oscillation period remained constant even as the droplets grew, exhibiting an anomalously weak size dependence. The high mobility of the droplet edges owing to the superfluidity was a crucial factor for the appearance of these anomalous modes. >>️

Keita Onodera, Ryuma Nagatomo, et al. Anomalous Oscillation Modes of Superfluid Pendant Droplets. Phys. Rev. Lett. 133, 216001. Nov 19, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.216001

Also: drop, droplet, droploid, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, transition

# gst: apropos of dances, drops that dance following snake- and ouroboros-shaped trajectories on lubricated surfaces.

<< Recently, (AA) observed a curious breath figure pattern when water condenses on solid surfaces coated with a thin lubricant oil film. Water drops of various sizes, ranging from tens of microns to several millimetres, start to perform a self-avoiding, serpentinelike dance. As the drop moves, it consumes smaller droplets along its path, converting interfacial energy into kinetic energy to sustain its motion. These self-avoiding drops preferentially avoid crossing their own paths as well as the paths of other drops; they can only intersect their previous paths once sufficient recondensation has occurred. This self-avoiding behavior arises because the previous path (..) contains little to no water content to fuel self-propulsion, so the drops continually seek areas with higher local water content. >>️

<< This intricate serpentine dance is driven by short-range interactions between droplets, mediated by overlapping menisci, similar to the Cheerios effect. Remarkably, long-range order spontaneously emerges from these short-range interactions, with the collective motion exhibiting self-similarity—breath figure patterns appear roughly similar across different scales. >>

<< The serpentine motions of the drops, which can span distances many times their diameters, eventually deplete the local lubricant film, causing a transition from serpentine to circular motion. This circular motion can be seen as a unique form of serpentine motion occurring in lubricant-poor regions. As the drops move, they continually redistribute the lubricant across the substrate, leading to a dynamic interplay between serpentine and circular motions. This ongoing redistribution can be visualized by illuminating the surface with diffused white light and capturing the resulting interference patterns with a digital camera. Variations in lubricant thickness produce different hues, creating a vibrant, colorful canvas and an intricate dance floor for the condensing drops. >>️

<< The phenomenon described in (AA) paper represents a fascinating example of active matter driven by condensation, rather than the more commonly observed chemical reactions or Marangoni effects. >>

Marcus Lin, Fauzia Wardani, Dan Daniel. Dancing drops on lubricated surfaces. Phys. Rev. Fluids 9, 110504. Nov 22, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.110504

Marcus Lin, Solomon Adera, Joanna Aizenberg, Yao Xi, Dan Daniel. V0030: Serpents and Ouroboros: Emergent collective motion of condensate droplets. 76th Annual Meeting of the APS Division of Fluid Dynamics. Nov 19-21, 2023.

https://gfm.aps.org/meetings/dfd-2023/64ff56f3199e4c1bbe725834

Also: drop, droplet, droploid, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, dance

# gst: dynamics of small droplets in turbulent multiphase flows

AA << show unambiguously that the formation of small droplets is governed by the internal dynamics which occurs during the breakup of large drops and that the high vorticity and the extreme dissipation associated to these events are the consequence and not the cause of the breakup. >>️

M. Crialesi-Esposito, G. Boffetta, L. Brandt, et al. How small droplets form in turbulent multiphase flows. Phys. Rev. Fluids 9, L072301. Jul 29, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L072301

Also: drop, bubble, transition, turbulence, intermittency, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid,  bubble, transition, turbulence, intermittency

# gst: spontaneous bouncing, trampolining, and hovering behaviors of a levitating water droplet without constraints.

<< The levitating Leidenfrost (LF) state of a droplet on a heated substrate is often accompanied by fascinating behaviors such as star-shaped deformations, self-propulsion, bouncing, and trampolining. These behaviors arise due to the vapor flow instabilities at the liquid-vapor interface beneath the droplet at sizes typically comparable to the capillary length scale of the liquid. >>

AA << report on the spontaneous bouncing, trampolining, and hovering behavior of an unconstrained LF water droplet. (..) the water droplet exhibits an increase in bouncing height at specific radii with intermittent reduction in the height of bounce leading to a quiescent LF state. The reemergence of the trampolining behavior from the quiescent hovering state without any external forcing is observed at sizes as low as 0.1 times the capillary length. (AA) attribute the droplet bouncing behavior to the dynamics of vapor flow beneath the LF droplet. >>

AA << propose that the trampolining behavior of the droplet at specific radii is triggered by harmonic and subharmonic resonance between the natural frequency of the vapor layer and Rayleigh frequency of the droplet. This proposed mechanism of resonance-driven trampolining of LF droplets is observed to be applicable for different liquids irrespective of the initial volume and substrate temperatures, thus indicating a universality of the behavior. (AA) attribute the intermittent trampolining events to the change in the natural frequency of the droplet and the vapor layer due to evaporative mass loss. >>

Pranjal Agrawal, Susmita Dash. Reemergence of Trampolining in a Leidenfrost Droplet. arXiv: 2408.02335v1 [physics.flu-dyn]. Aug 5, 2024. 

https://arxiv.org/abs/2408.02335

Also: drop, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, behav, behaviour

# gst: buckling instability in a chain of sticky bubbles

<< A slender object undergoing an axial compression will buckle to alleviate the stress. Typically the morphology of the deformed object depends on the bending stiffness for solids, or the viscoelastic properties for liquid threads. >>️

AA << study a chain of uniform sticky air bubbles that rise due to buoyancy through an aqueous bath. A buckling instability of the bubble chain with a characteristic wavelength is observed.  >>️

<< If a chain of bubbles is produced faster than it is able to rise, the dominance of viscous drag over buoyancy results in a compressive stress that is alleviated by buckling the bubble chain. >>️

<< Unlike other systems, in which buckling arises from a cost associ­ated with bending, to our knowledge this is the first study of drag-induced buckling with no intrinsic cost to bending—a buckling instability with a characteristic lengthscale emerges as a result of hydrodynamics. >>

️

Carmen L. Lee and Kari Dalnoki-Veress. Buckling instability in a chain of sticky bubbles. Phys. Rev. Research 6, L022062. Jun 14, 2024. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.L022062

Also: bubble, instability, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, instability, drop, droplet, droploid, transition 

# gst: breakup of Janus droplet in a bifurcating microchannel

<< Droplet breakup is frequently observed in natural and industrial processes (..)  Although valuable insights on the breakup mechanisms of single-phase droplets in microchannels have been provided over the past decades, the breakup physics of complex emulsions is still poorly understood. >>️

<< Spatially asymmetric Janus microdroplets, distinct from single-phase or double emulsion droplets possessing one uniform interface with the ambient phase, are anticipated to show unique breakup behaviors, which has not been explored.  >>️

AA << conduct both microfluidic experiments and three-dimensional lattice Boltzmann simulations to investigate the dynamic breakup of ionic liquid (IL)-water Janus droplets in an assembled 3D-printed microchannel with a bifurcation. >>️

<< Three different flow regimes are identified: (i) division into two daughter Janus droplets, (ii) breakup into a single-phase droplet and a smaller Janus droplet, and (iii) nonbreakup.  >>️

AA << find that the strong constraint effect of the main channel and large Ca_av (average capillary numbers) values are essential to the symmetrical breakup of Janus droplets. The tunnel between the mother droplet and the wall of the main channel, which allows the lateral shift of the Janus droplet, and moderate flow rates facilitate the breakup of the IL single-phase portion of Janus droplets.  >>

<< Through 90° rotation of the splitting microchannel, (AA) elucidate the distinctions in Janus droplet behaviors under two baffle orientations. Potential impacts of the oblique flow characteristic of [bmim]⁢Fe⁢Cl4-water Janus droplets on the droplet breakup are discussed. >>️

️

Hao Wang, Shiteng Wang, et al. Dynamic breakup of Janus droplet in a bifurcating microchannel. Phys. Rev. Fluids 9, 064203. Jun 11, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.064203 

Also: 'Janus' in FonT https://flashontrack.blogspot.com/search?q=janus

Also: 'drop', 'droplet', 'droploid', in https://www.inkgmr.net/kwrds.html 

Keywords: gst, Janus, drop, droplet, droploid

# gst: apropos of evaporation, puncturing of active drops

<< By virtue of self-propulsion, active particles impart intricate stresses to the background fluids. (..) this active stress can be utilized to greatly control evaporation dynamics of active drops. >>

AA << discover a new phenomenon of puncturing of the active drops, where the air-liquid interface of the drop undergoes spontaneous tearing and there occurs a formation of a new three-phase contact line due to the liquid-air interface hitting the liquid-solid interface through evaporation-driven mass loss. Post puncturing, (AA) see an inside-out evaporation of the drop, where the new contact line sweeps towards the pinned outer contact line of the drops, contrasting regular drops that straightaway shrink to zero volume with self-similar shape. >>

<< Furthermore, (..) the activity inside the drops can manipulate the three-phase contact-line dynamics, which for contractile drops can result in an up to 50% enhanced lifetime of the drop and 33% quicker evaporation for extensile drops. By analyzing the flux distribution inside the drop, (AA) gain insights on nonintuitive deposition patterns (e.g., ring galaxy type deposits that demonstrate controllable spatial gradients in the concentrations of the deposited particles) of active particles, which are oftentimes biological substances or bimetallic nanoparticles of interest. >>

Ghansham Rajendrasingh Chandel, Vishal Sankar Sivasankar, Siddhartha Das. Evaporation of active drops: Puncturing drops and particle deposits of ring galaxy patterns. Phys. Rev. Fluids 9, 033603. Mar 27, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.033603

Also: drop, particle, evaporation, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, particle, evaporation, transition, drop interactions, droplet, droploid

# gst: multi-component droplets may exhibit self-lubricating effects

<< Over the past decade, there has been a growing interest in the study of multicomponent drops. These drops exhibit unique phenomena, as the interplay between hydrodynamics and the evolving physicochemical properties of the mixture gives rise to distinct and often unregulated behaviors. >>

<< Of particular interest is the complex dynamic behavior of the drop contact line, which can display self-lubrication effect. The presence of a slipping contact line in self-lubricating multicomponent drops can suppress the coffee-stain effect, conferring valuable technological applications. >>

Huanshu Tan, Detlef Lohse, Xuehua Zhang. Self-Lubricating Drops. arXiv: 2403.01207v1 [physics.flu-dyn]. Mar 2, 2024

https://arxiv.org/abs/2403.01207

Also: drop droplet droploid, in https://www.inkgmr.net/kwrds.html

Keywords: drop, droplet, droploid, multicomponent drops, drop contact line, self-lubrication

# gst: droplets scoot like caterpillars.

<< From swells in an ocean to ripples in a puddle, the shearing effect of wind blowing over a liquid is visible at all scales. This shear determines the interactions between Earth’s atmosphere and its surface water and, researchers now explain, the movement of liquid droplets that crawl up and down the window of a moving car in the rain. In a series of experiments, (AA) show that airflow triggers surface waves that cause such droplets to crawl like caterpillars before they break apart. >>️

<< At first, the airflow across the droplet’s surface caused the droplet to extend into an oval shape. The droplet also began to tilt, with the liquid piling up at the droplet’s downwind edge. When the drag force exerted by the airflow overcame the capillary force between the glycerin and the glass, the droplet began to slide and to stretch out even more. Surface waves then developed on the elongated droplet and traveled toward its leading edge. The waves induced a stable caterpillar-like motion, with the droplet stretching and contracting along its length. Eventually, beyond a threshold length that depended on the droplet’s volume, the caterpillar was no longer able to withstand the shearing force and broke into several droplets. >>️

AA << say that the behavior follows the same pattern as that of an elongated droplet sliding along an incline. >>

️

Rachel Berkowitz. Droplets Scoot Like Caterpillars. Physics 16, s110. Sep 1, 2023.

https://physics.aps.org/articles/v16/s110  

A. Chahine, J. Sebilleau, R. Mathis, D. Legendre. Caterpillar like motion of droplet in a shear flow. Phys. Rev. Fluids 8, 093601. Sep 1, 2023.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.093601

Also: drop, bubble, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, bubble, transition

# gst: analogy between quasi-2D and 3D liquid drops.

<< Liquid drops are everywhere around us and important in numerous technological applications. Here, (AA) demonstrate a quasi-two-dimensional (Q2D) analogy to the regular, often close to axisymmetric, three-dimensional (3D) drops. >>️

<< The Q2D drops are created by confining liquids between vertical walls, leading to formation of low aspect ratio capillary bridges that are deformed by gravity. When stationary, the Q2D drops adopt projected shapes that are analogous to 3D sessile drops, ranging from circular drops to puddles. >>️

<< When moving, the Q2D drops exhibit capillary and fluid mechanical behaviours analogous to 3D drops, including impacts and sliding on pseudo-surfaces. The Q2D drops also exhibit considerably more complex phenomena such as levitation, instabilities and pattern formation when subjected to external electric, magnetic and flow fields -- all seen also in regular 3D drops. >>️

<< 3D-Q2D analogy suggests that the diverse and often complicated phenomena observed in 3D drops can be studied in the Q2D geometry, >>

️

Tytti Kärki, Into Pääkkönen, et al. Quasi-Two-Dimensional Drops. arXiv: 2401.11845v1 [physics.flu-dyn]. Jan 22, 2024.

https://arxiv.org/abs/2401.11845

Also: drop, analogy, in https://www.inkgmr.net/kwrds.html

Keywords: gst, drop, droplet, droploid, analogy

# gst: compression and fracture of ordered and disordered droplet rafts

AA << simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. >>

<< For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. >>

<< In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. >>

AA << also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. >>

️

Pablo Eduardo Illing, Jean-Christophe Ono-dit-Biot, et al. Compression and fracture of ordered and disordered droplet rafts. Phys. Rev. E 109, 014610. Jan 17, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.014610

Also: drop, defect, fracture, crack, in https://www.inkgmr.net/kwrds.html

Also:  raft   https://flashontrack.blogspot.com/search?q=raft  

zattera (quasi-stochastic poetry) https://inkpi.blogspot.com/2005/04/1864-onda-di-liberazione.html  

randa (quasi-stochastic poetry) https://inkpi.blogspot.com/search?q=randa

Keywords: gst, drop, droplet, raft, defect, fracture, crack

# gst: myriad of complex dynamics from the atomization of acoustically levitated droplets

AA << report the dynamics of a droplet levitated in a single-axis acoustic levitator. The deformation and atomization behavior of the droplet in the acoustic field exhibits a myriad of complex phenomena, in sequences of steps. These include the primary breakup of the droplet through stable levitation, deformation, sheet formation, and equatorial atomization, followed by secondary breakup which could be umbrella breakup, bag breakup, bubble breakup or multistage breakup depending on the initial size of the droplet. >>

<< Both the primary and the secondary breakup of the droplet admit interfacial instabilities such as Faraday instability, Kelvin Helmholtz (KH) instability, RT instability, and RP instability and are well described with visual evidence. >>️

Sunil K. Saroj, Rochish M. Thaokar. Atomisation of an acoustically levitated droplet: Experimental observations of a myriad of complex phenomenon. arXiv: 2307.00400v1 [physics.flu-dyn]. Jul 1, 2023.

https://arxiv.org/abs/2307.00400

Also:  drop, transition, instability in https://www.inkgmr.net/kwrds.html

Keywords: gst, drop, droplet, transition, instability

# gst: nonmonotonic appearance- disappearance behaviors of two unequal-sized miscible liquid drops

<< the coalescence process of two miscible liquid drops exhibits a nonmonotonic behavior of partial coalescence from appearance to disappearance and then reappearance with decreasing surface tension ratio. The strong lifting force of the intense Marangoni flow causes the reappearance of partial coalescence at higher surface tension difference between two drops. When the Ohnesorge number increases, high viscous forces restrict the propagation of Marangoni flow and do not favor the pinch-off, even in the presence of a significant surface tension difference. The generation of secondary drops at a considerable surface tension difference is also prevented for small parent drop size ratio. >>️

Swati Singh, Arun K. Saha. Effect of surface tension gradients on coalescence dynamics of two unequal-sized drops. Phys. Rev. Fluids 8, 053604. May 24, 2023. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.053604

Also:  'drop' in https://www.inkgmr.net/kwrds.html  

Keywords: gst, behavior, drop, drop breakup, drop coalescence, drop interactions, droplet, droploid

# gst: apropos of transitions, droplet trajectories during single and collective bursting bubbles

<< Mechanisms of droplet production from bursting bubbles have been extensively studied for single bubbles, but remain sparsely investigated in more complex collective settings. >>️

<< In the collective bubbling experiment, subsurface quasimonodisperse bubbles are rising up to the surface where, depending on the surfactant concentration, they can either merge or assemble in rafts of monodisperse bubbles. Drop trajectories are recorded, analyzed, and shown to exhibit uniquely distinctive features for the different production mechanisms: centrifuge film drops are ejected sideways, and jet drops are ejected vertically. Different single-burst scalings are finally compared to the experimental size-velocity relationships, and reveal that drops coming from collective bubble bursting appear slower and more scattered than when coming from single bursting bubbles. >>️

B. Neel and L. Deike. Velocity and size quantification of drops in single and collective bursting bubbles experiments. Phys. Rev. Fluids 7, 103603. Oct 5, 2022. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.7.103603

Also: 'when a superbubble can generate trains of shock waves'. Mar 6, 2019.

https://flashontrack.blogspot.com/2019/03/gst-astro-when-superbubble-can-generate.html

Also: 'transition', 'droplet', 'droploid', 'bubble', in: https://www.inkgmr.net/kwrds.html

Keywords: gst, transition, drop, droplet, droploid, bubble, collective dynamics,  fluid dynamics

PS: << they can either merge or assemble in rafts of monodisperse bubbles >> ; this is poetry, without unnecessary adjectives, anzicheforse ... FonT. Wed June 14, 2023 16:58 (cest)

# gst: when droplets are capable of self-propulsion as if they were surfing on a self-generated wave.

<< active droplets can move autonomously or oscillate between confining walls (..). Those behaviors could provide a clue about how life emerged from inanimate material. >>️

<< in the past decades, it has become clear that weak physical interactions among biomolecules are a crucial part of the answer. Such interactions allow some molecules to stay together transiently while avoiding others, which can lead to the spontaneous formation of droplets whose composition differs from their surroundings. Although biochemist Alexander Oparin suggested such ideas a century ago (..), experimental corroboration arrived only recently >>️

<< The key contribution of Demarchi and his collaborators is to demonstrate that droplet drift can enhance the heterogeneity of substrate and product. The resulting positive feedback allows droplets to move continuously as if they were surfing on a self-generated wave. >>️

David Zwicker. Droplets Come to Life. Physics 16, 45. Mar 20, 2023. 

https://physics.aps.org/articles/v16/45

AA << find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division. >>

️

Leonardo Demarchi, Andriy Goychuk, et al. Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence. Phys. Rev. Lett. 130, 128401. Mar 20, 2023.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.128401

Also

'drop', 'droplet', 'droploid', 'transition' in 

https://www.inkgmr.net/kwrds.html

Keywords: gst, drop, droplet, waves, transition, liquid-liquid phase transition, nonequilibrium systems

# gst: when a soliton juggles ('catches' and 'throws') droplets

<< Jugglers normally work with solid objects, but a research team has now demonstrated a system that juggles liquid drops. (AA)  have previously shown that liquid drops can bounce in place above the surface of the same liquid—or bounce while moving across the surface—if the container is continuously vibrated (..) In these past experiments, the surface was nearly flat, except for waves generated by the bouncing drop. In the new work by undergraduate student Camila Sandivari of the University of Chile and her colleagues, the vibrations cause the liquid surface to form a large standing wave that actively “catches” and “throws” the drop during each cycle of its oscillation. The trapping of the drop is similar in principle to other types of wave traps, such as laser-based optical tweezers, and the system could potentially lead to new types of traps for larger objects. >>

AA << placed water mixed with a dye and a surface-tension-reducing agent in a 20-cm-long, 2.6-cm-wide basin that supports an unusual type of surface wave when the basin is vibrated in a specific frequency range. In this wave, rather than a series of oscillating peaks and valleys, there is only a single standing wave peak, called a soliton. However, this peak doesn’t oscillate uniformly across the basin’s short dimension (the width). A peak appears at one of the long walls coincident with a valley at the opposite wall, and then the peak and the valley switch places moments later, keeping a relatively flat “node” line along the central long axis of the basin. >>

AA << used a pipette to place a few-millimeter-wide drop of the same fluid just above the oscillating soliton, close to one of the long walls, and found that drops could be juggled for up to 90 minutes. The team attributes this unusual stability in part to a property of the soliton: if the drop wanders off-center, the oscillating surface wave pulls it back toward its center, similar to the way the laser field in optical tweezers is able to stably hold a small particle at its center. >>

David Ehrenstein. Juggling Water Drops. Physics 16, 21. Feb 10, 2023. 

https://physics.aps.org/articles/v16/21

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

https://flashontrack.blogspot.com/search?q=droploids

keyword 'goccia' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=goccia

keyword 'solitons' in FonT

https://flashontrack.blogspot.com/search?q=soliton

https://flashontrack.blogspot.com/search?q=solitons

Keywords: gst, solitons, drop, droplet, droploids, goccia

# gst: apropos of modulational instabilities, the case of vortex-ring quantum droplets in a radially-periodic potential.

FIG. 11: (Color online) Typical examples of stable nested patterns with soliton and vortex QDs (quantum droplets)  which were created in adjacent radial troughs. In panels (a1-b4) the pattern was created from the initial dynamical states with parameters (N,S,On) = (46,0,2) and (N,S,On) = (35,1,1) in the outer and inner troughs, respectively. In panels (c1-d4) the input was taken with parameter sets (N,S,On) = (120,1,3) and (N,S,On) = (46,0,2) in the outer and inner troughs.

AA << establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates. >>️

<< another noteworthy option is to construct a two-ring complex in which one vortex-ring component is subject to the MI  (modulational instability), hence it is replaced by an azimuthal soliton (or maybe several solitons), (..), while the vortex component trapped in another potential trough avoids the azimuthal MI and remains essentially axisymmetric. >>️

<< Examples of such heterogeneous robust states, produced by simulations of Eq. (3), are displayed in Fig. 11. Panels 11(a1-b4) show a complex in which the MI takes place in the outer circular trough, producing an azimuthal soliton which performs rotary motion, while the inner vortex ring is  modulationally stable. An opposite example is produced in Figs. 11(c1-d4), where the outer vortex ring remains stable against azimuthal perturbations, while the MI creates a soliton exhibiting the rotary motion in the embedded (inner) circular trough. The rotation direction of the soliton is driven by the vorticity sign of the underlying QD (quantum droplet). It is relevant to mention that the multi-ring potential considered here holds different vortex-ring or azimuthal-soliton states nearly isolating them from each other. (..) An additional problem, which is left for subsequent analysis, is interplay between adjacent radial modes in the case when the separation between the adjacent rings is essentially smaller. >>️

Bin Liu, Yi xi Chen, et al. Vortex-ring quantum droplets in a radially-periodic potential. arXiv: 2212.05838v1 [nlin.PS]. Dec 12, 2022.

https://arxiv.org/abs/2212.05838

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

https://flashontrack.blogspot.com/search?q=droploids

keyword 'goccia' in Notes 

(quasi-stochastic poetry): 

https://inkpi.blogspot.com/search?q=goccia

keyword 'instability' | 'instabilities' in FonT

https://flashontrack.blogspot.com/search?q=instability

https://flashontrack.blogspot.com/search?q=instabilities

keyword 'instabile' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=instabile

Keywords: gst, drop, droplet, vortex, vortices, vortexes, vorticity, instability,  modulational instabilities

# gst: apropos of transitions, the transition from sticking to slipping.

<< From hydrogels and plastics to liquid crystals, soft solids cover a wide array of synthetic and biological materials that play key enabling roles in advanced technologies >>️

<< Attempts to study the interactions between soft solids and liquids have largely focused on the wetting of soft solids and its resulting deformation at equilibrium or in a quasi-static state. Here, (AA) consider the frequently encountered case of unsteady wetting of a liquid on a soft solid and show that transient deformation of the solid is necessary to understand unsteady wetting behaviours. >>️

AA << find that the initial spreading of the liquid occurs uninterrupted in the absence of solid deformation. This is followed by intermittent spreading, in which transient deformation of the solid at the three-phase contact line (CL) causes the CL motion to alternate alternation between CL sticking and slipping. (They) identify the spreading rate of liquids and the viscoelastic reacting rate of soft solids as the two competing factors in dictating intermittent spreading. (They)  formulate and validate experimentally the conditions required for the contact line to transition from sticking to slipping. By considering the growing deformation of soft solids as dynamic surface heterogeneities, (AA) proposed conditions for stick-slip transition in unsteady wetting on soft solids broaden the classical theory on wetting hysteresis on rigid solids. >>️

Surjyasish Mitra, Quoc Vo, Marcus Lin, Tuan Tran. Unsteady wetting of soft solids. arXiv:2211.07043v1 [cond-mat.soft]. Nov 13, 2022.

https://arxiv.org/abs/2211.07043

Also

keyword 'drop' | 'droplet' | 'droploids' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

https://flashontrack.blogspot.com/search?q=droploids

keyword 'goccia' in Notes 

(quasi-stochastic poetry) 

https://inkpi.blogspot.com/search?q=goccia

Keywords: gst, behav, behaviour, transition, soft solids, drop, droplet, sticking, slipping.

# gst: apropos of transitions, evaporating binary microdroplets with phase segregation

<< Phase segregation triggered by selective evaporation can emerge in multicomponent systems, leading to complex physiochemical hydrodynamics. Recently, Li et al. (2018) and Kim & Stone (2018) reported a segregative behavior (i.e., demixing) in an evaporating binary droplet. In this work, by means of experiments and theoretical analysis, (AA) investigate the flow dynamics after the occurrence of the phase segregation. >>

<< First, (AA) experimentally reveal the overall physiochemical hydrodynamics of the evaporation process, including the segregative behavior and the resulting flow structure close to the substrate. By quantifying the evolution of the radial flow, (they) identify three successive life stages of the evaporation process. >>

<< At Stage I, a radially outward flow is observed. It is driven by the Marangoni effect. At the transition to Stage II, the radial flow partially reverses, starting from the contact line. This flow breaks the axial symmetry and remarkably is driven by the segregation itself. Finally at Stage III, the flow decays as the evaporation gradually ceases. At this stage the segregation has grown to the entire droplet, and the flow is again controlled by the Marangoni effect. The resulting Marangoni flow homogenizes the distribution of the entrapped volatile water over the whole droplet. >>️

Yaxing Li, Pengyu Lv, et al. Physiochemical hydrodynamics of the phase segregation in an evaporating binary microdroplet.arXiv:2208.07861v1 [physics.flu-dyn]  Aug 16, 2022.

https://arxiv.org/abs/2208.07861

Marangoni effect. 

https://en.m.wikipedia.org/wiki/Marangoni_effect   

https://youtu.be/vGb6t5Gfq6s   

Also

keyword 'drop' | 'droplet' in FonT

https://flashontrack.blogspot.com/search?q=drop

https://flashontrack.blogspot.com/search?q=droplet

Keywords: gst, droplet, transition, evaporation, phase transition, phase segregation, Marangoni flow

# gst: apropos of transitions, two aspects of intermittency

<< intermittency produces significant probability of rare events that may locally accelerate the collision rates by a large factor in comparison with estimates using typical events. >>

<< Increasing intermittency of turbulence destroys the theory not via stronger bursts, but rather via increase of characteristic sizes of regions of calm and quiescent flow. ([AA️] remind that these two aspects of intermittency go together: increase of regions of calm flow and at the same time increased probability of strong bursts ([8] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov, (Cambridge University Press, New York, 1995).). >>

Itzhak Fouxon, Seulgi Lee, Changhoon Lee. Intermittency and collisions of fast sedimenting droplets in turbulence.  arXiv:2205.06972v1 [physics.flu-dyn]. May 14, 2022. 

https://arxiv.org/abs/2205.06972

Also

keyword 'intermittency' in FonT

https://flashontrack.blogspot.com/search?q=intermittency

keyword 'intermittenza|e' | 'intermittente|i' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=intermittenza

https://inkpi.blogspot.com/search?q=intermittenze

https://inkpi.blogspot.com/search?q=intermittente

https://inkpi.blogspot.com/search?q=intermittenti

Keywords: gst, intermittency, collision, drop, droplet, turbulence