# gst: the dynamics of a collective bubble (in a foam) that collapse in a droplet

<< Foams have unique properties that distinguish them from ordinary liquids and gases, and are ubiquitously observed in nature, both in biological systems and industrial products. (..) understanding how bubbles in a foam collapse is an important aspect for product longevity and tailoring physical properties. >>

<< Once a crack appears near the border and a collapse front is formed, (AA) find that the curvature of the front reverses as it migrates, followed by the emergence and emission of droplets. >>

<<  It is particularly interesting to note how the shape of the front changes as it migrates. >>

Naoya Yanagisawa, Marie Tani, Rei Kurita. Dynamics and mechanism of liquid film collapse in a foam. Soft Matter 17, 1738-45. doi: 10.1039/ D0SM02153A. Feb 17, 2021.

https://pubs.rsc.org/en/content/articlelanding/2021/SM/D0SM02153A#!divAbstract   

<< An initial crack in a film creates a RVPB (released vertical plateau border). A second crack event in the film causes a "collapse front" to be formed which sweeps up the RVPB before its shape begins to flatten and invert, finally leaving a droplet. >>

When foams collapse (and when they don't). Tokyo Metropolitan University. Mar 01, 2021. 

https://phys.org/news/2021-03-foams-collapse-dont.html   

Also

keyword 'drop' or 'droplet' in FonT

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

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

# gst: a striking analogy between solid–solid and solid–drop frictions

AA << report that the lateral adhesion force between a liquid drop and a solid can also be divided into a static and a kinetic regime. This striking analogy with solid–solid friction is a generic phenomenon that holds for liquids of different polarities and surface tensions on smooth, rough and structured surfaces >>

Nan Gao, Florian Geyer, et al. How drops start sliding over solid surfaces. Nature Physics doi: 10.1038/nphys4305 Nov 6, 2017

https://www.nature.com/articles/nphys4305

AA << acknowledges that their experiments are just the beginning in trying to fully understand the nature of friction between drops and solid objects >>

Bob Yirka. Droplet friction found to be similar to that of solid objects. Nov 8, 2017

https://m.phys.org/news/2017-11-droplet-friction-similar-solid.html

# 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: 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: to find a separation between plunging and spilling wave breakers

<< While understanding breaking waves is crucial for the development of parametrizations used in ocean wave modeling for both deep and shallow water, the complete process of wave breaking is not well understood. Here (AA) present direct numerical simulations of two-dimensional solitary waves that shoal and break on a uniform beach in shallow water, with the presence of storm surge represented by an inshore region. >>️

They << classify wave breaker types and find a separation between plunging and spilling breakers when scaled by breaking amplitude and depth. (AA) compare energy dissipation during the breaking process with results from the literature without storm surge.  >>️

They << conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse, and further discuss possibilities for a general parametrization of wave breaking valid across different depth regimes. >>️

Hunter Boswell, Guirong Yan, Wouter Mostert. Characterizing energy dissipation of shallow-water wave breaking in a storm surge. Phys. Rev. Fluids 8, 054801. May 5, 2023. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.054801

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

Keywords: gst, waves, soliton, drop 

# chem: acoustic levitation techniques to perform chemistry in floating droplets

<<  Beauchamp (Jack Beauchamp) is doing work in what he calls "lab-in-a-drop" chemistry, in which chemical reactions are performed within a drop of liquid suspended in midair through acoustic levitation. >>

Performing chemistry in floating droplets. California Institute of Technology. Jul 29, 2019.

https://m.phys.org/news/2019-07-chemistry-droplets.html  

Chaonan Mu, Jie Wang, et al. Mass Spectrometric Study of Acoustically Levitated Droplets Illuminates Molecular‐Level Mechanism of Photodynamic Therapy for Cancer involving Lipid Oxidation. Angewandte Chemie International Edition. Volume 58, Issue 24. doi: 10.1002/anie.201902815. Apr 23, 2019.

https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201902815 

# gst: ️apropos of spontaneous active matter, the active droploids.

<< Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, (AA) take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. >>️

<< These structures hinge on mutually coupled structure formation processes of the colloids, which form an engine, and the surrounding solvent, which phase separates in regions of high colloidal density and encapsulates the engine within a droplet shell.  >>

️

Jens Grauer, Falko Schmidt, et al. Active droploids. arXiv:2109.10677v1 [cond-mat.soft]. Sep 22, 2021.

https://arxiv.org/abs/2109.10677

Also

keyword 'drop' | 'droplet' in FonT

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

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

keyword 'goccia' in Notes (quasi-stochastic poetry): 

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

keywords: gst, drops, droplets, colloids, active matter, active droploids, self-assembly, solitons.

# gst: apropos of transitions, when a liquid droplet takes a turn (as a swimming behavior of amoebas)

Masatoshi Ichikawa and coll.  << have analyzed the conditions that cause self-propelling droplets to take linear or curved trajectories. The team studied water droplets between 60 and 800 μm across as they moved through oil that contained a surfactant. The droplets moved as a result of the Marangoni effect, in which an unequal distribution of surfactant molecules on the surface of each droplet creates a surface-tension gradient. (They) found that larger droplets tended to follow more tightly curved paths than smaller droplets. To understand the cause of this difference, Ichikawa and coll.  created a 3D model describing the concentration of surfactant on the surface of the droplets. They also studied the droplets’ internal flow, by observing the paths of small tracer particles. They characterized this flow as the sum of multiple patterns of fluid motion present in each droplet, including radial, dipolar, and quadrupolar motion. These patterns of motion were determined by the surface-tension gradients created by the uneven surfactant distribution on each droplet. In turn, such patterns controlled how the droplets moved. In particular, the team found that the angular difference between the dipolar and quadrupolar flows within droplets was strongly correlated with more curved droplet trajectories. In larger droplets, this angle changed more easily, causing the tightly curved trajectories. The researchers say that this fundamental mechanism may also influence the swimming behavior of amoebas.  >>️

Sophia Chen. When Liquid Droplets Take a Turn. Physics 14, s109. Aug 19, 2021.

https://physics.aps.org/articles/v14/s109

Saori Suda, Tomoharu Suda, et al. Straight-to-Curvilinear Motion Transition of a Swimming Droplet Caused by the Susceptibility to Fluctuations. Phys. Rev. Lett. 127, 088005. Aug 19, 2021.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.088005

Also

keyword 'drop' | 'droplet' in FonT

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

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

# gst: dynamics and interactions of multiple bright droplets and bubbles, and interactions of kinks with droplets and with antikinks.

<< Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink-antikink interactions are repulsive, generating counter-propagating shock waves. >> 

 

G. C. Katsimiga, S. I. Mistakidis, et al. Interactions and dynamics of one-dimensional droplets, bubbles and kinks. arXiv: 2306.07055v2 [cond-mat.quant-gas]. Jul 26, 2023.

https://arxiv.org/abs/2306.07055

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

Keywords: gst, drop, bubble, kink, wave, soliton, homoclinic orbits

# gst: exploring the lifespan of a liquid droplet

<< Current theories state that the droplet's diameter-squared decreases in proportion to time (classical law); however, this period only accounts for a small portion of the drop's evolution. As the diameter approaches the unobservable micro- and nano-scale, molecular dynamics have to be used as virtual experiments and these show a crossover to a new behaviour, with the diameter now reducing in proportion to time (nano-scale law). >>

<< It is fascinating that intuition based on everyday observations are a hindrance when attempting to understand nanoscale flows, so that, as in this research, one has to lean on theory to enlighten us. >>  James Sprittles.

The lifespan of an evaporating liquid drop. University of Warwick. Oct 10, 2019.     https://m.phys.org/news/2019-10-lifespan-evaporating-liquid.html

Rana A.S., Lockerby D.A., Sprittles J.E.  Lifetime of a Nanodroplet: Kinetic Effects and Regime Transitions. Phys. Rev. Lett. 123, 154501 Oct 9, 2019.     https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.154501   

# 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: 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: 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: fingerprints of reality: water drops that vibrate, flames that oscillate, and viscous fluids that form rivulets ...

<< In one of this year’s three winning videos, a drop of blue-dyed water at the bottom of an anise-oil and alcohol mixture begins to grow and shake, eventually pinching off a fragment that floats up. The process repeats several times. Created by now four-time Gallery-of-Fluid-Motion winner Oscar Enríquez of Carlos III University of Madrid and his colleagues, the visuals are accompanied by a soundtrack featuring a musical improvisation by a trio consisting of Enríquez on percussion, a violinist, and a clarinetist. Each instrument in the trio represents one of the three fluids. >>

Award-Winning Fluid Videos. APS. Physics 11, 121. Nov 21, 2018.

https://physics.aps.org/articles/v11/121

# 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

# gst: apropos of transitions, perspectives on viscoelastic flow instabilities; the 'porous individualism'

<< given the observation that disorder can suppress the transition to elastic turbulence in 2D porous media (..), it has been unclear whether and how this transition manifests in disordered 3D media — though elastic turbulence has been speculated to underlie the long-standing observation that the macroscopic flow resistance of an injected polymer solution can abruptly increase above a threshold flow rate in a porous medium, but not in bulk solution >>️

AA << found that the transition to unstable flow in each pore is continuous, arising due to the increased persistence of discrete bursts of instability above a critical value of the characteristic (Weissenberg no.) Wi; however, the onset value varies from pore to pore. This observation that single pores exposed to the same macroscopic flow rate become unstable in different ways provides a fascinating pore-scale analog of “molecular individualism” [P.  De Gennes, Molecular individualism. Science 276, 1999–2000 (1997)], in which single polymers exposed to the same extensional flow elongate in different ways; the authors therefore termed it “porous individualism”, although it is important to note that here, this effect is still at the continuum (not molecular) scale. Thus, unstable flow is spatially heterogeneous across the different pores of the medium, with unstable and laminar regions coexisting >>

AA << quantitatively established that the energy dissipated by unstable pore-scale fluctuations generates an anomalous increase in flow resistance through the entire medium that agrees well with macroscopic pressure drop measurements. >>

Sujit S. Datta, Arezoo M. Ardekani, et al. Perspectives on viscoelastic flow instabilities and elastic turbulence. arXiv: 2108.09841v1 [physics.flu-dyn]. Aug 22, 2021. 

https://arxiv.org/abs/2108.09841

Also

keyword 'transition' | 'transitional' in FonT

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

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

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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

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

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

keywords: gst, droplet, fluctuations, disorder, instability, viscoelastic flow instability, turbulence, elastic turbulence, individualism, porous individualism, transition

# life: exponential post-Donald (without Donald), how AI could interfere (drive) next political elections.

<< Recent news that the Republican National Committee (RNC) has used an AI-generated video to criticize Joe Biden shows how likely AI is to transform our upcoming elections. >>️

<< Through templates that are easy and inexpensive to use, we are going to face a Wild West of campaign claims and counter-claims, with limited ability to distinguish fake from real material and uncertainty regarding how these appeals will affect the election. >>️

<< In the coming year, response times may drop to minutes, not hours or days. AI can scan the internet, think about strategy, and come up with a hard-hitting appeal. >>️

<< AI provides an inexpensive way to generate instant responses without having to rely on highly-paid consultants or expert videographers. >>️

<< AI enables very precise audience targeting, which is crucial in political campaigns. >>️

<< AI likely will democratize disinformation by bringing sophisticated tools to the average person interested in promoting their preferred candidates as well. People no longer must be coding experts or video wizards to generate text, images, video, or programs. They don’t necessarily have to work for a troll farm to create havoc with the opposition. They can simply use advanced technologies to spread the messages they want. In that sense, anyone can become a political content creator and seek to sway voters or the media. >>️

Darrell M. West. How AI will transform the 2024 elections. May 3, 2023.

https://www.brookings.edu/blog/techtank/2023/05/03/how-ai-will-transform-the-2024-elections/

Also: 'ai', 'analogy', 'Potus', 'RAG-time', 'CTZ', 'Donald' in https://www.inkgmr.net/kwrds.html

Keywords: life, ai, analogy, potus, RAG, CTZ, Donald

# behav: spreading conflicts through monkey societies

<< How does conflict spread through a society? One way to think of conflict spreading is to picture an epidemic, with aggressive individuals "infecting" others and causing them to join the fight >>

<< It appears that it is not individuals who control the length of fights, but the relationships between pairs of individuals >>

AA << found evidence for a more complicated structure behind >>

AA << found evidence that conflict duration is strongly affected by the first interaction, which sets the tone for the fight. If the first interaction is brief, then following episodes are likely to be just as brief. A long drawn out initial brawl, however, will be followed by similarly difficult episodes. This, Flack [Jessica Flack] says, "is a signature of collective memory," meaning "the duration of the conflict is not just determined by individuals independently deciding whether to continue fighting or drop out, but through their joint memory for the past and subsequent collective decision-making." >>

How conflicts spread through monkey societies. Sep 7, 2017

https://m.phys.org/news/2017-09-conflicts-monkey-societies.html

Edward D. Lee, Bryan C. Daniels, et al.  Collective memory in primate conflict implied by temporal scaling collapse. Journal of the Royal Society Interface. doi: 10.1098/rsif.2017.0223 Sep 6 2017.

http://rsif.royalsocietypublishing.org/content/14/134/20170223

# gst: exploring the on-demand dynamical generation of a plethora of dispersive shock waves arising in attractive one-dimensional droplet-bearing environment.

AA << demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment with the aid of step-like initial conditions. Dispersive regularization of the ensuing hydrodynamic singularities occurs due to the competition between meanfield repulsion and attractive quantum fluctuations. This interplay delineates the dominance of defocusing (hyperbolic) and focusing (elliptic) hydrodynamic phenomena respectively being designated by real and imaginary speed of sound. >>

<< Surprisingly, dispersive shock waves persist across the hyperbolic-to-elliptic threshold, while a plethora of additional wave patterns arise, such as rarefaction waves, traveling dispersive shock waves, (anti)kinks and droplet wavetrains. >>

AA << results pave the way for unveiling a multitude of unexplored coherently propagating waveforms in such attractively interacting mixtures. >>

Sathyanarayanan Chandramouli, Simeon I. Mistakidis, Garyfallia C. Katsimiga, Panayotis G. Kevrekidis. 

Dispersive shock waves in a one-dimensional droplet-bearing environment. arXiv: 2404.02998v2 [nlin.PS]. Apr 5, 2024. 

https://arxiv.org/abs/2404.02998

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

Keywords: gst, waves, drops 

# gst: the auto assembly of a drop (from thermal capillary waves)

<< after single or multiple bridges form due to the presence of thermal capillary waves, the bridge growth commences in a thermal regime. Here, the bridges expand linearly in time much faster than the viscous-capillary speed due to collective molecular jumps near the bridge fronts. Transition to the classical hydrodynamic regime only occurs once the bridge radius exceeds a thermal length scale l_(T) ~ sqrt(Radius). >>

Sreehari Perumanath, Matthew K. Borg, et al. Droplet Coalescence is Initiated by Thermal Motion. Phys. Rev. Lett. 122, 104501 Mar 13, 2019.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.104501

Supercomputer sheds light on how droplets merge. University of Edinburgh. Mar 20, 2019.

https://m.phys.org/news/2019-03-supercomputer-droplets-merge.html