# gst: the way bubbles gallop.

<< ️Bubbles are more than fleeting pockets of air trapped in liquid: they exhibit an ever-expanding repertoire of intriguing behaviors. From da Vinci's sketches of their swirling paths to modern-day studies of their erratic dances under acoustic waves, the rich dynamics of bubbles have long captured the attention of everyday observers, engineers, and scientists alike. When exposed to periodic sound waves, bubbles can shift from regular pulsations to rapid zigzagging, mimicking the randomness of Brownian motion. Under sudden pressure changes, they may collapse violently, producing cavitation—intense shock waves capable of damaging solid surfaces. In extreme cases, the implosion may become so intense that the bubble emits a spark of light. >>

<< ️Bubbles can also challenge common intuition: they may appear to violate Archimedes' principle, sinking against gravity in oscillating fluids, and carbonated drinks. Despite centuries of explorations, new and often surprising bubble phenomena continue to emerge. One such example is the recently discovered “galloping” bubble, introduced in (AA) recent publication. Here, (They) showcase this new mechanism of bubble locomotion, highlighting its rich dynamics and striking visual appeal. >>

Jian H. Guan, Saiful I. Tamim, Connor W. Magoon, et al. The way bubbles gallop. Phys. Rev. Fluids 10, 110507. Nov 20, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/fbdh-fnzv

Gallery of Fluid Motion. https://doi.org/10.1103/APS.DFD.2024.GFM.V2684816

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

Keywords: gst, bubble, galloping bubbles, galloping threshold, galloping motion, galloping mechanism, instability, galloping instability, drops, droplets, droploids, transitions.

# gst: why and when merging surface nanobubbles jump.

<< Gas bubble accumulation on substrates reduces the efficiency of many physicochemical processes, such as water electrolysis. For microbubbles, where buoyancy is negligible, coalescence-induced jumping driven by the release of surface energy provides an efficient pathway for their early detachment. >>

<< At the nanoscale, however, gas compressibility breaks volume conservation during coalescence, suppressing surface energy release and seemingly disabling this detachment route. >>

<< Using molecular dynamics simulations, continuum numerical simulations, and theoretical analysis, (AA) show that surface nanobubbles with sufficiently large contact angles can nevertheless detach after coalescence. In this regime, detachment is powered by the release of pressure energy associated with nanobubble volume expansion. This (AA) finding thus establishes a unified driving mechanism for coalescence-induced bubble detachment across all length scales. >>

Yixin Zhang, Xiangyu Zhang, Detlef Lohse. Why and when merging surface nanobubbles jump. arXiv: 2509.22934v1 [cond-mat.soft]. Sep 26, 2025.

https://arxiv.org/abs/2509.22934

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

Keywords: gst, bubbles, surface nanobubbles, surface energy release, coalescence, coalescence-induced jumping, coalescence-induced bubble detachment.

# gst: role of evaporation in stability of foam films and foams.

<< ️Understanding the stability of foam films and foams remains a challenge, despite the considerable efforts provided by the scientific community to refine their physical descriptions. This persistent difficulty underscores the interplay of various complex factors. Recently, the role of evaporation has attracted attention for its dual impact: it can either enhance stability or accelerate bursting. >>

<< ️To depict a comprehensive overview on soapy objects, (AA) propose first a short description on the evaporation of drops to present some key results on the evaporation-induced cooling and the consequences on the internal flows generated by Marangoni effects. Then, (They) review the literature on foam films and foams, examining three distinct systems: pure liquids, nonvolatile, and volatile surface active molecules. ️(AA) show that evaporation of foam films and foams can lead to significant variations of temperature. In conclusion, (They) identify a series of open questions and suggest potential research pathways to address these challenges. >>

François Boulogne, Emmanuelle Rio. Role of evaporation in stability of foam films and foams. Phys. Rev. E 112, 031001. Sep 9, 2025.

https://journals.aps.org/pre/abstract/10.1103/52dh-hnnx 

arXiv: 2509.08958v1 [cond-mat.soft]. Sep 10, 2025. 

https://arxiv.org/abs/2509.08958

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

Keywords: gst, bubbles, drops, evaporation. 

# gst: reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing.

AA << ️describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence of the transition, infinitesimal parameter variations allow switching between uniform distribution and clusters in single-species models, and between mixed and sorted states in multi-species contexts, without hysteresis. >>

Their << main technical contribution is a universal expansion for the size of vacuum bubbles that arise in this phase transition and a quantitative analysis of the effect of noise. >>

Arnd Scheel, Angela Stevens. Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing. arXiv: 2507.10406v1 [math.DS]. Jul 14, 2025.

https://arxiv.org/abs/2507.10406

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

Keywords: gst, particles, bubbles, noise, short-range repulsion, long-range attraction, phase transitions.

# gst: experimental investigation of turbulence modulation by deformable bubbles

<< In this work (AA) experimentally investigate the turbulence modulation in the wake of deforming bubbles in homogeneous and isotropic turbulence, in the regime where the turbulence fluctuation is stronger than or comparable to the bubble rising velocity. >>

<< In a quiescent or weak turbulence, the wake has a persistent direction due to the buoyancy. In turbulence, however, (Their) results suggest that the decorrelation time for the slip velocity roughly equals the bubble-sized eddy turn over time. It suggests that, when turbulence becomes intense enough, the slip velocity changes its direction and magnitude so frequently that a wake barely has time to develop. >>

<< As a result, both the intensity and length of the wake are significantly modified. Nevertheless, with sufficient bubble Reynolds number, the wake, albeit limited, can still modulate surrounding turbulence. >>

<< The results suggest that the local turbulence is augmented by the bubble wake, and the amount of augmentation depends heavily on the bubble Reynolds number, the orientation of the bubble semimajor axis relative to the slip velocity, and the bubble deformation. >>️

Xu Xu, Shiyong Tan, et al. Experimental investigation of turbulence modulation by deformable bubbles. Phys. Rev. Fluids 10, 033605. March 31, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.033605

Also: bubble, disorder & fluctuations, turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, deformable bubbles, bubble wake, bubble-bubble interaction, disorder & fluctuations, turbulence, turbulence modulation, surrounding turbulence, vortex, slip velocity, buoyancy

# gst: apropos of bubble rearrangements, transition from slip to scraping as critical-like behavior in foam dynamics.

<< Jamming systems, including colloids, emulsions, foams, and biological tissues, undergo significant deformation during processes like material scraping or wound self-healing. To adequately spread a foam or cream over a surface, external force must be applied to artificially scrape it. Notably, the transition from slip to scraping when foam is manipulated using a rigid plate remains poorly understood. >>

<< Systematic observations of the internal foam structure during scraping were conducted, and the scraping length was qualitatively analyzed by varying the scraping velocity. (AA) study reveals that the transition from slip to scraping is driven by the sequential propagation of bubble rearrangements. Furthermore, the scraping length diverges towards the transition point, with a critical exponent of approximately 0.61. >>

<< These findings align with directional percolation theory, underscoring the robustness of the theoretical framework. >>

Masaya Endo, Rei Kurita. Critical-like behavior in foam dynamics: Transition from slip to scraping. Phys. Rev. Research 7, 023013. Apr 3, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023013

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

Keywords: gst, bubble, bubble rearrangements, foam, jamming, transition, criticality, scraping,  percolation

# gst: friction-induced bubble edge curvature in flowing 2D confined foams

AA << investigate the flow of quasi-2D liquid foams, composed of a single monolayer of bubbles in close contact and confined between two glass plates in a Hele-Shaw cell, with a specific emphasis on understanding how bubble shapes evolve in response to varying flow speeds. Utilizing an experimental setup capable of displacing a substantial number of bubbles in the spanwise direction, while the bubble shapes remain stationary as the bubbles themselves are advected in a plug flow, (They) reveal an average bubble anisotropy characterized by elongated bubbles in the streamwise direction and curved bubble edges in a preferential orientation. >>

<< Notably, these effects intensify with increasing flow speeds. While the bubble anisotropy is created at the entrance of the cell, (AA) study establishes a clear connection between bubble edge curvature and orientation, confinement thickness, frictional forces with the plates, and the inherent anisotropy of the bubbles. >>

Christophe Raufaste, Lauren Rose, et al. Friction-induced bubble edge curvature in flowing two-dimensional confined foams. Phys. Rev. Fluids 10, 023301. Feb 5, 2025. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.10.023301 

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

Keywords: gst, bubble, foam, friction, surface tension

# gst: equilibrium and breakup regimes of stretched soap bubbles

AA << combine experiments and theoretical derivations to study the evolution of a stretched soap bubble and compare it with an open film to highlight the effect of volume conservation. (They) identify a critical length for both surfaces, beyond which a bottleneck develops in the middle and begins to shrink irreversibly, ultimately pinching off into multiple compartments. >>

<< Before leaving the equilibrium regime, surface energy minimization governs the shape, which can be addressed theoretically via the variational method. In contrast to open films, soap bubble volume conservation introduces a Lagrange multiplier, analogous to a pressure difference, mediating long-range shape evolution. >>

<< By examining how boundary constraints influence deformation, (AA) contrast the bubble's convex-to-concave transition with the behavior of soap films under similar conditions. (Their) analysis of equilibrium and breakup regimes reveals critical differences between bubble and film stability profiles, shedding light on universal behaviors in non-equilibrium fluid mechanics, with implications for biological and material sciences.

>>️

Wei-Chih Li, Chih-Yao Shih, et al. How soap bubbles change shape while maintaining a fixed volume of air? arXiv: 2412.17870v1 [physics.flu-dyn]. Dec 21, 2024. 

https://arxiv.org/abs/2412.17870

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

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

# gst: apropos of puddles, how to design and stabilize a Leidenfrost puddle

<< Leidenfrost puddles exhibit erratic bubble bursts that release vapor trapped beneath the liquid, becoming amorphous and unstable. (AA) report a method to stabilize and design a Leidenfrost puddle. >>

<< When a thin hydrophilic layer with a suitable design is placed over the liquid, the puddle adopts the layer shape due to adhesive forces and becomes stable. (AA) show a variety of puddle designs with the required layer dimensions to avoid vapor accumulation, as well as wetting and buoyancy conditions. >>

<< With the layer, the puddle evaporation rate increases significantly and can be modified by varying the layer dimensions. Finally, an illustrative use of this method in a cooling process is presented. >>️

F. Pacheco-Vázquez, M. Aguilar-González, L. Victoria-García. Designing Leidenfrost Puddles. Phys. Rev. Lett. 133, 234001. Dec 4, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.234001 

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

Keywords: gst, drops, bubbles, instability, transition

# gst: intermittency of bubble deformation in turbulence.

<< The deformation of finite-sized bubbles in intense turbulence exhibits complex geometries beyond simple spheroids as the bubbles exchange energy with the surrounding eddies across a wide range of scales. (AA)  study investigates deformation via the velocity of the most stretched tip of the deformed bubble in three dimensions, as the tip extension results from the compression of the rest of the interface by surrounding eddies. >>

<< The results show that the power spectrum based on the tip velocity exhibits a scaling akin to that of the Lagrangian statistics of fluid elements, but decays with a distinct timescale and magnitude modulated by the Weber number based on the bubble size. This indicates that the interfacial energy is primarily siphoned from eddies of similar sizes as the bubble. >>

<< Moreover, the tip velocity appears much more intermittent than the velocity increment, and its distribution near the extreme tails can be explained by the proposed model that accounts for the fact that small eddies with sufficient energy can contribute to extreme deformation. >>

<< These findings provide a framework for understanding the energy transfer between deformable objects and multiscale eddies in intense turbulence. >>

Xu Xu, Yinghe Qi, et al. Intermittency of Bubble Deformation in Turbulence. Phys. Rev. Lett. 133, 214001. Nov 19, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.214001

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

Keywords: gst, bubble, turbulence, intermittency

# gst: apropos of bubbles, the case of bubbles collapsing near a wall.

AA << study examines the pressure exerted by a cavitation bubble collapsing near a rigid wall. A laser-generated bubble in a water basin undergoes growth, collapse, second growth, and final collapse. Shock waves and liquid jets from non-spherical collapses are influenced by the stand-off ratio γ, defined as the bubble centroid distance from the wall divided by the bubble radius. (AA) detail shock mechanisms, such as tip or torus collapse, for various γ values. High-speed and Schlieren imaging visualize the microjet and shock waves. The microjet's evolution is tracked for large γ, while shock waves are captured in composite images showing multiple shock positions. Quantitative analyses of the microjet interface, shock wave velocities, and impact times are reported. Wall-mounted sensors and a needle hydrophone measure pressure and compare with high-speed observations to assess the dominant contributions to pressure changes with γ, revealing implications for cavitation erosion mechanisms. >>️

Roshan Kumar Subramanian, Zhidian Yang, et al. Bubble collapse near a wall. Part 1: An experimental study on the impact of shock waves and microjet on the wall pressure. arXiv: 2408.03479v2 [physics.flu-dyn]. Aug 8, 2024. 

https://arxiv.org/abs/2408.03479

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

Keywords: gst, bubble, bubble collapse 

# gst: extreme events in two-coupled chaotic oscillators.

This AA study << focuses on the emergence of extreme events in a system of diffusively and bidirectionally two coupled Rössler oscillators and unraveling the mechanism behind the genesis of extreme events. (AA) find the appearance of extreme events in three different observables: average velocity, synchronization error, and one transverse directional variable to the synchronization manifold. >>

<< The emergence of extreme events in average velocity variables happens due to the occasional in-phase synchronization. The on-off intermittency plays for the crucial role in the genesis of extreme events in the synchronization error dynamics and in the transverse directional variable to the synchronization manifold. The bubble transition of the chaotic attractor due to the on-off intermittency is illustrated for the transverse directional variable. >>

S. Sudharsan, Tapas Kumar Pal, et al. Extreme events in two-coupled chaotic oscillators. arXiv: 2409.15855v1 [nlin.CD]. Sep 24, 2024. 

https://arxiv.org/abs/2409.15855

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

Keywords: gst, transition, bubble transition, extreme events

# gst: vortex structures under dimples and scars in turbulent free-surface flows

<< Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. >>️

AA << explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. >>️

<< The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale λT, this probability is independent of Reynolds and Weber number. >>️

<< Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately λT/4. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. >>️

AA << findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes. >>

Jørgen R. Aarnes, Omer Babiker, et al. Vortex structures under dimples and scars in turbulent free-surface flows. arXiv: 2409.05409v1 [physics.flu-dyn]. 

9 Sep 2024.

https://arxiv.org/abs/2409.05409

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

Keywords: gst, vortex, turbulence, waves, bubble, drop, transition

# 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: collapse of a toroidal bubble inducing shock waves

<< When bubbles collapse near a wall, they typically experience an asymmetric deformation. This collapse leads to the creation of a jet that strikes the bubble interface, causing the formation of a toroidal bubble and the subsequent release of a water-hammer shock. >>️

AA << findings demonstrate that shock waves emitted from the toroidal bubble consistently propagate toward the central axis of the torus, resulting in significant pressure shocks along the axis, similar to the water-hammer shock formed during the collapse of a spherical bubble. >>️

<< In contrast, weak pressure waves are generated in the transverse directions, leading to relatively weaker pressure peaks. Furthermore, the wall-pressure peak induced by the toroidal bubble is approximately three times higher than that induced by the spherical bubble. >>️

Cheng Liu, Xiaobin Yang, et al. Investigations on the shock wave induced by collapse of a toroidal bubble. Phys. Rev. E 110, 015103. Jul 16, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.015103

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

Keywords: gst, bubble, drop, waves, collapse

# gst: tracking four-way coupled particles in turbulence

<< In many natural and industrial applications, turbulent flows encompass some form of dispersed particles. Although this type of multiphase turbulent flow is omnipresent, its numerical modeling has proven to be a remarkably challenging problem. >>

AA << present an efficient method for point-based simulation of particles in turbulence that are four-way coupled. In contrast with traditional one-way coupled simulations, where only the effect of the fluid phase on the particle phase is modeled, this method additionally captures the back-reaction of the particle phase on the fluid phase, as well as the interactions between particles themselves. >>

AA << focus on the most challenging case of very light particles or bubbles, which show strong clustering in the high-vorticity regions of the fluid. >>

️

Xander M. de Wit, Rudie P. J. Kunnen, et al. Efficient point-based simulation of four-way coupled particles in turbulence at high number density. Phys. Rev. E 110, 015301. Jul 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.015301  

Also: particle, bubble, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, bubbles, turbulence

# 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: bubble phases sliding over periodically modulated substrates

AA << analyze a bubble-forming system composed of particles with competing long-range repulsive and short-range attractive interactions driven over a quasi-one-dimensional periodic substrate. >>️

They << find various pinned and sliding phases as a function of substrate strength and drive amplitude. When the substrate is weak, a pinned bubble phase appears that depins elastically into a sliding bubble lattice. For stronger substrates, (AA) find anisotropic bubbles, disordered bubbles, and stripe phases. Plastic depinning occurs via the hopping of individual particles from one bubble to the next in a pinned bubble lattice, and as the drive increases, there is a transition to a state where all of the bubbles are moving but are continuously shedding and absorbing individual particles. This is followed at high drives by a moving bubble lattice in which the particles can no longer escape their individual bubbles. >>️

<< When the bubbles shrink due to an increase in the attractive interaction term, they fit better inside the pinning troughs and become more strongly pinned, leading to a reentrant pinning phase. For weaker attractive terms, the size of the bubbles becomes greater than the width of the pinning troughs and the depinning becomes elastic with a reduced depinning threshold. >>

️

C. Reichhardt, C.J.O. Reichhardt. Sliding dynamics for bubble phases on periodic modulated substrates. Phys. Rev. Research 6, 023116. May 2, 2024.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.023116

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

Keywords: gst, bubble, pinned bubble, elastic, transition

# gst: apropos of synchronization of large bubble clouds, self-oscillating acoustic bubbles that bounce

<< Self-oscillations underlie many natural phenomena such as heartbeat, ocean waves, and the pulsation of variable stars. (..) In this study, (AA) consider two closely spaced bubbles pulsating in the kHz range in response to ultrasonic excitation. A translational bouncing motion emerges from their interaction with a much lower frequency than the bubble pulsation frequency. >>

Their analysis << reveals that the observed bubble bouncing exhibits the main features of self-oscillation, such as negative damping and the emergence of a limit cycle. These results highlight unexpected nonlinear effects in the field of microbubbles and give insights into the understanding of synchronization in large bubble clouds. >>️

Gabriel Regnault, Alexander A Doinikov, et al. Phenomenon of self-oscillation in bubble dynamics: Bouncing acoustic bubbles. arXiv: 2404.05822v1 [physics.flu-dyn]. Apr 8, 2024.

https://arxiv.org/abs/2404.05822

Also: bubble, bouncing, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, self-oscillation, bouncing, behavior, collective behavior, bouncing motion, synchronization

# gst: when volatile droplets dance across a surface erratically (along random trajectories)

<< When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. >>️

<< Contrary to this intuition, due to thermal Marangoni contraction, the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. >>️

Pallav Kant, Mathieu Souzy, et al. Autothermotaxis of volatile drops. Phys. Rev. Fluids 9, L012001. Jan 31, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L012001

Rachel Berkowitz. Hot Surfaces Make Droplets Move Erratically. Physics 17, s14. Jan 31, 2024. 

https://physics.aps.org/articles/v17/s14 

Also: drop, bubble, erratic

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

Keywords: gst, drop, bubble, erratic, thermotaxis, autothermotaxis