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In flotation, a bubble acts as a carrier for attached particles. The properties of the gas–liquid interface of the bubble are one of the main factors determining the bubble motion and flotation efficiency. Monitoring of the bubble motion may deliver interesting information about the state of the gas–liquid interface. In the case of pure liquids, a bubble surface is fully mobile, while the presence of surface-active substances (e.g., surfactants) causes diminishing bubble velocity due to the retardation of the interface fluidity. The theoretical prediction of the terminal velocity value for the bubble has been investigated for over a century, delivering a number of various models describing bubble motion in a liquid. This narrative review is devoted to the motion of the bubble in stagnant liquids and is divided into three main sections describing: (i) experimental techniques for tracking bubble motion, (ii) bubble motion and shape deformation in clean water, and (iii) bubble motion in solutions of surface-active substances.

The Weather Research and Forecasting (WRF) Double-Moment 7-Class (WDM7) cloud microphysics scheme was developed to parameterize cloud and precipitation processes explicitly for mesoscale phenomena in the Korean Integrated Model system. However, the WDM7 scheme has not been evaluated for any precipitating convection system over the Korean peninsula. This study modified WDM7 and evaluated simulated convection during summer and winter. The suggested modifications included the integration of the new fall velocity–diameter relationship of raindrops and mass-weighted terminal velocity of solid-phase precipitable hydrometeors (the latter is for representing mixed-phase particles). The mass-weighted terminal velocity for snow and graupel has been suggested by Dudhia et al. (2008) to allow for a more realistic representation of partially rimed particles. The WDM7 scheme having an additional hail category does not apply this terminal velocity only for hail. Additionally, the impact of enhanced collision-coalescence (C-C) efficiency was investigated. An experiment with enhanced C-C efficiency overall improved the precipitation skill scores, such as probability of detection, equitable threat score, and spatial pattern correlation, compared with those of the control experiment for the summer and winter cases. With application of the new mass-weighted terminal velocity of solid-phase hydrometeors, the hail mixing ratio at the surface was considerably reduced, and rain shafts slowed down low-level winds for the winter convective system. Consequently, the simulated hydrometeors were consistent with observations retrieved via remote sensing. The fall velocity–diameter relationship of raindrops further reduced the cloud ice amount. The proposed modifications in our study improved the simulated precipitation and hydrometeor profiles, especially for the selected winter convection case.

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.

In ultra-deep and large well sections, high collapse stresses and diminished annular return velocity present significant challenges to wellbore cleaning. With increasing depth, rising temperature and pressure constrain the regulation of displacement and drilling fluid rheology, impairing the fluid’s capacity to transport cuttings effectively. A precise understanding of cuttings settlement behavior and terminal velocity is therefore essential for optimizing their removal. This study accounts for variations in wellbore temperature and pressure, incorporates non-spherical cuttings and wellbore diameter parameters, and develops accordingly a simplified model to predict terminal settlement velocity. The cuttings carrying ratio is introduced as a metric for evaluating wellbore cleanliness. Findings reveal that temperature and pressure fluctuations can alter terminal velocity by up to 3.4%. Cuttings shape plays a crucial role, with block-shaped cuttings requiring higher annular return velocity than flake-shaped ones at the same carrying ratio. As wellbore size increases, the minimum required carrying flow rate rises nonlinearly, though the rate of increase gradually declines. For a Φ444.5 mm wellbore, a carrying ratio of at least 0.6 is recommended. Terminal velocity decreases with increasing consistency coefficient, particularly in high-viscosity regimes. The proposed carrying ratio offers a more accurate and practical assessment of wellbore cleanliness.

Passively dispersed organisms do not expend energy during movement; this lack of agency suggests that the distance dispersed by these species is predominantly affected by extrinsic abiotic factors. However, theory predicts that greater dispersal has ecological and evolutionary advantages under some circumstances (e.g., stressful environments). If the biological traits that underlie passive dispersal respond phenotypically to environmental cues, these species may be able to maintain or improve dispersal distance in response to local stressors. We empirically examined context-dependent dispersal, and verified the hypothesis that the traits of an invasive, wind-dispersed plant species plastically affect predicted dispersal distances under drought conditions. We found that the effect is strongest among tall individuals that are most likely to contribute to spread, and that dispersal trait covariation among taller stressed individuals matches expectations from a fluid dynamical model. These responses probably contribute to this species' success as a fugitive invader in complex landscapes.

We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\\unicode[STIX]{x1D706}}\\approx 200{-}500$ , while the particle Stokes number based on the Kolmogorov scale varies between $St_{\\unicode[STIX]{x1D702}}=O(1)$ and $O(10)$ . Clustering is confirmed to be most intense for $St_{\\unicode[STIX]{x1D702}}\\approx 1$ , but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and with sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of $St_{\\unicode[STIX]{x1D702}}\\approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.

Plants cover a large fraction of the Earth’s land mass despite most species having limited to no mobility. To transport their propagules, many plants have evolved mechanisms to disperse their seeds using the wind 1 – 4 . A dandelion seed, for example, has a bristly filament structure that decreases its terminal velocity and helps orient the seed as it wafts to the ground 5 . Inspired by this, we demonstrate wind dispersal of battery-free wireless sensing devices. Our millimetre-scale devices weigh 30 milligrams and are designed on a flexible substrate using programmable, off-the-shelf parts to enable scalability and flexibility for various sensing and computing applications. The system is powered using lightweight solar cells and an energy harvesting circuit that is robust to low and variable light conditions, and has a backscatter communication link that enables data transmission. To achieve the wide-area dispersal and upright landing that is necessary for solar power harvesting, we developed dandelion-inspired, thin-film porous structures that achieve a terminal velocity of 0.87 ± 0.02 metres per second and aerodynamic stability with a probability of upright landing of over 95%. Our results in outdoor environments demonstrate that these devices can travel 50–100 metres in gentle to moderate breeze. Finally, in natural systems, variance in individual seed morphology causes some seeds to fall closer and others to travel farther. We adopt a similar approach and show how we can modulate the porosity and diameter of the structures to achieve dispersal variation across devices. A dandelion-inspired wireless solar-powered sensing device weighing 30 milligrams that transmits data through radio backscatter achieves dispersal over a wide area by travelling on the breeze, and successfully lands upright.

Contrasting with its sluggish behavior on standard solids, water is extremely mobile on superhydrophobic materials, as shown, for instance, by the continuous acceleration of drops on tilted water-repellent leaves. For much longer substrates, however, drops reach a terminal velocity that results from a balance between weight and friction, allowing us to question the nature of this friction. We report that the relationship between force and terminal velocity is nonlinear. This is interpreted by showing that classical sources of friction are minimized, so that the aerodynamical resistance to motion becomes dominant, which eventually explains the matchless mobility of water. Our results are finally extended to viscous liquids, also known to be unusually quick on these materials.

To calculate the dynamic peak overpressure of the shock wave of a shell-packed charge and assess their blasting power, this paper constructed a function relationship between terminal velocity, loading ratio, test point position, and equivalent charge mass based on the test result and the dynamic scattering characteristics of explosive products. This model quantifies the effect of terminal ballistic parameters on the dynamic peak overpressure of shock waves for the first time, and the error between the model calculation result and the experimental result is less than 12%. In addition, by reconstructing the dynamic peak overpressure space-time field of shock waves and analyzing the influence of terminal ballistic parameters on dynamic peak overpressure of shock wave, it was found that the height had the biggest influence on the dynamic peak overpressure of shock wave with the influence coefficient of -11896 Pa/m, followed by the fall angle with the influence coefficient of 37.4 Pa/°, and then the terminal velocity with the influence coefficient of 16.6 Pa/(m/s).

When a liquid jet plunges into a pool, it can generate a bubble-laden jet flow underneath the surface. This common and simple phenomenon is investigated experimentally for circular jets to illustrate and quantify the role played by the net gas/liquid void fraction on the maximum bubble penetration depth. It is first shown that an increase in either the impact diameter or the jet fall height to diameter ratio at constant impact momentum leads to a reduction in the bubble cloud size. By measuring systematically the local void fraction using optical probes in the biphasic jet, it is then demonstrated that this effect is a direct consequence of the increase in air content within the cloud. A simple momentum balance model, including only inertia and the buoyancy force, is shown to predict the bubble cloud depth without any fitting parameters. Finally, a Froude number based on the bubble terminal velocity, the cloud depth and also the net void fraction is introduced to propose a simple criterion for the threshold between the inertia-dominated and buoyancy-dominated regimes.