Bouncing Regimes Research Articles

Pancake bouncing of impacting nanodroplets on smooth and nanopillared surfaces

Reducing the contact time of impacting droplets on solid surfaces has become a research focus due to its promising application prospects in self-cleaning, anti-erosion, and anti-icing. In this study, the pancake bouncing of nanodroplets is investigated through molecular dynamics simulations, achieving a remarkable reduction in contact time. Two distinct patterns of pancake bouncing are identified when nanodroplets impact smooth and nanopillared surfaces with different bouncing mechanisms. The first pancake bouncing pattern with holes on smooth surfaces is attributed to internal-flow collision induced by multiple retraction centers. The second pancake bouncing pattern on nanopillared surfaces results from the storage and release of sufficient surface energy due to liquid penetration and requires satisfying both the timescale and energy criterion. Subsequently, theoretical models for two criteria are developed, which promote two parameter groups (−(s2 + 2ws)h(wcosθ0)−1 and We–1/3Re–1/3R02) corresponding to the surface and droplet. Based on these two parameter groups, a phase diagram is established and indicates the triggering conditions for the second pancake bouncing patterns. Finally, it is further revealed that by increasing the pillar height from smooth to nanopillared surfaces, the bouncing regime is transformed from the first pancake bouncing pattern, regular bouncing, to the second pancake bouncing pattern.

Atomistic simulations of oblique collisions between crystalline and amorphous SiC nanoparticles: Mechanisms of deformation and scaling coefficients of restitutions

Systematic atomistic simulations of oblique collisions between spherical crystalline, 6H and 3C, and amorphous SiC nanoparticles (NPs) are performed in the bouncing and fragmentation regimes for the particles with diameters from 8 nm to 30 nm, impact velocities from 100 ms−1 to 5000 ms−1, and in the whole range of the geometric impact parameter. The critical sticking velocity of 6H-SiC NPs reduces from ∼490 ms−1 to ∼150 ms−1 when the NP diameter increases from 10 nm to 30 nm. Below the melting threshold, the collision of crystalline NPs induces the formation of localized zones of densified material, while the remaining parts of NPs are not affected by plastic deformations. The impact of amorphous NPs results in the plastic deformation of significant parts of the NP material and much larger irreversible losses of mechanical energy. The post-collision translational and rotational velocities of crystalline NPs as well as coefficients of restitution (CORs) demonstrate weak dependence on the NP size if the NP diameter is greater than 20 nm. At constant impact velocity, the normal COR only marginally varies for head-on and oblique collisions, when the collision angle is smaller than ∼53°. The tangential center-of-mass and point-of-contact CORs, as functions of the impact parameter, demonstrate extremal behavior with the minima at collision angles from ∼27° to ∼37°. The normal COR exhibits a linear decay as a function of the impact velocity where the slope coefficient is different below and above the melting threshold. The tangential CORs attain the minimum values at the impact velocity of ∼300 ms−1. The obtained results are summarized in the form of fitting equations for CORs as functions of the impact parameter and velocity, which can be readily used to predict the post-collision translational and angular velocities of NPs in large-scale simulations of granular gas flows.

Impact of nanodroplets on solid spheres

Rising nanoscale technologies arouse interest in investigating the impact dynamics of nanodroplets. In this work, the impact of nanodroplets on solid spheres is investigated by the molecular dynamics simulation method, to comprehensively report outcome regimes and reveal the curvature effect, in wide ranges of Weber numbers (We) from 1.5 to 235.8, diameter ratios (λ) of nanodroplets to solid spheres from 0.3 to 5, and contact angles (θ) from 105° to 135°. Five outcomes are identified, including deposition, bouncing, splash, covering, and dripping. The former three outcomes are found in the high diameter ratio range (λ > 1), showing similar dynamic behaviors with impacts on flat surfaces, whereas in the low diameter ratio range (λ ≤)1, splash disappears, and covering and dripping take place additionally. At each contact angle, the outcomes are recorded in λ-We phase diagrams. It is found that the bouncing, splash, covering, and dripping are all promoted by decreasing diameter ratios; in addition, the critical Weber numbers for trigging bouncing and splash increase with decreasing θ. However, the critical We of the boundary between the bouncing to other regimes in the low diameter ratio range is not sensitive to wettability owing to the relatively small diameter of solid spheres. For quantitatively describing the curvature effect, the boundaries between the deposition and bouncing regimes in the high diameter ratio range and between the bouncing and other regimes in the low diameter ratio range are established. Both the established models show satisfactory agreement with the boundaries in the phase diagrams.

Dynamics of droplet impact on a superhydrophobic disk

An experimental study is performed to investigate the effect of tangential velocity on the dynamics of a water droplet impacting on a spinning superhydrophobic surface. It is revealed that an increase in the tangential velocity results in the spreading of a droplet from symmetrical to asymmetrical shape on the superhydrophobic surface. Moreover, depending on the impact and tangential velocities, three behaviors are observed: bouncing, symmetrical splashing, and asymmetrical splashing. In the bouncing regime, it is found that the droplet contact time is independent of impact velocity and decreases as the tangential velocity increases. However, the maximum spreading diameter in this regime is a function of both the impact and the tangential velocities. Furthermore, a splashing threshold defined as WeRe1/21−kRe−1/2V/U2=K is introduced to estimate the transition between the bouncing, symmetrical splashing, and asymmetrical splashing regimes. It is revealed that the value of K in the present work (i.e., superhydrophobic spinning disk) is approximately 60% less than the K value obtained by other researchers for the case of aluminum spinning disk. Moreover, two values are found for k to define the boundaries between these three observed regimes.

Splashing behavior of impacting droplets on grooved superhydrophobic surfaces

During water droplet impingement onto a rice-leaf-inspired grooved superhydrophobic surface, the unidirectional textures can reduce the solid–liquid contact time through modifying the droplet impact dynamics. The influence of the groove geometry on the splashing of impacting droplets is still unrevealed. In this study, we experimentally identify the droplet bouncing and splashing regimes on grooved superhydrophobic surfaces of varying parameters. Asymmetric spreading and retracting of droplets are observed on the surfaces, accompanied by obvious liquid jets generated within the grooves. As the impact velocity increases, secondary droplets are ejected from the rim of the liquid jets, which is the onset of droplet splashing on the grooved superhydrophobic surfaces. We find that the critical Weber number for the splash of liquid jets decreases with the groove width but increases with the droplet diameter. Scaling analysis is performed to model the splashing criteria and explain its dependence on groove parameters and droplet properties. This research advances the understanding of droplet splashing dynamics on textured superhydrophobic surfaces, which is promising for some agricultural and industrial applications.

Non-linear resonant torus oscillations as a model of Keplerian disc warp dynamics

ABSTRACT Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime – non-linear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel non-linear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here, we uncover two distinct non-linear regimes as the warp amplitude is increased. Initially, we find a smooth modulation theory that describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalized secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory that predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasize the essential activation of non-linear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.

Theoretical Modelling of Droplet Extension on Hydrophobic Surfaces

In this work, droplet impact dynamics on hydrophobic surfaces under different wettability and impact conditions are examined numerically. Multi-phase finite volume simulations are carried out by employing volume-of-fluid scheme and are validated against experimental results. Numerous droplet impact experiments are performed by varying Weber number, Reynolds number and substrate contact angle. Sticking, bouncing and splitting regimes are identified. It is observed that, for the same Reynolds number, the droplet attaches, rebounds or fragments depending on the Weber number. A semi-analytical representation using a single mass-spring-dashpot model is employed for the prediction of droplet height evolution during spreading and retraction. The spring and damping coefficients required for the model are estimated from the empirical correlations for contact time and restitution coefficients obtained from the simulations. Even though the Reynolds number is found to influence the coefficient of restitution significantly, it is found to have negligible influence on contact time. The theoretical forecasting exhibited good agreement with simulated results and it gives a significant reduction in computational time compared to the conventional full-field continuum simulations.

Faraday waves under perpendicular electric field and their application to the walking droplet phenomenon

Vertically oscillating fluid surfaces have been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic waves in similar configurations. In the present work, the unification of both effects and their consequences on the stability of the surface. Given the versatility of electromagnetic fields, application to the phenomenon of walking droplets is suggested; the dispersion relation and bouncing regimes of and the force on the droplets are revisited, and feasible experimental configurations are proposed.

An experimental study of binary collisions of miscible droplets with non-identical viscosities

The dynamics of binary collisions of equi-diameter droplets with non-identical viscosities have been investigated experimentally and compared to previously generated data from identical droplet collisions (Al-Dirawi and Bayly in Phys Fluids 31(2):027105, 2019). Three hydroxypropyl methylcellulose (HPMC) aqueous solutions, 2%, 4%, and 8% HPMC, were used to generate the droplets of different viscosities, 2.8, 8.2, and 28.4 mPa s, respectively. High-speed imaging techniques were applied to observe and capture the collision outcomes. Collision outcomes were characterised and regime maps were generated. The non-identical viscosity droplet collisions produced regime maps with well-defined boundaries which are comparable in shape to the conventional regime maps of identical droplet collisions. The boundaries of the bouncing and reflexive separation regimes of the non-identical collisions show intermediate position between the identical cases of the low and the high viscosity droplets. However, the boundary of the stretching separation regimes of the non-identical collisions showed good agreement with the boundary of the identical case of the lower viscosity droplet. Moreover, the ability of models developed for predicting the regimes boundaries of collisions of identical viscosity droplets was assessed for the non-identical collisions. They proved capable in the non-identical cases, and the changes in adjustable parameters were consistent with the underlying physical basis of the models.Graphic abstract

Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies

We study the evolution of spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a non-singular bounce as in loop quantum cosmology, but with far more complex modified Friedmann dynamics with higher order than quadratic terms in energy density. For the kinetic energy dominated bounce, we obtain analytical solutions using different approximations and compare with numerical evolution for various physical variables. The relative error turns out to be less than $0.3\%$ in the bounce regime for both of the potentials. Generic features of dynamics, shared with loop quantum cosmology, are established using analytical and numerical solutions. Detailed properties of three distinct phases in dynamics separating bounce regime, transition stage and inflationary phase are studied. For the potential energy dominated bounce, we qualitatively describe its generic features and confirm by simulations that they all lead to the desired slow-roll phase in the chaotic inflation. However, in the Starobinsky potential, the potential energy dominated bounce cannot give rise to any inflationary phase. Finally, we compute the probability for the desired slow-roll inflation to occur in the chaotic inflation and as in loop quantum cosmology, find a very large probability for the universe to undergo inflation.

Droplet impact on cross-scale cylindrical superhydrophobic surfaces

Reducing the contact time between impacting droplets and superhydrophobic surfaces has attracted much attention in recent years due to the importance of controlling heat and mass transfer. Previous researchers have proposed several methods, such as lifting the droplets before the retraction, accelerating the retraction process, or splashing the droplets. One example includes symmetry-breaking surfaces, which were used to accelerate the droplet retraction to realize the fast detachment. However, the dependence of the contact time on impact velocity and surface structure scale remains unclear. Here, we experimentally study the droplet impact dynamics on cross-scale cylindrical superhydrophobic surfaces. The reduction of the contact time is achieved on the surfaces with a ridge smaller or larger than the droplets, spanning different bouncing regimes. We describe the droplet behaviors and propose theoretical models from the view of retraction speed to explain the contact time variations. The maximum reduction is observed to occur when the ridge diameter is close to that of the droplets, which is also predicted by the models.

Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio.

A thermodynamically consistent free energy model for fluid flows comprised of one gas and two liquid components is presented and implemented using the entropic lattice Boltzmann scheme. The model allows a high density ratio, up to the order of O(10^{3}), between the liquid and gas phases, and a broad range of surface tension ratios, covering partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of the fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive, and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.

Drops bouncing off macro-textured superhydrophobic surfaces

Recent experiments with droplets impacting macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. Here we present a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantifies the roles played by various external and internal forces. For the first time, accurate three-dimensional simulations involving realistic macro-textured surfaces are performed. After demonstrating that simulations reproduce experiments in a quantitative manner, the study is focused on analysing the flow situations beyond current experiments. We show that the experimentally observed reduction of contact time extends to higher Weber numbers, and analyse the role played by the texture density. Moreover, we report a nonlinear behaviour of the contact time with the increase of the Weber number for imperfectly coated textures, and study the impact on tilted surfaces in a wide range of Weber numbers. Finally, we present novel energy analysis techniques that elaborate and quantify the interplay between the kinetic and surface energy, and the role played by the dissipation for various Weber numbers.

Spatially and temporally resolved measurements of the temperature inside droplets impinging on a hot solid surface

Heat transfers at the impact of a droplet on a hot solid surface are investigated experimentally. Millimeter-sized water droplets impinge a flat sapphire window heated at 600 °C. The time evolution of the droplet temperature is characterized using the two-color laser-induced fluorescence technique. For that, a Q-switched Nd:YAG laser is used for the excitation of the fluorescence to obtain instantaneous images of the droplet temperature. Water is seeded with two fluorescent dyes, one sensitive to temperature (fluorescein disodium) and the other not (sulforhodamine 640). Owing to a wavelength shift between the dyes’ emissions, the fluorescence signal of the dyes can be detected separately by two cameras. The liquid temperature is determined with a good accuracy by doing the ratio of the images of the dyes’ fluorescence. A critical feature of the method is that the image ratio is not disturbed by the deformation of the impacting droplet, which affects the signals of the dyes almost identically. Experiments are performed in the conditions of film boiling. A thin vapor film at the interface between the droplet and the solid surface prevents the deposition of liquid on the hot solid surface. Measurements highlight some differences in the rate of heat transfers and in the temperature distribution within the droplet between the bouncing and splashing regimes of impact.

Could Gravitons from a Prior Universe Survive a (LQG Inspired) “Quantum Bounce” to Re-Appear in Our Present Universe?

We ask the question if a formula for entropy, as given by with a usual value ascribed of initial entropy of the onset of inflation can allow an order of magnitude resolution of the question of if there could be a survival of a graviton from a prior to the present universe, using typical Planckian peak temperature values of . We obtain values consistent with up to 1038 gravitons contributing to an energy value of if we assume a relic energy contribution based upon each graviton initially exhibiting a frequency spike of 1010 Hz. The value of is picked from looking at the aftermath of what happens if there exists a quantum bounce with a peak density value of [1] in a regime of LQG bounce regime radii of the order of magnitude of meters. The author, in making estimates specifically avoids using , by setting the chemical potential for ultra high temperatures for reasons which will be brought up in the conclusion.

Bounce regime of droplet collisions: A molecular dynamics study

Droplet collisions have complex dynamics, which can lead to many different regimes of outcomes. The head-on collision and bounce back regime has been observed in previous experiments but numerical simulations using macro- or mesoscale approaches have difficulties reproducing the phenomena, because the interfacial regions are not well resolved. Previous molecular dynamics (MD) simulations have not reproduced the bounce regime either but have reported the coalescence and/or shattering regimes. To scrutinize the dynamics and mechanisms of binary collisions especially the interfacial regions, head-on collision processes of two identical nano-droplets with various impact velocities both in vacuum and in an ambient of nitrogen gas are investigated by MD simulations. With the right combination of the impact velocity and ambient pressure, the head-on collision and bounce back phenomenon is successfully reproduced. The bounce phenomena are mainly attributed to the “cushion effect” of the in-between nitrogen molecules and evaporated water molecules from the two nano-droplets. The analysis has verified and also extended the current gas film theory for the bounce regime through including the effects of evaporated water molecules (vapour). Some similarities and some dissimilarities between nanoscale and macro-/meso-/microscale droplet collisions have been observed. The study provides unprecedented insight into the interfacial regions between two colliding droplets.

Phase diagram for droplet impact on superheated surfaces

We experimentally determine the phase diagram for impacting ethanol droplets on a smooth, sapphire surface in the parameter space of Weber number $\mathit{We}$ versus surface temperature $T$. We observe two transitions, namely the one towards splashing (disintegration of the droplet) with increasing $\mathit{We}$, and the one towards the Leidenfrost state (no contact between the droplet and the plate due to a lasting vapour film) with increasing $T$. Consequently, there are four regimes: contact and no splashing (deposition regime), contact and splashing (contact–splash regime), neither contact nor splashing (bounce regime), and finally no contact, but splashing (film–splash regime). While the transition temperature $T_{L}$ to the Leidenfrost state depends weakly, at most, on $\mathit{We}$ in the parameter regime of the present study, the transition Weber number $\mathit{We}_{C}$ towards splashing shows a strong dependence on $T$ and a discontinuity at $T_{L}$. We quantitatively explain the splashing transition for $T<T_{L}$ by incorporating the temperature dependence of the physical properties in the theory by Riboux & Gordillo (Phys. Rev. Lett., vol. 113(2), 2014, 024507; J. Fluid Mech., vol. 772, 2015, pp. 630–648).

Superhydrophobic-like tunable droplet bouncing on slippery liquid interfaces.

Droplet impacting on solid or liquid interfaces is a ubiquitous phenomenon in nature. Although complete rebound of droplets is widely observed on superhydrophobic surfaces, the bouncing of droplets on liquid is usually vulnerable due to easy collapse of entrapped air pocket underneath the impinging droplet. Here, we report a superhydrophobic-like bouncing regime on thin liquid film, characterized by the contact time, the spreading dynamics, and the restitution coefficient independent of underlying liquid film. Through experimental exploration and theoretical analysis, we demonstrate that the manifestation of such a superhydrophobic-like bouncing necessitates an intricate interplay between the Weber number, the thickness and viscosity of liquid film. Such insights allow us to tune the droplet behaviours in a well-controlled fashion. We anticipate that the combination of superhydrophobic-like bouncing with inherent advantages of emerging slippery liquid interfaces will find a wide range of applications.

Pancake bouncing on superhydrophobic surfaces.

Engineering surfaces that promote rapid drop detachment1,2 is of importance to a wide range of applications including anti-icing3–5, dropwise condensation6, and self-cleaning7–9. Here we show how superhydrophobic surfaces patterned with lattices of submillimetre-scale posts decorated with nano-textures can generate a counter-intuitive bouncing regime: drops spread on impact and then leave the surface in a flattened, pancake shape without retracting. This allows for a four-fold reduction in contact time compared to conventional complete rebound1,10–13. We demonstrate that the pancake bouncing results from the rectification of capillary energy stored in the penetrated liquid into upward motion adequate to lift the drop. Moreover, the timescales for lateral drop spreading over the surface and for vertical motion must be comparable. In particular, by designing surfaces with tapered micro/nanotextures which behave as harmonic springs, the timescales become independent of the impact velocity, allowing the occurrence of pancake bouncing and rapid drop detachment over a wide range of impact velocities.

Influence of a local change of depth on the behavior of walking oil drops

Bouncing liquid silicone oil drops on a vertically oscillating bath of the same liquid were studied experimentally. The different bouncing regimes previously described in the literature were observed, with transitions depending mainly on the droplet size and the forcing acceleration of the oil bath. In a particular range of forcing amplitudes, just below the Faraday instability threshold where standing waves appear on the free surface, walking drops traveling at a constant velocity over the surface were observed, consistent with previous studies. The influence of a local change of depth on this walking behavior was studied by submerging an obstacle in the oil bath. Notably different to the study of Eddi et al. (2009) [1], the depth change was such that walking was still observed over the obstacle. Previously unobserved drop trajectories, including trapping of a walking drop over the obstacle, crossing for non-normal drop approach to the obstacle, and reflection from the rear face of the obstacle were observed and explained in light of recent results and models in the literature.