Spherical Bubble Research Articles

The Nusselt number of a hot sphere levitated by a volatile pool

When placed at the surface of a volatile liquid, a sphere of hot dense non-volatile material remains suspended until it cools sufficiently. The duration of this ‘inverse Leidenfrost’ phenomenon depends on the Nusselt number $Nu$ of the sphere, itself determined by flow in the film of vapour separating particle and liquid. It is shown that provided the Nusselt number is large, it can be calculated numerically using only the Laplace relation and the equations governing the thin film; patching to a solution for the outer thick film is not necessary. This method is demonstrated by using it to determine $Nu$ for a sphere sufficiently small that in the governing equations, the acceleration due to gravity is negligible except where multiplied by the density of the sphere. Numerical results giving $Nu$ as a function of a dimensionless measure of sphere weight are supplemented with analysis showing that, when the weight is of the order of the maximum supportable by surface tension alone, the film consists of a spherical bubble cap bounded by its contact rim. The solutions for these regions are coupled: although the apparent contact angle $\chi$ for the cap is determined within the rim, its value depends on the flow rate arriving from the cap as well as on the additional evaporation from the rim. The latter acts to reduce $\chi$ from the value it would otherwise have, thereby reducing the thickness of the entire cap. For the example treated here, the value of $Nu$ is doubled by this mechanism.

IRROTATIONAL FLOW DUE TO FORCED OSCILLATIONS OF A BUBBLE

Abstract The behaviour of an axisymmetric bubble in a pure liquid forced by an acoustic pressure field is analysed. The bubble is assumed to have a sharp deformable interface, which is subject both to surface tension and to Rayleigh viscosity damping. Two modelling regimes are considered. The first is a linearized solution, based on the assumption of small axisymmetric deformations to an otherwise spherical bubble. The second involves a semi-numerical solution of the fully nonlinear problem, using a novel spectral method of high accuracy. For large-amplitude nonspherical bubble oscillations, the fully nonlinear solutions show that a complicated resonance structure is possible and that curvature singularities may occur at the interface, even in the presence of surface tension. Rayleigh viscosity at the interface prevents singularity formation, but eventually causes the bubble to become purely spherical unless shape-mode resonances occur. An extended analysis is also presented for purely spherical bubbles, which allows for a more detailed study of the effects of resonance and the Rayleigh viscosity at the bubble surface.

Dynamic Sliding Mode Control of Spherical Bubble for Cavitation Suppression

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mechanical parts such as centrifugal pumps. The difference in pressure in a fluid is the result of varying temperatures. One way to eliminate cavitation is to reduce the radius of the bubbles to zero before they reach high-pressure areas, using a robust approach. In this paper, sliding mode control is used for this purpose due to its invariance property. To force the radius of the bubbles toward zero and prevent chattering, a new dynamic sliding mode control approach is used. In dynamic sliding mode control, chattering is removed by passing the input control through a low-pass filter, such as an integrator. A general model of the spherical bubble is used, transferred to the state space, and then a state proportional-integral feedback is applied to obtain a linear system with a new input control signal. A comparison is also made with traditional sliding mode control using state feedback, providing a trusted comparison.

Linear pressure waves in mono- and poly-disperse bubbly liquids: Attenuation and propagation speed in slow and fast and evanescent modes

Using volumetric averaged equations from a two-fluid model, this study theoretically investigates linear pressure wave propagation in a quiescent liquid with many spherical gas bubbles. The speed and attenuation of sound are evaluated using the derived linear dispersion. Mono- and poly-disperse bubbly liquids are treated. To precisely describe the attenuation effect, some forms of bubble dynamics equations and temperature gradient models are employed. Focusing on the dissipative effect, we analyze the stop band that occurs in the linear dispersion relation. In the two-fluid model, even if the dissipation effect is considered, the inconvenience that the wavenumber diverges to infinity in the resonance frequency cannot be resolved. Additionally, the validity of terminating that wavenumber value in the middle of the frequency is demonstrated. To determine a linear dispersion relation that can exactly predict thermal conduction and acoustic radiation, wave propagation velocities and attenuation coefficients are compared with some experimental data and existing models. The results show that thermal conduction and acoustic radiation should be set appropriately to accurately predict the propagation velocity and attenuation except in the high frequency range, the phase velocity in the resonance frequency range, or the attenuation in the high frequency range.

A generalized kinetic theory of Ostwald ripening in porous media

Partially miscible bubbles (e.g., CO2) trapped inside a porous medium and surrounded by a wetting phase (e.g., water) occur in a number of applications including underground hydrogen storage, geologic carbon sequestration, and the operation of electrochemcial devices such as fuel cells and electrolyzers. Such bubbles evolve due to a process called Ostwald ripening that is driven by differences in their interfacial curvature. For spherical bubbles, small bubbles shrink and vanish while feeding into larger ones, resulting in one large bubble at equilibrium. Within the confinement of a porous medium, however, bubbles can attain a distribution of sizes at equilibrium that have identical curvature. This work concerns itself with the formulation of a kinetic theory that predicts the statistical evolution of bubble states, defined as the sizes of the pores within which bubbles are trapped and the extent to which those pores are saturated with bubbles. The theory consists of a population balance equation and appropriate closure approximations. Systematic comparisons against a previously published pore network model (PNM) are conducted to validate the theory. Our theory generalizes existing variants in the literature limited to spherical bubbles trapped in homogeneous media to non-spherical (deformed) bubbles inside microstructures with arbitrary heterogeneity and spatial correlation in pore/throat sizes. We discuss the applicability, limitations, and implications of the theory towards future extensions.

Incorporating the cosmological constant in a modified uncertainty principle

This study explores the cosmological constant problem and modified uncertainty principle within a unified framework inspired by a void-dominated scenario for cosmology. In a recent paper [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Mon. Not. R. Astron. Soc. 511, L82 (2022)], voids were modeled as spherical bubbles of similar average sizes, and the surface energy on the voids’ borders was calculated across various scales in a heuristic manner. We show that these result in a significant discrepancy of approximately [Formula: see text] between the cosmological constant values from the minimum to the maximum radii of bubbles. Furthermore, when considering the generalized form of the uncertainty principle with both minimum and maximum lengths, i.e. [Formula: see text], a similar order of discrepancy is observed between [Formula: see text] and [Formula: see text], indicating that [Formula: see text]. As a primary outcome of this finding, we offer a novel uncertainty principle that incorporates a nonzero cosmological constant.

Numerical simulation of scattering of TWIPS by underwater air bubble

Abstract The interaction of water with the subsurface of sea-ice leads to the generation of air bubbles. This heterogeneity results in additional challenges for unmanned underwater vehicles (UUV) conducting active detection in the upper water column of the Arctic Ocean. Under excitation by a high-amplitude acoustic source, asymmetric oscillations of the bubble are generated due to the high compressibility of gas, which further leads to acoustic scattering showing nonlinear characteristics. The corresponding signals may interfere with or even mask the echoes from potential targets, which are often linear scatterers, ultimately impairing the UUV’s active sensing capabilities under the sea-ice. Twin Inverted Pulse Sonar (TWIPS) is an underwater detection technique consisting of sending two pulse signals of equal amplitude but with opposing phases, benefiting from the difference in the responses of the bubble and target and the resulting echo signals for the eventual distinguishing. In this study, a numerical modeling of underwater bubbles for the acoustic study is developed by making use of both multiphysics and moving mesh features of Comsol. Numerical simulations were conducted to investigate the nonlinear feature of acoustic scattering from air bubbles. These results are then compared with analytical results for verification. Monochromatic signals and TWIPS at different frequencies are used as excitation signals, and the response of spherical air bubbles and the resulting scattered wave field are calculated, compared, and analyzed.

On the transient dynamics of laser-induced cavitation bubbles near the end of a slender cylinder

In this work, we perform high-speed imaging and numerical simulation to investigate the transient dynamics of cavitation bubbles near the end of a slender cylinder. The bubble dynamics can be categorized into four distinct regimes in terms of the types of bubble collapse, corresponding to the regular jet, needle jet, in-phase double jets, and anti-phase double jets, respectively, depending on two dimensionless parameters, the normalized cylinder radius η (=rc/Rmax, where rc is the cylinder radius and Rmax is the spherical bubble radius at maximum expansion), and the dimensionless standoff distance γ (=SD/Rmax, where SD is the standoff distance between the end surface of the cylinder and bubble center). The peak velocity of the liquid jet could easily reach a supersonic state in the regime of the needle jet when the cavitation bubble collapses near a slender cylinder, and the maximum jet velocity can reach up to 635 m/s. Quantitative analysis of the evolution of pressure distribution also indicates that the end surface of the cylinder will have strong hydrodynamic pressure loading, particularly for the case of η=0.3 and γ ranging from 0.5 to 0.83. Additionally, we find that the collapse time of the cavitation bubble near a slender cylinder is close to the Rayleigh collapse time. We believe that our findings can be valuable in mitigating or utilizing cavitation near solid cylinders.

Theoretical study on the movements of bubbles

The radial and translational motions of multiple interacting spherical bubbles are obtained using classical Newton mechanics. It is seen that bubbles not only move in straight line, but also in circular motion. The tracks of the bubbles show that the interactions among them include attractive, repulsive and dynamic equilibrium. There are three types of straight line corresponding to attraction, coexistence of attraction and repulsion and dynamic equilibrium, and two types of circular movement corresponding to attraction and dynamic equilibrium. The results can provide an explanation for cavitation chain and profile in cavitation field.

Experimental study on the effect of Tin-doped copper oxide capillary-porous surfaces on pool boiling heat transfer performance

The novel tin-doped copper oxide capillary-nano-porous surfaces were created using the easy and affordable sol-gel method. The pool's boiling incipience wall superheat on a capillary-nano-porous surface was lower than a non-coating surface. Bubble flow visualization investigation demonstrates that the coating's shape can significantly affect the processes involved in improving heat transmission. An investigation of the nano-porous surface's long-term stability was conducted using water. Repeated cycles of studies on created nano-porous surfaces revealed a little divergence in wall superheat and surface shape. The present study's tin-doped copper oxide coated surface (Sn-CuO-600) has a higher CHF (critical heat flux) and HTC (heat transfer coefficient). Heat transmission by boiling rises when a substantial quantity of bubbles are rapidly evacuated from the heating exterior. It is observed that a greater quantity of tiny, spherical bubbles are continually growing on the superhydrophilic Sn-CuO-600 surface. Compared to the plain copper surface, the Sn-CuO-600 surface experiences a significant reduction in bubble departure times. The rate of bubble formation is increased by superhydrophilic surfaces, which also reduce bubble dimensions and release times. Consequently, the Sn-CuO-600 surfaces exhibit superior heat transfer ability throughout boiling.

Design of eco-friendly antifreeze peptides as novel inhibitors of gas-hydration kinetics.

In this study, peptides designed using fragments of an antifreeze protein (AFP) from the freeze-tolerant insect Tenebrio molitor, TmAFP, were evaluated as inhibitors of clathrate hydrate formation. It was found that these peptides exhibit inhibitory effects by both direct and indirect mechanisms. The direct mechanism involves the displacement of methane molecules by hydrophobic methyl groups from threonine residues, preventing their diffusion to the hydrate surface. The indirect mechanism is characterized by the formation of cylindrical gas bubbles, the morphology of which reduces the pressure difference at the bubble interface, thereby slowing methane transport. The transfer of methane to the hydrate interface is primarily dominated by gas bubbles in the presence of antifreeze peptides. Spherical bubbles facilitate methane migration and potentially accelerate hydrate formation; conversely, the promotion of a cylindrical bubble morphology by two of the designed systems was found to mitigate this effect, leading to slower methane transport and reduced hydrate growth. These findings provide valuable guidance for the design of effective peptide-based inhibitors of natural-gas hydrate formation with potential applications in the energy and environmental sectors.

Viscous Rayleigh–Taylor instability at a dynamic interface in spherical geometry

In their study, Terrones et al. [“Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface,” Phys. Fluids 32, 094105 (2020)] elucidated that investigations into the viscous Rayleigh–Taylor instability (RTI) in spherical geometry at a quiescent interface yield significant physical insights. Yet, the complexity amplifies when addressing a dynamic spherical interface pertinent to engineering and scientific inquiries. The dynamics of RTI, particularly when influenced by the Bell–Plesset effects at such interfaces, offers a rich tapestry for understanding perturbation growth. The evolution of this instability is describable by a coupled set of equations, allowing numerical resolution to trace the radius evolution and instability characteristics of a bubble akin to the implosion scenario of a fusion pellet in inertial confinement fusion scenarios. The investigation encompasses the impact of viscosity, external pressure, discrete mode, and a surface-tension-like force on the interfacial instability. In general, the oscillation of the bubble radius exhibits a decay rate that diminishes with increasing Reynolds number (Re). It is important to note that the growth of the perturbed amplitude is not only solely determined by the mechanical properties of the fluid but also by the dynamics of the interface. The low-order modal (n<20) disturbance is dominant with relatively high Reynolds numbers. There is a specific mode corresponding the maximum in amplitude of perturbation in the linear phase, and the mode decreases as the Re decreases. The application of external pressure noticeably accelerates the bubble's oscillation and impedes its shrinkage, thereby preventing the bubble from collapsing completely. The increase in external pressure also promotes the transition from the first peak to the trough of the disturbance. At higher-order modes, the fluctuation of the disturbance curve tends to be uniform. The ultrahigh-order modes require a strong enough pressure to be excited. In addition, the smaller Weber number (We) helps to accelerate the bubble oscillation and promote the fluctuation of the disturbance amplitude, but has no significant effect on the time of the disturbance peak. These findings contribute to a deeper understanding of interfacial instabilities in the context of spherical bubbles and, especially, for the dynamics of fusion capsules in inertial confinement fusion.

Muzzle bubble dynamics characterization of underwater launching

To comprehensively understand the dynamic behavior of muzzle bubbles during underwater launching, an emptying process aligned with the muzzle flow characteristics is established and an evaporative condensation mechanism is modeled according to the high temperature and pressure properties of the propellant gas. Utilizing the spherical bubble theory, which comprises the inflation process and evaporative condensation effects, the dynamics of muzzle bubbles and their corresponding pressure waves are investigated. The numerical simulation results well agree with the experimental observations in terms of bubble radius and near-field pressure waves. Furthermore, the influence of two key factors on the bubble dynamics is examined: underwater launching depth and initial muzzle pressures. The results illustrate that the inflation process needs to be accurately described for precise pressure wave predictions. Using the evaporation condensation model, the bubble radius and frequency can be accurately characterized. Moreover, the launching depth influences the free expansion radius and oscillation frequency mostly due to the increase in hydrostatic pressure, which decreases by 33% and increases by 150% in the 1–20 m range, respectively. The initial muzzle pressure affects the initial expansion velocity and initial shock wave mainly due to the increase in the mass flow rate, which increase by 56% and 82% in the 35–65 MPa range, respectively.

Investigations on the shock wave induced by collapse of a toroidal bubble.

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. In this study, we present a systematic analysis of the collapse of a toroidal bubble in an open field or adjacent to a flat wall using high-fidelity numerical simulation. To maintain the sharpness of the interface, we employ the interface compression technique and the boundary variation diminishing approach within the two-phase model. Our 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. Based on the directional characteristics of pressure wave propagation from collapsing toroidal bubbles, toroidal-shaped pressure vessels can be designed as buoyancy materials for deep submersibles. This design enables the focused release of energy in a specific direction, effectively minimizing the destructive chain reaction caused by the implosion.

Numerical simulation for pressure fluctuations caused by the growth of a single boiling bubble

The pressure fluctuations caused by the rapid volume changes during the initial growth stage for a single bubble are crucial excitations of boiling induced vibration. Therefore, it is necessary to accurately model the dynamic behavior of bubbles during this stage to obtain reasonable excitation forces, which can be used to estimate the vibration response of structures. The present study develops a dynamics model, which is verified and validated to be applicable to the growth of spherical bubbles in infinite superheated liquid and hemispherical bubbles growing on a vertical heated surface. The effects of mass transfer are considered for the vapor-liquid interface motion, and the temperature variations at the liquid side are determined by the finite difference method. The numerical data match well with the theoretical and experimental results, and the characteristics of the excitation forces caused by a single boiling bubble are obtained and analyzed. In addition, the influences of superheat, accommodation coefficient for phase change, and the temperature gradient at the liquid side on excitation forces caused by bubble growth are studied. The results show that the temperature distributions near the heated surface strongly affect the frequency domain characteristics of the excitation forces.

Data-driven acoustic control of a spherical bubble using a Koopman linear quadratic regulator.

Koopman operator theory has gained interest as a framework for transforming nonlinear dynamics on the state space into linear dynamics on abstract function spaces, which preserves the underlying nonlinear dynamics of the system. These spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to nonlinear systems. Here, a Koopman linear quadratic regulator (KLQR) was used to acoustically control the nonlinear dynamics of a single spherical bubble, as described by the well-known Rayleigh-Plesset equation, with several objectives: (1) simple harmonic oscillation at amplitudes large enough to incite nonlinearities, (2) stabilization of the bubble at a nonequilibrium radius, and (3) periodic and quasiperiodic oscillation with multiple frequency components of arbitrary amplitude. The results demonstrate that the KLQR controller can effectively drive a spherical bubble to radially oscillate according to prescribed trajectories using both broadband and single-frequency acoustic driving. This approach has several advantages over previous efforts to acoustically control bubbles, including the ability to track arbitrary trajectories, robustness, and the use of linear control methods, which do not depend on initial guesses.

Effects of surface tension on the collapse time of an empty bubble

The collapse of an empty spherical bubble in an ideal liquid, in the absence of viscosity and surface tension, was studied by Lord Rayleigh. Using energy conservation, he derived an exact expression for the total collapse time as a function of the initial radius of the bubble, the density of the liquid, and the far-field pressure. In the present work, we extend Rayleigh's expression to include surface tension effects. Results are found to depend on a dimensionless parameter ϵ that measures the ratio between the work done by surface tension and that done by pressure during the collapse. This parameter is small for large bubbles but can be of order unity or larger for bubbles of small radius and, eventually, small pressure. We show that the ratio between the collapse time in the presence of surface tension and Rayleigh's collapse time is proportional to a definite integral that is a smooth, monotonically decreasing function of ϵ. This function can be easily bounded analytically for any value of ϵ, yielding a simple and accurate approximation for the collapse time that, for all practical purposes, provides a complete analytical solution to the problem at hand. We finally extend results to the case of a hyperspherical collapsing empty bubble.

Bubble Characteristics Required for the Complete Removal of Alumina Inclusions from Steel Melts

Gas bubbling can be an effective means to float out alumina inclusions from liquid steel in a ladle. However, large spherical cap bubbles are formed when using porous plugs, as the liquid steel is nonwetting to the porous refractory. These bubbles rise rapidly through the liquid steel, forming a fast‐moving bubble plume, restricting contact times. Sized microbubbles, by contrast, have now been generated in liquid metals by shearing methods, involving linear crossflows to an entering flow of gas, or alternatively by rotational shearing. Combined with these convective shearing forces, local kinetic energy of turbulence can also play an important part in determining final microbubble size distributions. As microbubbles have much smaller rise velocities and present a far greater inclusion capture surface area than those of a single large bubble of the same gross volume, this will allow us to remove sub‐50 μm inclusions from liquid steel. It is expected that this goal will require a redesign of current ladle shrouds.

Cavity shape measurement on propeller blade surface by combination line CCD camera measurement method

ABSTRACT A new combination-line-CCD camera method has been developed to accurately measure three-dimensional propeller blade cavitation shapes and volumes, which strongly correlate with pressure fluctuations. The effectiveness of this system was validated through model experiments conducted in NMRI's large cavitation tunnel using a propeller for a 749GT coastal vessel. The accuracy was verified by comparing the estimated pressure fluctuation, derived from the cavity volume, with the pressure sensor measurements. In the estimation, the unsteady cavity is replaced by a moving spherical bubble with a varying radius, and the pressure fluctuation induced by the sphere is calculated. Applying the proposed method to the experimental cavity shape data yielded pressure fluctuation estimates that closely matched the pressure sensor measurements. This result demonstrates the strong correlation between the time variability of the cavity volume and the pressure fluctuation induced by cavitation in the model tests.

Experimental and Theoretical Design of Reinforced Bubble Deck Concrete (RBDC) Slab: A Review

Slabs are vital for supporting loads and forming the foundation for structures' floors and roofs, classified as one-way or two-way based on deflection characteristics. A recent innovation in construction, the Reinforced Bubble Deck Concrete (RBDC) slab, integrates spherical or elliptical hollow bubbles within the slab for reinforcement, reducing concrete usage without compromising structural integrity. This unconventional approach diverges from traditional methods. The manuscript thoroughly reviews existing literature on the design and testing of Reinforced Bubble Deck Concrete slabs, aiming to explore their diverse characteristics as observed in international research studies. Findings demonstrate that these slabs offer a sustainable and cost-effective alternative to traditional floor slabs. Their capacity to reduce weight while maintaining strength suggests they could revolutionize construction practices, potentially replacing conventional floor slabs in various projects.