Circular Bubble Research Articles

Radius evolution for the synchronous collapse of a circular vapor bubble cluster

The radius evolution for the synchronous collapse motion of a circular vapor bubble cluster in an ideal and infinite fluid is studied. With the assumption that all bubbles are evenly distributed around the circumference and have the same initial conditions, we establish the associated governing equation for this case from a modified Rayleigh–Plesset equation. The inverted analytical solution in the form of t=t(r) and analytical approximations in the form of r=r(t) for the radius evolution to the initial value problem of the dimensionless governing equation are derived. These novel analytical approximations extend the previous ones for a single bubble by adding the effects of surface tension and multiple bubbles. In addition, we point out that the analytical results and dynamic behaviors for multiple bubbles will degenerate into the corresponding ones for single bubbles when the radius of the bubble cluster approaches to infinity.

Electrical Impedance Tomography of Industrial Two-Phase Flow Based on Radial Basis Function Neural Network Optimized by the Artificial Bee Colony Algorithm.

In electrical impedance tomography (EIT) detection of industrial two-phase flows, the Gauss-Newton algorithm is often used for imaging. In complex cases with multiple bubbles, this method has poor imaging accuracy. To address this issue, a new algorithm called the artificial bee colony-optimized radial basis function neural network (ABC-RBFNN) is applied to industrial two-phase flow EIT for the first time. This algorithm aims to enhance the accuracy of image reconstruction in electrical impedance tomography (EIT) technology. The EIDORS-v3.10 software platform is utilized to generate electrode data for a 16-electrode EIT system with varying numbers of bubbles. This generated data is then employed as training data to effectively train the ABC-RBFNN model. The reconstructed electrical impedance image produced from this process is evaluated using the image correlation coefficient (ICC) and root mean square error (RMSE) criteria. Tests conducted on both noisy and noiseless test set data demonstrate that the ABC-RBFNN algorithm achieves a higher ICC value and a lower RMSE value compared to the Gauss-Newton algorithm and the radial basis function neural network (RBFNN) algorithm. These results validate that the ABC-RBFNN algorithm exhibits superior noise immunity. Tests conducted on bubble models of various sizes and quantities, as well as circular bubble models, demonstrate the ABC-RBFNN algorithm's capability to accurately determine the size and shape of bubbles. This outcome confirms the algorithm's generalization ability. Moreover, when experimental data collected from a 16-electrode EIT experimental device is employed as test data, the ABC-RBFNN algorithm consistently and accurately identifies the size and position of the target. This achievement establishes a solid foundation for the practical application of the algorithm.

Low-temperature cross-sensitivity strain sensor based on a microbubble Fabry-Pérot interferometer with a thin wall

A Fabry-Pérot interferometer (FPI) strain sensor with low-temperature cross-sensitivity is prepared by a simple, cost-effective, and safe process. The sensor is fabricated by splicing two segments of the single-mode fiber and several arc discharges to form a unique circular bubble and a thin wall. The thin air-bubble wall deforms more easily under stress due to the good stress concentration ability of the tapered structure, resulting in a high strain sensitivity of 10.78 pm/µε. The temperature sensitivity of the sensor is 1.24 pm/°C and the temperature cross-sensitivity is 0.115 με/°C in the temperature range of 25 to 200 °C, which reduces the temperature-induced measurement error. The experimental results show that the sensor with good stability and repeatability has large commercial potential in measuring strain in complex environments.

English

Recently, there has been a high interest in using lightweight aluminum foams for automotive, railway and aerospace operations. Because of its high ductility and deformability, Aluminum foam is generally used for energy absorption for crashworthiness applications. To keep safe and avoid occupant injuries, it is necessary to absorb the kinetic energy generated during impact. Thus, to absorb high kinetic energy, the crash box material needs a special material microstructure, which is light in weight and can absorb further energy than the being one like CaCo3, CBC, or SiC. B4C etc. In particular, the analysis of energy absorption of aluminum foam in automotive for energy absorption applications is limited. The main objective of this exploration is to analyze and optimize the porosity size and voids percentage on impact energy absorption of aluminum foam using a numerical approach. For this purpose, first, fifteen CAD Al foam samples were developed by using Digimat multi-scale material modeling software. Second, cubic elements with circular bubble shape at 5, 10 and 15 void percentage and at 1.5 mm, 2 mm,2.5 mm, 3 mm and 3.5 mm bubble sizes were modeled. Finally, the numerical analysis of impact energy by using ANSYS workbench19.2 Explicit dynamics by applying initial low velocity was performed. The parameters were compared to each other to optimize the proper percentage composition and cell size for the best energy absorption applications. The effects of bubble shape, foaming agent and percentage composition on energy immersion were discussed. In this study, the analysis was fulfilled by determining and comparing the energy absorptions of all the models and, finally, comparing them with existing foaming agents.

Interactions between a central bubble and a surrounding bubble cluster

The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally spaced and own the same initial conditions as the central bubble. The unified theory for bubble dynamics [35] is applied to model the interaction between the central bubble and the circular bubble cluster. To account for the effect of the propagation time of pressure waves, the emission source of the wave is obtained by interpolating the physical information on the time axis. An underwater explosion experiment with two bubbles of different scales is used to validate the theoretical model. The effect of the bubble cluster with a variation in scale on the pulsation characteristics of the central bubble is studied.

Performance tests of geodetic receivers with tilt sensors in obstructed environments using the NRTK GNSS technique

Abstract The Department of Lands (DOL), Thailand, has adopted the Network-based Real-Time Kinematic (NRTK) Global Navigation Satellite System (GNSS) surveying technique using a Virtual Reference Station (VRS) to support cadastral surveys since 2011. Determining accurate coordinates of parcel boundary markers at building corners or near fences and walls is difficult because a GNSS range pole cannot be leveled with a circular bubble. This study aims to evaluate the performance of the receivers equipped with tilt sensors for horizontal and vertical positioning. Two types of tilt sensors used for evaluation were a magnetometer and micro-electro-mechanical system (MEMS) and an inertial measurement unit (IMU). Conducting the NRTK GNSS surveying tests was based on the pole tilt angles of 0°, 15°, 25°, 35°, and 45° from a plumb line in controlled and obstructed environments. The IMU-based tilt sensor had more advantage of accurately positioning over the MEMS sensor. The results showed that using the IMU, better than 4 cm horizontal positioning accuracy was achievable when the pole was tilted by 15° or less under non-multipath and open-sky conditions. The vertical accuracy was of a few centimeter levels and least sensitive to tilt angles using either type of sensor. However, none of the sensors precisely compensated for pole tilt in strong-multipath and complex environments, causing increased horizontal errors in decimeter levels.

Plasma breakdown in bubbles passing between two pin electrodes

The ignition of plasmas in liquids has applications from medical instrumentation to manipulation of liquid chemistry. Formation of plasmas directly in a liquid often requires prohibitively large voltages to initiate breakdown. Producing plasma streamers in bubbles submerged in a liquid with higher permittivity can significantly lower the voltage needed to initiate a discharge by reducing the electric field required to produce breakdown. The proximity of the bubble to the electrodes and the shape of the bubbles play critical roles in the manner in which the plasma is produced in, and propagates through, the bubble. In this paper, we discuss results from a three-dimensional direct numerical simulation (DNS) used to investigate the shapes of bubbles formed by injection of air into water. Comparisons are made to results from a companion experiment. A two-dimensional plasma hydrodynamics model was then used to capture the plasma streamer propagation in the bubble using a static bubble geometry generated by the DNS The simulations showed two different modes for streamer formation depending on the bubble shape. In an elliptical bubble, a short electron avalanche triggered a surface ionization wave (SIWs) resulting in plasma propagating along the surface of the bubble. In a circular bubble, an electron avalanche first traveled through the middle of the bubble before two SIWs began to propagate from the point closest to the grounded electrode where a volumetric streamer intersected the surface. In an elliptical bubble approaching a powered electrode in a pin-to-pin configuration, we experimentally observed streamer behavior that qualitatively corresponds with computational results. Optical emission captured over the lifetime of the streamer curve along the path of deformed bubbles, suggesting propagation of the streamer along the liquid/gas boundary interface. Plasma generation supported by the local field enhancement of the deformed bubble surface boundaries is a mechanism that is likely responsible for initiating streamer formation.

Bubbles of nothing in binary black holes and black rings, and viceversa

We argue that expanding bubbles of nothing are a widespread feature of systems of black holes with multiple or non-spherical horizons, appearing as a limit of regions that are narrowly enclosed by the horizons. The bubble is a minimal cycle that links the Einstein-Rosen bridges in the system, and its expansion occurs through the familiar stretching of space in black hole interiors. We demonstrate this idea (which does not involve any Wick rotations) with explicit constructions in four and five dimensions. The geometries of expanding bubbles in these dimensions arise as a limit of, respectively, static black hole binaries and black rings. The limit is such that the separation between the two black holes, or the inner hole of the black ring, becomes very small, and the horizons of the black holes correspond to acceleration horizons of the bubbles. We also explain how a five-dimensional black hole binary gives rise to a different type of expanding bubble. We then show that bubble spacetimes can host black hole binaries and black rings in static equilibrium, with their gravitational attraction being balanced against the background spacetime expansion. Similar constructions are expected in six or more dimensions, but most of these solutions can be obtained only numerically. Finally, we argue that the Nariai solution can be regarded as containing an expanding circular bubble of nothing.

Unraveling hidden rules behind the wet-to-dry transition of bubble array by glass-box physics rule learner

A liquid–gas foam, here called bubble array, is a ubiquitous phenomenon widely observed in daily lives, food, pharmaceutical and cosmetic products, and even bio- and nano-technologies. This intriguing phenomenon has been often studied in a well-controlled environment in laboratories, computations, or analytical models. Still, real-world bubble undergoes complex nonlinear transitions from wet to dry conditions, which are hard to describe by unified rules as a whole. Here, we show that a few early-phase snapshots of bubble array can be learned by a glass-box physics rule learner (GPRL) leading to prediction rules of future bubble array. Unlike the black-box machine learning approach, the glass-box approach seeks to unravel expressive rules of the phenomenon that can evolve. Without known principles, GPRL identifies plausible rules of bubble prediction with an elongated bubble array data that transitions from wet to dry states. Then, the best-so-far GPRL-identified rule is applied to an independent circular bubble array, demonstrating the potential generality of the rule. We explain how GPRL uses the spatio-temporal convolved information of early bubbles to mimic the scientist’s perception of bubble sides, shapes, and inter-bubble influences. This research will help combine foam physics and machine learning to better understand and control bubbles.

Advanced analysis of bubble columns: Comparison of Euler/Lagrange simulations and experiments under CO2 chemisorption conditions

The chemical absorption reaction of CO2 in a circular bubble column reactor was simulated with an Euler/Lagrange CFD method and results were compared with data from a laboratory scale bubble column. The experimental data comprises gas holdup and bubble size distributions obtained with ultrafast X-ray tomography and hydroxide ion conversion obtained with a wire-mesh sensor. Large Eddy Simulation (LES) is used for calculating the fluid flow and modelling the turbulence in the continuous phase, considering the effect of sub-grid-scale (SGS) turbulence on bubble motion, and also SGS turbulence modification by bubbles. Lagrangian bubble tracking is conducted considering all relevant forces, bubble oscillation via stochastic generation of eccentricity and motion angle and consequently non-steady mass transfer via a dynamic Sherwood number. The comparison of experimental and simulation results shows very good agreement for the given data.

Numerical study of interactions between shock waves and a circular or elliptic bubble in air medium

The interaction of shock waves with bubbles is of interest in a variety of areas, such as shock wave lithotripsy, cavitation erosion, and sonoluminescence. For these, the spatial technology, which is based on the five-equation model and the finite volume method, is employed to numerically study this issue in this paper. Research on the interaction between shock waves and circular bubbles indicates that the generation and distribution of vorticity have an important influence on the deformation of the bubble interface, and the vorticity will accelerate the turbulent mixing of the two-phase gas. In addition, the interaction processes between shock waves and elliptic bubbles aligned horizontally and elliptic bubbles aligned vertically in air medium with different aspect ratios are investigated. Results show that the time required to generate the transverse jet and vortex structure decreases, and the deformation degree and the collapse speed increase when increasing the aspect ratio of elliptic bubbles aligned horizontally. For elliptic bubbles aligned vertically, the position of the transverse jet is related to the aspect ratio; the greater the aspect ratio, the farther the jet position is from the centerline.

Field and flume tank experiments investigating the efficacy of a bubble curtain to keep harmful jellyfish out of finfish pens

In recent years, salmon aquaculture has struggled to mitigate the impact of harmful jellyfish species in northern Europe and beyond. Typically, large aggregations of jellyfish are carried by currents through salmon pens, leading to unsustainable mortality levels in some years. One potential solution that has been regularly proposed is the creation of a ‘bubble curtain’ around fish pens. A bubble curtain is created by releasing compressed air from a perforated tube at depth, forming a plume of bubbles that entrain the water to create a vertical current. This study investigated the efficacy of a bubble curtain as a jellyfish barrier at several aquaculture locations in Ireland and in a controlled flume tank. Field tests on bubble curtains provided mixed results: a high air flow 8 m linear bubble curtain set at 5 m depth effectively deflected large compass jellyfish (Chrysaora hysoscella), whereas, a low air flow ca. 800 m circular bubble curtain set at 5 m depth, around a salmon farm, did not significantly impact the abundance of small hydromedusae on either side of the bubble curtain. Flume tank experiments demonstrated that increased wave height and increased air flow increased jellyfish transport through the curtain and the lateral movement was consistent with Stokes drift, i.e. an elliptical motion that includes forward movement with each wave. These results suggest that sites with relatively high wave energy may be unsuitable for bubble curtain use and that the variable size and shape of jellyfish may be an important factor in jellyfish and bubble curtain interactions.

Morphological Stability of the Bubble Surface in the Dynamic Growth Regime. 2D Case

We perform linear analysis of morphological stability of a circular bubble growing nonstationary in a 2D liquid disregarding the variation of temperature and viscosity. The media are treated as incompressible, and the pressure in the bubble is assumed to be constant. Beginning from a certain critical size (kinetic spinodal), a transition from stable to unstable growth is observed, which differs in principle from the known solution for the 3D case. An approximate equation is derived for calculating the spinodal.

Stokes waves with constant vorticity: folds, gaps and fluid bubbles

The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the irrotational flow setting. The associated linearized operator is self-adjoint, whereby the modified Babenko equation is efficiently solved by the Newton-conjugate gradient method. For strong positive vorticity, a ‘fold’ appears in the wave speed versus amplitude plane, and a ‘gap’ as the vorticity strength increases, bounded by two touching waves, whose profile contacts with itself at the trough line, enclosing a bubble of air. More folds and gaps follow for stronger vorticity. Touching waves at the beginnings of the lowest gaps tend to the limiting Crapper wave as the vorticity strength increases indefinitely or, equivalently, gravitational acceleration vanishes, while the profile encloses a circular bubble of fluid in rigid body rotation at the ends of the gaps. Touching waves at the beginnings of the second gaps tend to the circular vortex wave on top of the limiting Crapper wave in the infinite vorticity limit, or the zero gravity limit, and the circular vortex wave on top of itself at the ends of the gaps. Touching waves for higher gaps accommodate more circular bubbles of fluid.

On suitability of phase-field and algebraic volume-of-fluid OpenFOAM® solvers for gas–liquid microfluidic applications

Microfluidic devices often contain several phases. Their design can be supported by interface-resolving numerical simulations, requiring accurate methods and validated computer codes. Especially challenging are submillimetre air bubbles in water due to their large density contrast and dominance of surface tension. Here, we evaluate two numerical methods implemented in OpenFOAM®, namely the standard solver interFoam with an algebraic volume-of-fluid method relying on a sharp interface representation and phaseFieldFoam relying on the phase-field method with diffuse interface representation. For a circular bubble in static equilibrium, we explore the impacts of uniform grid resolution and bubble size on bubble shape, mass conservation, pressure jump and spurious currents. While the standard interFoam solver exhibits excellent mass conservation with errors below 0.1% on fine grids, it lacks the accuracy to predict reasonable physics for a bubble in microfluidic systems. At higher resolution, large spurious currents significantly displace and deform the bubble, which is oscillating with resolution dependent mode and frequency. Furthermore, the pressure jump is consistently underestimated by more than 10%. The solver phaseFieldFoam suffers from much larger mass losses of up to 2%, which decrease as the ratio between interface thickness and bubble diameter decreases provided the diffuse interface region is adequately resolved. Spurious currents are very low and the bubble remains circular preserving its initial position with an error in pressure jump below 1%.

Directional raids by army ants as an adaption to patchily distributed food: a simulation model

ABSTRACTA typical colony of Neotropical army ants (subfamily Ecitoninae) regularly raids a large area around their bivouac by forming a narrow directional column that can reach up to one hundred meters in length. The raid is finished and then relaunched 12–17 times, each time toward different orientation. After completing all bouts the colony relocates to a new area. A hypothetical alternative to this foraging mode is raiding radially and symmetrically by expanding the search front in every direction like a circular bubble. Using an existing agent-based modeling software that simulates army ants’ behavior, we compared the two possible modes of foraging in different food distributions. Regardless of the food patch abundance, the radial raiding was superior to the directional raiding when food patches had low quality, and the directional raiding was favorable when the patches were rich. In terms of energy efficiency, the radial raiding was the better strategy in a wide range of conditions. In contrast, the directional raiding tended to yield more food per coverage area. Based on our model, we suggest that the directional raiding by army ants is an adaptation to the habitats with abundance of high-quality food patches. This conclusion fits well with the ecology of army ants.

Effect of wall wettability condition on drift-flux parameters in lead–bismuth two-phase flow in circular and annular bubble columns

ABSTRACT Lead–bismuth two-phase flow in a cylindrical vessel and annulus was experimentally investigated by varying the surface wettability of the vessel wall. The test section used in this study was a cylindrical stainless vessel with/without inner sleeve to change the hydraulic diameter. Volume-averaged void fraction was measured by varying the surface wettability of the test section, which was enhanced by using a soldering flux. Measured void fraction was compared with existing two-phase flow correlations and with one-dimensional theoretical simulations assuming one-dimensional drift-flux model. From experimental results, measured distribution parameters of the lead–bismuth two-phase flow are much larger than that of ordinary two-phase flow regardless of the surface wettability. In the present work, the one-dimensional analysis was carried out for the cylindrical vessel to reproduce the distribution parameter. From the simulation results, predicted value for the cylindrical vessel showed good agreement with experimental results. However, in annulus, the distribution parameters in annulus were underestimated by the present model. It was suggested that, in case of annulus, steeper void fraction profile might be formed near the inner surface for poor wettability condition.

Application of Circular Bubble Plume Diffusers to Restore Water Quality in a Sub-Deep Reservoir.

Circular bubble plume diffusers have been confirmed as an effective technology for the restoration of the deep water system, but have never been applied in sub-deep water system. In this study, circular bubble plume diffusers were used, for the first time, to restore water quality in the Aha Reservoir, a typical sub-deep reservoir in Southwest China. Axisymmetric intrusive gravity currents were formed with a horizontal radius of 250 m at the equilibrium depth and the intrusion of oxygen-enriched water occurred within the depth of 10–14 m, while thermal stratification remained intact. A total of 95% of the imported oxygen was dissolved, but most was consumed by organic matter and other reduced substances within the hypolimnion. The oxygen consumption of organic matter, NH4+ and remaining reduced materials, accounted for 41.4–52.5%, 25% and 13.3–24.4% of the total imported oxygen, respectively. Compared with the control sites, dissolved oxygen level in the hypolimnion increased 3–4 times, and concentrations of NH4+, total Fe and total Mn were reduced by 15.5%, 45.5% and 48.9%, respectively. A significant decrease in total phosphorus and nitrogen concentrations was observed in the experimental zone (0.04–0.02 mg/L and 1.9–1.7 mg/L, respectively). This indicates that circular bubble plumes have great potential for oxygenation of the hypolimnion and improving water quality in the sub-deep water system. Nevertheless, further efforts are needed to improve the discrete bubble model to elaborate the oxygen transmission dynamics and the plume formation processes in sub-deep water systems, incorporating oxygen consumption processes.

Discovery of a Synchrotron Bubble Associated with PSR J1015–5719

Abstract We report the discovery of a synchrotron nebula, G283.1−0.59, associated with PSR J1015−5719. Radio observations using the Molonglo Observatory Synthesis Telescope and the Australia Telescope Compact Array at 36, 16, 6, and 3 cm reveal a complex morphology. The pulsar is embedded in the “head” of the nebula with fan-shaped diffuse emission. This is connected to a circular bubble of 20″ radius and a collimated tail extending over 1′. Polarization measurements show a highly ordered magnetic field in the nebula. It wraps around the edge of the head and shows an azimuthal configuration near the pulsar, then switches direction quasi-periodically near the bubble and in the tail. Together with the flat radio spectrum observed, we suggest that this system is most plausibly a pulsar wind nebula (PWN), with the head as a bow shock that has a low Mach number and the bubble as a shell expanding in a dense environment. The bubble could act as a magnetic bottle trapping the relativistic particles. A comparison with other bow-shock PWNe with higher Mach numbers shows similar structure and B-field geometry, implying that pulsar velocity may not be the most critical factor in determining the properties of these systems. We also derive analytic expressions for the projected standoff distance and shape of an inclined bow shock. It is found that the projected distance is always larger than the true distance in three dimensions. On the other hand, the projected shape is not sensitive to the inclination after rescaling with the projected standoff distance.

A Flexible Coupled Level Set and Volume of Fluid (flexCLV) method to simulate microscale two-phase flow in non-uniform and unstructured meshes

An innovative Flexible Coupled Level Set (LS) and Volume of Fluid (VOF) algorithm (flexCLV) to simulate two-phase flows at the microscale on unstructured and non-uniform meshes is proposed. The method combines the advantages of the VOF method in terms of mass conservation and the LS method in terms of accuracy of the surface tension implementation and can handle both 2D and 3D domains discretized by either structured hexaedra or unstructured tetrahedral grids with high aspect ratio elements, thus guaranteeing flexibility and robustness. The method is implemented within the VOF-based OpenFOAM’s solver interFoam, which is retained as the base algorithm for the interface advection, while the surface tension force is calculated by using the level set function reconstructed from the VOF’s fraction. The method is first validated in static flow conditions by simulating a circular bubble at equilibrium and then in dynamic flow conditions by studying a freely bubble rising in both 2D and 3D domains discretized by both structured and unstructured meshes. The proposed flexCLV algorithm is then used to simulate the dynamics of confined bubbles in circular microchannels in the low capillary number regime. 2D and 3D mesh grids with high aspect ratio elements are utilized to discretized the liquid film at the tube’s walls. The numerical results are compared with the available literature and simulations performed with the original interFoam solver in terms of bubble shape and velocity, thickness of the liquid film and amplitude of the bubble tail oscillations. Results compare very well with the experimental measurements and demonstrate the superior accuracy of the coupled flexCLV method with respect to the original VOF method when surface tension and accurate interface representation play a fundamental role. Importantly, the present study also provides a precious insight on the time-dependent patterns appearing on the bubble surface in the visco-inertial regime, which could be here investigated in detail.