Soap Bubbles Research Articles

Dynamics of radial threshold solutions for generalized energy-critical Hartree equation

Abstract In this paper, we study long time dynamics of radial threshold solutions for the focusing, generalized energy-critical Hartree equation and classify all radial threshold solutions. The main arguments are the spectral theory of the linearized operator, the modulational analysis and the concentration compactness rigidity argument developed by T. Duyckaerts and F. Merle to classify all threshold solutions for the energy critical NLS and NLW in [T. Duyckaerts and F. Merle, Dynamic of threshold solutions for energy-critical NLS, Geom. Funct. Anal. 18 2009, 6, 1787–1840, T. Duyckaerts and F. Merle, Dynamics of threshold solutions for energy-critical wave equation, Int. Math. Res. Pap. IMRP 2008 2008, Art ID rpn002], later by D. Li and X. Zhang in [D. Li and X. Zhang, Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions, J. Funct. Anal. 256 2009, 6, 1928–1961, D. Li and X. Zhang, Dynamics for the energy critical nonlinear wave equation in high dimensions, Trans. Amer. Math. Soc. 363 2011, 3, 1137–1160] in higher dimensions. The new ingredient here is to solve the nondegeneracy of positive bubble solutions with nonlocal structure in H ˙ 1 ⁢ ( ℝ N ) {\dot{H}^{1}(\mathbb{R}^{N})} (i.e. the spectral assumption in [C. Miao, Y. Wu and G. Xu, Dynamics for the focusing, energy-critical nonlinear Hartree equation, Forum Math. 27 2015, 1, 373–447]) by the nondegeneracy result of positive bubble solution in L ∞ ⁢ ( ℝ N ) {L^{\infty}(\mathbb{R}^{N})} in [X. Li, C. Liu, X. Tang and G. Xu, Nondegeneracy of positive bubble solutions for generalized energy-critical Hartree equations, preprint 2023, https://arxiv.org/abs/2304.04139] and the Moser iteration method in [S. Dipierro, M. Medina and E. Valdinoci, Fractional Elliptic Problems with Critical Growth in the Whole of ℝ n \mathbb{R}^{n} , Appunti. Sc. Norm. Super. Pisa (N. S.) 15, Edizioni della Normale, Pisa, 2017], which is related to the spectral analysis of the linearized operator with nonlocal structure, and plays a key role in the construction of the special threshold solutions, and the classification of all threshold solutions.

Kaluza–Klein bubble with massive scalar field

A well-known soliton (bubble) solution of five-dimensional Kaluza–Klein General Relativity is modified by imposing mass on the scalar field. By forcing the scalar field to be short-range, the failure of the original bubble solution to satisfy the equivalence principle is remedied, and the bubble acquires gravitational mass. Most importantly, the mass is quantized, even in this classical setting, and has a value mP/(4α), where mP is the Planck mass, and α is the fine-structure constant. This result applies for any choice of scalar-field mass, as it is an attractor for the field equations.

3D-printed acoustic metasurface with encapsulated micro-air-bubbles for frequency-selective manipulation.

Acoustic waves provide an effective method for object manipulation in microfluidics, often requiring high-frequency ultrasound in the megahertz range when directly handling microsized objects, which can be costly. Micro-air-bubbles in water offer a solution toward low-cost technologies using low-frequency acoustic waves. Owing to their high compressibility and low elastic modulus, these bubbles can exhibit significant expansion and contraction in response to even kilohertz acoustic waves, leading to resonances with frequencies determined and tuned by air-bubble size. The resonances amplify vibrational amplitude and generate localized turbulence, enabling selective, non-invasive, and high-precision manipulation of microsized objects. However, conventional bubble formation relies on the shear force of the liquid flow and bubble surface tension, facing challenges of instability and random vibration that can impair manipulation precision and performance. To address these issues, we propose a coupled vibration structure with 3D-printed circular microsized air holes encapsulated by a PDMS film. These airholes act as artificial micro-air-bubbles, with their expansion and contraction stabilized by acoustic hard boundaries. The PDMS film further regulates vibration modes through the interaction between air movement and the film's vibration, eliminating randomness. Compared to conventional air-bubbles held by surface tension, these artificial air-bubbles are mechanically stable, allowing for enhanced gas volume changes and stronger forces for object manipulation. We experimentally confirm the stable vibration modes and their frequency-dependent behavior using laser Doppler vibrometry. Precise aggregation, rotation, and separation of micro-objects are demonstrated by adjusting the film's vibration mode. Furthermore, we propose a metasurface design featuring a multi-size microbubble array for frequency-selective manipulation, enabling flexible control of sample trajectory by changing the exciting frequency of an embedded piezoelectric transducer. Our low-frequency acoustic metasurface device offers a versatile, cost-effective solution for drug screening and automated sample handling.

A numerical study of two identical CO2 bubbles rising side by side in water coupled with mass transfer

ABSTRACT In contrast to the relatively straightforward rising dynamics of single bubbles, the behavior of multiple bubbles involves a more intricate interplay of flow field dynamics, trajectory patterns, morphological changes, and mass transfer phenomena. To reveal the coalescence characteristics and mass transfer effects of CO2 bubbles during the rising process, this study developed a coupled mass transfer numerical model for bubbles. The Volume of Fluid (VOF) method was used in combination with a mass transfer code for solving the model. The effects of bubble pair initial spacing and liquid viscosity on the coalescence and mass transfer were discussed. The numerical simulation results show that as the initial distance between the two bubbles decreases, the interaction force between the bubbles increases, and the possibility of bubble coalescence increases, the coalescence behavior reduces the contact area and thus decreases the amount of CO2 dissolved about 24.07%. When the initial viscosity of the liquid phase is low, there is an oscillation in the bubble velocity, and the two bubbles tend to merge. As the initial viscosity of the liquid phase increases, resistance increases, causing a decrease in bubble velocity. Consequently, the path of bubble ascent shifts from “approach-repulsion-approach” to “continuous repulsion.” The viscous resistance reduces the gas–liquid contact area, resulting in a corresponding decrease in the mass transfer rate, the dissolution amount of carbon dioxide decreased by approximately 24.42% in this case. The exploration of coupled fluid dynamics and mass transfer phenomena at the multi-bubble scale holds paramount importance in guiding the design and exploration of gas–liquid two-phase flow systems.

Craniolacuna, cribriform skull associated with myelomeningocele and chiari type II malformation: A case report.

Cranial lacuna is a low density radiological image of the cranial vault giving the appearance of beaten copper, the rarefaction zones which are several, producing radiologically a "soap bubble" or "honeycomb" effect. due either to an absence of the internal and external tables or to the absence of a single table or to localized demineralization. They are either physiological or pathological. They are associated with neurological malformations especially hydrocephalus, myelomeningocele and chiari type II malformations. We report the case of a newborn aged one day, admitted for the management of myelomeningocele associated with a chiari type II malformation and a lacunar skull diagnosed postnatally. The newborn is a male, 39 weeks pregnancy, cesarean section. Weight 3500 g, Apgar: 7/10, 8/10. Mother: G6/P5. His clinical examination reveals good skin-mucosal coloration, eupnea, slight axial hypotonia, normal cardiopulmonary auscultation, permeable choanae and esophagus, cranial perimeter at 33 cm, ruptured spina bifida. The skull X-ray reveals a beaten copper appearance of the skull with marked convolutions. The normal chest X-ray. The Abdomino-Pelvic ultrasound finds bilateral uretero-hydronephrosis more marked on the left, with distended bladder and signs of neurogenic bladder. The normal echocardiogram. The brain CT scan reveals a type 2 Chiari malformation, absence of hydrocephalus, The negative infectious assessment, The correct renal assessment, The newborn received neurosurgical management of spina bifida, with a reserved neurological prognosis. This condition is associated with neurological malformations that can have a poor prognosis. Prognosis is reserved in the event of an association with a myelomeningocele because it is dominated by the risk of infection and the dark neurological outcome. The lacunar images resolve spontaneously after 4 to 6 months.

An adaptive level-set/square-root-conformation representation/discontinuous Galerkin method for simulating viscoelastic two-phase flow systems

A new numerical method, which is based on the coupling of adaptive mesh technique, level set (LS) method, square-root-conformation representation (SRCR) approach, and discontinuous Galerkin (DG) method within the dual splitting framework, is developed for viscoelastic two-phase flow problems. This combination has been more effective than expected. The LS method is performed to capture the moving interface due to its efficiency and simplicity when dealing with the significant interface deformations. The dual splitting scheme is applied to decouple the whole system into subequations, which circumvent the limitation of the Ladyzhenskaya-Babuška-Brezzi condition. The SRCR approach is employed to reconstruct the Oldroyd-B constitutive equation to solve the high Weissenberg number problem. The high-order DG method is performed for the spatial discretizations of equations to deal with the convection-dominated problems. In addition, the reinitialization method of the LS function and a simple mass correction technique are applied to guarantee the mass conservation in calculation. In this coupled method, there is no need to require reinitialization within every time step but after suitable time steps. Meanwhile, the adaptive mesh technique is implemented in the coupling procedure, which greatly improves the computational efficiency. The coupled algorithm is performed to simulate the swirling deformation flow, Rayleigh–Taylor instability and bubble rising problems. And the influences of the parameters on the rising speed and shape of bubble in viscoelastic liquid are analyzed in detail. The numerical results indicate that the coupled algorithm is effective and accurate for simulating the interface evolution problems with complex topological structure changes, and can guarantee the mass conservation property.

Effects of gas distributor on hydrodynamics in gas–liquid bubble column by visual experiments and CFD simulations

Effects of gas distributor on hydrodynamics in gas–liquid bubble column by visual experiments and CFD simulations

Mechanistic model of wall heat transfer for vertical subcooled boiling flow

Nucleate boiling rate is significantly affected by heat flux partitioning from the heated wall during subcooled boiling flow. Therefore, precisely modeling wall heat flux partitioning is crucial for the realistic prediction of boiling two-phase flows. In this study, a new mechanistic model based on bubble dynamics and associated heat transfer mechanisms is proposed for wall heat flux partitioning under vertical subcooled boiling flow. The proposed model categorizes the wall heat flux into four components: evaporation, nucleation quenching, sliding transient conduction, and forced convection. Unlike previous models, the nucleation quenching and sliding transient conduction components, both triggered by sliding bubbles, are modeled separately owing to their different active times in the new model. Additionally, the proposed model incorporates suppression factors into the existing model for nucleation site density to address boiling suppressions induced by subcooled liquid and static bubble interactions. Evaluation results reveal that the new model, including its closure models, exhibits a good prediction capability in a wide range of thermal-hydraulic conditions covering 298–3527 kg/m2s of mass flux, 100–6000 kW/m2 of heat flux, 5–83.3 K of liquid subcooling, and 1–6 bar of pressure.

Electrochemical regeneration of CO2 absorbent in a microreactor

This study investigates an Electrochemically Mediated Amine Regeneration (EMAR) process for CO2 capture using a novel microreactor design. We examined gas–liquid flow patterns and bubble evolution in microchannels, analyzing the effects of flow rate and electrical current on CO2 output, Faraday efficiency, and energy consumption. A periodic electrode polarity switching protocol significantly extended reactor lifetime. While promising for small-scale applications, the EMAR microreactor faces challenges in energy reduction for large-scale implementation. This work provides insights into electrochemical microreactor design for CO2 capture, contributing to advancements in this field.

Bubble-Assisted Sample Preparation Techniques for Mass Spectrometry.

This review delves into the efficacy of utilizing bubbles to extract analytes into the gas phase, offering a faster and greener alternative to traditional sample preparation methods for mass spectrometry. Generating numerous bubbles in liquids rapidly transfers volatile and surface-active species to the gas phase. Recently, effervescence has found application in chemical laboratories for swiftly extracting volatile organic compounds, facilitating instantaneous analysis. In the so-called fizzy extraction, liquid matrices are pressurized with gas and then subjected to sudden decompression to induce effervescence. Alternatively, specifically designed effervescent tablets are introduced into the liquid samples. In situ bubble generation has also enhanced dispersion of extractant in microextraction techniques. Furthermore, droplets from bursting bubbles are collected to analyze non-volatile species. Various methods exist to induce bubbling for sample preparation. The polydispersity of generated bubbles and the limited control of bubble size pose critical challenges in the stability of the bubble-liquid interface and the ability to quantify analytes using bubble-based sample preparation techniques. This review covers different bubble-assisted sample preparation methods and gives practical guidance on their implementation in mass spectrometry workflows. Traditional, offline, and online approaches for sample preparation relying on bubbles are discussed. Unconventional bubbling techniques for sample preparation are also covered.

Design, optimization, and autonomous construction of Martian infrastructure including slabs using in-situ CO2-based polyethylene

A crucial development in 21st-century space exploration is the establishment of human settlements on Mars. In recent years, Mars exploration rovers have been deployed, and studies investigating human journeys to Mars have been conducted, with the objective of a human-crewed mission to Mars before 2050. This study presents an innovative approach to designing and optimizing Martian habitats by using in-situ CO2-based polyethylene (PE) as a construction material for Martian buildings and greenhouses. It seeks to develop sustainable and resilient habitats on Mars, leveraging local resources to address the environmental challenges specific to the Martian environment. The research targets several key areas: realistic construction techniques, effective utilization of in-situ materials, and building resilience under the harsh Martian conditions. These conditions include radiation, micrometeoroid impacts, low atmospheric pressure, low gravity, wind storms, temperature extremes, Paschen discharge, and marsquakes. Finite element analysis (FEA) of several pressurized spherical structures is used to design and optimize for minimum material usage, inspired by soap bubbles that naturally stick together with separating walls. The proposed habitat design features a central spherical structure surrounded by nine smaller spheres, optimized for material efficiency. It is demonstrated that utilizing two layers of 0.1 m thick PE and a 0.5 m thick CO2 layer in between them offers significant protection against Martian environmental loads such as radiation shielding and thermal insulation. It facilitates light transmission into the building. This study offers a realistic structural system for buildings and greenhouses that can be constructed using in-situ materials and is suitable for an optimal 539-day stay on Mars. The proposed autonomous robotic arm technology can perform all necessary tasks, from producing PE to automatically assembling the Mars Spherical Building (MSB), including in-place slab printing.

Bubble velocities and oscillon precursors in first-order phase transitions

Metastable ‘false’ vacuum states are an important feature of the Standard Model of particle physics and many theories beyond it. Describing the dynamics of a phase transition out of a false vacuum via the nucleation of bubbles is essential for understanding the cosmology of vacuum decay and the full spectrum of observables. In this paper, we study vacuum decay by numerically evolving ensembles of field theories in 1+1 dimensions from a metastable state. We demonstrate that for an initial Bose-Einstein distribution of fluctuations, bubbles form with a Gaussian spread of center-of-mass velocities and that bubble nucleation events are preceded by an oscillon — a long-lived, time-dependent, pseudo-stable configuration of the field. Defining an effective temperature from the long-wavelength amplitude of fluctuations in the ensemble of simulations, we find good agreement between theoretical finite temperature predictions and empirical measurements of the decay rate, velocity distribution and critical bubble solution. We comment on the generalization of our results and the implications for cosmological observables.

Suppression of bubbles in unstable active liquids via fast evaporation.

A common intuition in thermodynamics is that bubbles can spontaneously grow in unstable liquids, which will be detrimental to a variety of physical and chemical processes, such as evaporation-induced self-assembly and electrocatalysis. Here, we show that this common intuition can be significantly reversed by demonstrating a suppression of bubbles in unstable active liquids induced by fast evaporation, which is in contrast to the bubble growth in passive liquids. Such anomalous bubble suppression can be attributed to an activity-induced inversion of pressure difference between bubbles and their surrounding liquid. Moreover, this pressure flip depends on the activity as well as the thermodynamics of passive liquids, and it can generate different kinetic pathways that allow controlling the bubble dynamics in unstable liquids. Our results establish a foundation for promoting applications of unstable active liquids in various physical and chemical processes.

VOF-based modeling study of surface oscillation behavior and gas–liquid stirring dynamics in the bottom-blown reactors

Gas bottom-blown reactors are widely employed in the chemical, metallurgical, and biochemical industries due to their superior mixing capabilities. This study numerically investigates the gas–liquid flow hydrodynamics and bubble dynamics in a bottom-blown system with a circular boundary using the volume of fluid approach. Following the experimental validation of the mathematical model, this study evaluates the effects of gas flow rates, liquid heights, and fluid medium properties on the dynamics of the bubble swarm, as well as on the surface behavior and the mixing characteristics of the flow field. The results indicate that: (1) Rising bubbles disturb the fluid flow, generating numerous vortices that facilitate momentum transfer for effective gas stirring; (2) The height of the liquid surface oscillation during the bottom-blown process exhibits significant temporal variation, with the peak showing clear lateral swings; (3) Due to the nonlinear interactions involving bubble coalescence and breakup during their ascent, along with constructive and destructive interference between liquid surface waves, the liquid surface can exhibit violent fluctuations at certain moments; (4) Bubble size and aspect ratio significantly influence liquid surface oscillations; (5) The bubble rising path displays instability due to vortex shedding, with some vortices forming at locations where the bubble shape changes abruptly. A prediction equation for bubble velocity is proposed: uc=σ5.2737Lcρc4.2737/16156μl9.5475.

Investigation on the primary resonance of a cylindrical bubble in compressible liquid

In the present paper, the paramount characteristics of the resonance of cylindrical bubbles in a compressible liquid are theoretically investigated with multi-scale analysis. Considering the liquid's compressibility, a dimensionless equation of the cylindrical bubble wall motion is established for the primary resonance under a single-frequency acoustic field. Comparing with the numerical results, the present analytical solution is verified in terms of accuracy. The key parameters on the characteristics of primary resonance are further explored including the equilibrium bubble radius, dimensionless amplitude of the acoustic field, and other detuning parameters. The main conclusions are given as follows: (1) During primary resonance, three typical nonlinear phenomena are observed: multivalued solutions, jumps, and hysteresis phenomena. (2) The liquid's compressibility affects the intensity of acoustic waves emitted by the bubbles during primary resonance. The maximum pressure at the bubble interface in the incompressible liquid is higher than that in the compressible liquid. (3) In the amplitude–frequency curve, the unstable region of the compressible liquid is smaller and the peak is lower than in the incompressible liquid.

A simulation study on the influence of marginal pinching upon liquid film dynamics

In fluid dynamics, the generation and bursting of surface bubble liquid films in surfactant-laden environments involve complex phenomena, one of which is marginal pinching at the film's foot—a crucial yet inadequately understood aspect due to experimental limitations. Considering its profound impact on liquid film drainage and lifetime, we utilize high-resolution numerical simulations incorporating a weakly compressible scheme and adaptive mesh refinement to dissect the marginal pinching dynamics with unprecedented detail. Our approach elucidates the pinching dynamics and tracks the evolution of film thickness during the critical late-stage drainage process. By leveraging detailed geometric data from pinched regions, we significantly refine existing drainage models, enhancing their predictive accuracy regarding rupture thickness and film lifetime across various viscosities, surfactant concentrations, and bubble sizes. This refined model demonstrates robust alignment with our simulation results. Furthermore, we establish a quantifiable relationship between the prefactor governing reverse flow induced by the Marangoni effect and surfactant concentration. The methodologies and findings of this study provide foundational knowledge that paves the way for optimized industrial processes and an enhanced understanding of natural phenomena.

Surface-deformability dependent contact time of bouncing droplets on sessile soap bubbles

HypothesisThe curvature of the free-standing liquid film is expected to modify its surface deformability, thereby affecting droplet bouncing dynamics and possibly tuning the liquid repellency performance in practical applications. ExperimentsIn this study, the bouncing dynamics of water droplets on sessile soap bubbles with different curvatures has been experimentally investigated using high-speed camera. FindsTo resist the impacting droplets, the soap bubbles is observed to show two types of deformation: the geometrical deformation caused by the total impacting force and the pressure distribution induced deformation from the droplet dynamics. The variation trend of the contact time of the droplet with the impact velocity is found to be highly dependent on the surface deformability of the soap bubble. This trend becomes non-monotonic when the soap bubble is large and more deformable. The decreasing contact time with increasing impact velocity can be well captured by a phenomenological model of coupled springs. The increasing contact time for the large soap bubbles at high impact velocities is due to the further compression of the soap bubble by the recoiling droplet, leading to the decoupling of the above two types of bubble deformation.

3D numerical investigation of bubble upflow condensation behaviors during subcooled flow boiling in mini-channel with VOSET

In the subcooled flow boiling process, bubble condensation is an inevitable basic phenomenon. This paper studies the condensation phenomenon of the single, double vertical/horizontal saturated bubbles rising in a three-dimensional mini-rectangular channel based on the interface capture method VOSET (coupled volume-of-fluid and level set method) and the phase transition model. Bubble condensation behaviors are investigated at different initial diameters, inlet velocity distributions, subcooling temperatures, bubble gaps, and arrangement for the two-bubble condensing system especially. The effects of these parametric on bubble motion trajectory, shape evolution, volume variation, and condensation rate are presented. The numerical results indicated that the initial bubble size and liquid subcooling play an important role in influencing the shape and volume variation of condensing bubble behaviors significantly, while the inlet velocity distribution only affects bubble motion trajectory. Furthermore, the interaction and coalescence between the bubbles will affect the bubble behaviors and the condensation rate. Finally, the condensation heat transfer coefficients at the bubble surfaces for different cases simulated in this paper are presented, seemingly first in the literature.

The Current Situation of the Housing Market Bubble in Chinas First-tier Cities

Abstract: With the progression of China's economy and urbanization, the real estate industry experienced rapid growth, accompanied by increasing speculative activities, which led to a continuous rise in housing prices and the formation of a bubble. Therefore, the focus of this study was the current state of China's real estate bubble and potential solutions. Given the issue of excessively high real estate prices, this study specifically examined the price trends and factors contributing to the real estate bubble in four Chinese cities: Beijing, Shanghai, Guangzhou, and Shenzhen. The research methodology was as follows: First, data on the price-to-income ratio was collected to analyze the current state of housing prices in China, revealing that housing prices were still far above their actual value and beyond a reasonable range, thereby indicating the severity of the real estate bubble in China. Second, by analyzing data and reviewing the literature, the factors contributing to China's real estate bubble were identified and categorized into two main groups: policy-related and economic. On the policy side, factors included policy reforms, monetary easing, and reductions in both the benchmark interest rate and the reserve requirement ratio. On the economic side, factors included the growth in per capita disposable income and speculative behavior. Finally, this paper analyzed how a property tax could curb speculative activities by increasing the cost of purchasing properties, thereby reducing demand and speculative behavior. The findings revealed that the real estate bubble in China's first-tier cities remained severe, and that a property tax could help curb speculative activities and slow the pace of bubble expansion.

Thermo‐rheological snapshot of melter feed conversion to glass

AbstractSlurry feed charged into an electric melter creates a layer of reacting and melting material (termed cold cap) that floats on the surface of molten glass. The rheological behavior of heated melter feed affects the spreading of slurry at the top of the cold cap and the stability of the primary foam, affecting cold‐cap coverage and melter plenum temperatures. The apparent viscosity of a high‐alumina high‐level waste melter feed was assessed by thermomechanical analysis, high‐temperature viscometer, and the hot stage microscopy method, yielding viscosity estimates from ≈107.5 Pa s at 550°C to ≈102.5 Pa s at 1050°C. As the temperature of feed materials increased, their state changed from rigid solid to dilatant fluid, to pseudoplastic bubbly liquid with dissolving solids, to fully developed foam, and finally to Newtonian glass melt.