Soap Bubbles Research Articles

Large Energy Bubble Solutions for Supercritical Fractional Schrödinger Equation with Double Potentials

Large Energy Bubble Solutions for Supercritical Fractional Schrödinger Equation with Double Potentials

Anomalous diffusion of hydrocarbon vapor through an aqueous foam bubble structure

Hydrocarbons are known as “anti-foamers” because they cause bubble rupture, coalescence, and reduce foaming. We show that the dynamics of bubble structure allows hydrocarbon vapors permeate rapidly when an aqueous foam is placed on a hydrocarbon pool. Two distinct foam layers are formed. Vapor accumulates in an expanding bottom layer at the foam-pool interface where bubbles grow rapidly, rupture, and coalesce. Simultaneously, vapor diffuses through a top layer having small bubble structure, which changes slowly due to Ostwald-ripening. Very little vapor accumulates in the top layer, which has a constant thickness equal to the initial foam thickness. Surprisingly, both accumulation in the bottom layer and diffusion through top layer occur at constant rates, which are independent of time and initial foam thickness. The vapor diffusion rate in the top layer should have decreased, inversely proportional to the initial foam thickness, based on classical diffusion theory; only the fluorosurfactant containing foam (RefAFFF) placed on gasoline follows the classical theory where the bottom foam layer is absent. Therefore, we propose a theory to show a linear increase in diffusion time with initial foam thickness using an effective diffusion-coefficient. Experiments show that this variation could be because of increased liquid drainage, drying, and bubble coarsening, which are not considered explicitly in the theory. We also describe a theory for the expanding bottom layer to show that most vapor formed at the pool surface accumulates for very volatile hydrocarbons. The vapor diffusion controls foam ignition. We show that the measured foam ignition time also increases linearly with initial foam thickness, qualitatively consistent with the predicted diffusion time. By employing different hydrocarbons, we show that the measured foam ignition times decrease inversely proportion to square root of hydrocarbon vapor concentration for a given surfactant. This could be because a surfactant exhibits different degrees of oleophobicity towards different hydrocarbons that can reduce vapor adsorption, solubility, and diffusion at a bubble surface. Different surfactants also exhibit different degrees of oleophobicity towards a given hydrocarbon (n-pentane) and increase ignition times by a factor of six: RefAFFF having the longest ignition time, followed by siloxane-polyoxyethylene formulation, and its individual surfactant components.

How viscous bubbles collapse: Topological and symmetry-breaking instabilities in curvature-driven hydrodynamics

The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetry-breaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles.

Wetting of soap bubbles on topographic surfaces

HypothesisThere is a relationship between the static contact angle of droplets and soap bubbles on flat homogeneous surfaces, therefore, it should be possible to derive a relationship between the static contact angle of a soap bubble on a periodic topographic surface and a droplet on a flat homogeneous surface. ExperimentsA free energy model of the static contact angle of soap bubbles on a topographic surface in the Cassie-Baxter state was derived. Polydimethylsiloxane surfaces of varying area fraction (0.125, 0.250, 0.500, 0.750, and 1.00) and periodic topographies (lined and pillared) were fabricated using 3D printed moulds for pattern transfer. A bubble goniometer was developed to accommodate bubbles of 40,000 ± 5,000 mm3 and 50,000 ± 5,000 mm3 volumes. Then, the static contact angle of bubbles of both volumes were measured on the varying topographic surfaces. FindingsThe derived predictions imply that the relationship between the static contact angle for bubbles on a flat homogeneous surface and on a composite surface, has the same form as the Cassie-Baxter equation for a droplet. The experimental results for the measured static contact angle for both bubble volumes on the varying surfaces had good agreement with the predicted trends.

Study on the synthesis of nanoparticles and their power characteristics in a bubble liquid membrane reactor

Abstract A bubble liquid film reactor is a new type of reactor used for preparing nanoparticles, which has strong inflation ability and dispersion, homogenization, and emulsification effects, especially suitable for preparing loose nanoparticles. In the actual production of enterprises, there is an urgent need to expand production capacity and scale up the reactor. Due to the lack of power characteristic data during the reaction process, it is difficult to select the motor, resulting in unnecessary energy and cost waste. Therefore, the power characteristic data of bubble liquid film reactors urgently needs to be studied. This article investigates the influence of operating conditions such as bubble cap diameter and immersion depth on stirring power and obtains the power characteristics during the operation of a bubble liquid film reactor. The results indicate that the larger the diameter of the bubble cap disk, the stronger the power consumption, but the smaller the power input capacity. The deeper the immersion depth, the higher the power consumption and the stronger the power input capability. Finally, fitting the dimensionless power standard formula provides a mathematical model for reactor amplification, providing theoretical guidance for enterprises to expand production lines and increase production capacity, and providing data support for motor selection.

Effect of liquid elasticity on transient cavitation bubbles in the tube

We investigate the effect of liquid elasticity on the transient cavitation bubbles confined in a tube both experimentally and theoretically. In experiments, the tube-arrest apparatus is used to generate cavitation bubbles near the tube bottom with various polyethylene oxide solutions. Our experiments show that bubble dynamics, particularly the maximum bubble length, are significantly influenced by liquid elasticity. We establish a double oscillator model for the liquid column to explain the experimental results and predict the bubble dynamics over a broader range. Finally, we propose that the reciprocal of the cavitation number Ca2 and prR/k determine the regimes of the liquid column separation, where pr is the reference pressure, R is tube radius, and k is the “stiffness coefficient” of the liquid column. Our work provides a quantitative scaling of the dynamics of large cylindrical cavitation bubbles in viscoelastic liquids during the transient process.

A multi-directional redundant 3D-LPT system for ship–flight–deck wind interactions

In the past years, volumetric velocimetry measurements with helium-filled soap bubbles as tracer particles have been introduced in wind tunnel experiments and performed at large-scale, enabling the study of complex body aerodynamics. A limiting factor is identified in the field of wind engineering, where the flow around ships is frequently investigated. Considering multiple wind directions, the optical access for illumination and 3D imaging rapidly erodes the measurement regions due to shadows and incomplete triangulation. This work formalizes the concepts of volumetric losses and camera redundancy, and examines the performance of multi-directional illumination and imaging for monolithic and partitioned modes. The work is corroborated by experiments around a representative ship model. The study shows that a redundant system of cameras yields the largest measurement volume when partitioned into subsystems. The 3D measurements employing two illumination directions and seven cameras, yield the time-averaged velocity field around the ship. Regions of flow separation and recirculation are revealed, as well as sets of counter-rotating vortices in several stations from the ship bow to the flight–deck. The unsteady regime at the flight–deck is examined by proper orthogonal decomposition, indicating that the technique is suited for the analysis of large-scale unsteady flow features.

Uniqueness and non-degeneracy of solutions for nonlinear fractional Schrödinger equation with perturbation

This paper concerned a fractional Schrödinger equation in whole space, for ɛ > 0 is a small parameter, ɛ2s(−Δ)su + V(x)u = |u|p−2u, where 12<s<1, N > 1 and 2<p<2NN−2s. We prove the non-degeneracy and uniqueness of bubble solutions by using local Pohozaev identity and finite dimensional reduction, which are the cornerstones to construct different type solutions.

Study on inclusion removal in two-strand tundish with gas curtain considering bubble-inclusion attachment

ABSTRACT Application of a gas curtain is one of the main means to improve the cleanliness of liquid steel in tundish. In particular, the bubble-inclusion attachment is one of the important ways to remove inclusions, which cannot be ignored. The bubble size and gas flow are the main parameters of the gas curtain. In this paper, the Euler–Lagrange–Lagrange approach is used to study the three-phase interaction behaviour of liquid steel, bubble, and inclusion. The effects of inclusion size, bubble diameter, and gas flow on inclusion removal rate were studied with normal continuous casting conditions. The calculation results show that the cleanliness of molten steel can be improved by replacing the dam with a gas curtain. In the range of gas flow rate from 1.35 to 2.15 Nm3 h−1, the removal rate of bubble-inclusion attachment and total inclusion removal rate increase with the increase of gas flow. In the range of diameter from 4.5 mm to 6.0 mm with the same gas flow, the total removal rate and bubble-inclusion attachment removal rate increase with the bubble size decrease. The results provide a reference for improving the cleanliness of molten steel by properly increasing the gas flow and reducing the bubble size in industrial operations.

Clinical outcome analysis of two approaches to trypan blue dyeing for DMEK

To evaluate the clinical implications of the different trypan blue dyeing techniques used during liquid bubble (LBT) and manual peel (MPT) DMEK lenticule preparation techniques. This study retrospectively compared the degree to which endothelial cells are preserved using selective Descemet Membrane (DM) staining (LBT) versus bath-staining (MPT) when performed by a single surgeon, sourced from a single eye bank. Endothelial cell density measured after the 3-month follow-up was 1805 and 1916 cells/mm2 respectively, differing significantly (p = 0.012). A double-scroll graft formation was found and maintained until implantation in 94% of preparations with bath staining and 50% of preparations using selective DM staining. Preoperative visual acuity was comparable between preparation techniques at 0.4 logMAR as well as postoperatively, at an average of 0.1 logMAR. Reducing chemical stress on the endothelium by avoiding any contact with trypan blue allows for a significantly higher degree of cell preservation. However, achieving the often-desired double-scroll graft formation was possible less frequently. It remains unclear which factors define the differences graft scrolling behavior observed between LBT and MPT.

Technical Aspects of Natural Gas Pyrolysis in Liquid Metal Bubble Column Reactors

The pyrolysis of low alkanes (in the following short “pyrolysis”) has already been investigated during the 1960s. However, none of the reactor systems used at the time are capable of continuous operation. Therefore, the Karlsruhe Institute of Technology has intensified the development of the promising liquid metal bubble column technology in recent years, which is capable of continuous operation. Various key aspects have been addressed, such as scale‐up and the pyrolysis of high‐caloric natural gas. Herein, further developments for a pilot scale system have been investigated, which concern increased throughput and long‐term operation capabilities. Careful evaluation of the impact of according measures has been done, which shows that the achieved scale‐up has only negligible effects on the pyrolysis outcome. The effects of the scale‐up on residence times are negligible. The bubble formation behavior depends on the throughput and the characteristics of the orifice. Wall effects are marginal. Fundamental minimization of weeping could not be confirmed. Reactor pre‐chambers in combination with tin collection chambers are recommended for further scale‐up. An increase in the volume flow should be examined. In terms of long‐term operation , head as well as feed pressure control is recommended.

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.

Mass transfer of gas–liquid two‐phase flow in asymmetric parallel microchannels with liquid feed splitting

AbstractDue to size limitations, the gas–liquid absorption capacity of a single microchannel is limited, making it difficult to achieve large‐scale CO2 capture. Therefore, the parallel microchannels combining the advantages of high efficiency and large throughput stand out. However, when the operating condition is high gas–liquid flow rate ratio, the liquid phase between bubbles almost disappears after multiple distributions, which affects the amount of gas–liquid absorption. In this study, the numbering‐up of the asymmetric parallel microchannels in the gas–liquid absorption process was investigated by splitting the liquid feed stream in two. The flow patterns under different operating conditions were obtained. The flow and distribution of gas–liquid two‐phase flow were investigated, and the reason of the distribution deterioration caused by appearance of long slug bubbles was explained by the pressure drop distribution. The total liquid mass transfer coefficient and bubble residence time were derived and obtained, and the mass transfer was further discussed.

Validating Volumetric Measurements Using Helium-Filled Soap Bubbles in a Turbulent Boundary Layer And Wake Of An Axisymmetric Body Of Revolution

This study focuses on the validation of a volumetric measurement technique to characterize the turbulent boundary layers (TBL) and wake of a slender axisymmetric body. Specifically, Lagrangian Particle Tracking (LPT) was employed to analyse a TBL subjected to an adverse pressure gradient (APG) and transverse curvature at the tail of an axisymmetric body, with a Reynolds number based on model length of 3.95×10 6 . For the LPT method, a seeding rake with 100 nozzles was used to disperse helium-filled soap bubbles (HFSB), which served as tracers. These tracers were illuminated by high-powered LED arrays, allowing their motion to be captured by three high-speed cameras at acquisition rates up to 20 kHz. A key aspect of this research was using shadowgraphy to measure the diameter of the bubbles exiting the nozzles and obtaining their statistical variations across the various nozzles in the seeding rake. The study identified that the diameter of bubbles averaged 0.45 mm, indicating a state of near-neutral buoyancy. The LPT results were then obtained using the shake-the-box (STB) tracking alogirthm, while ensemble bin-averaging of the scattered particle tracks was used to obtain turbulence statistics on a regular grid. To validate the LPT results, comparisons were made with time-resolved 2D Particle Image Velocimetry (TR-PIV) and highly resolved hot-wire anemometry. This comparative analysis revealed good agreement of the mean profiles across the methodologies, highlighting the robustness and accuracy of the LPT technique. While the turbulence levels in the outer layer were well captured by the LPT, some discrepancies were observed near the wall in both PIV and LPT data, indicating limitations in capturing small-scale phenomena. The implications of these findings, particularly in understanding the complex 3D flow effects of such TBLs and the resulting wake flow field are discussed.

Large-Scale Measurements Using Robotic Volumetric LPT With Shake-The-Box Inside A Vehicle Cabin: Influence Of Different Fan Speeds On The Flow Topology

In this work, the flow topology inside a passenger car cabin for different fan speeds of the heat, ventilation and air conditioning (HVAC) system is investigated using robotic volumetric Lagrangian Particle Tracking (LPT). The coaxial volumetric velocimeter (CVV), also called MiniShaker, in combination with a robotic arm enables the measurement of the complete passenger's side. In total 37 CVV perspectives (sub-volumes) were measured. At each position 3000 double frame images were recorded. The interior was painted black and the mannequin was wrapped with black aluminum foil in order to keep reflections at a low level. Experimental results for three different fan speeds using helium-filled soap bubbles (HFSB) as tracers and Shake-the-Box (StB) algorithm for the three-dimensional LPT data analyses show that the flow topology changes significantly with increasing fan speeds. At higher fan speeds the flow fields show the highest complexity with four vortices.

On-Site Characterization of Automotive Diffuser Aerodynamics by 3D LPT

This investigation proposes a novel LPT facility featuring Helium-Filled Soap Bubbles flow tracers, LED illumination and two high-speed cameras to characterize the dominating flow patterns within automotive underbodies. A remote control (RC) car model, fitted with custom-made floor and diffusers, traverses a region of seeded air following the Ring of Fire methodology. Underground-placed cameras view the car through a transparent panel, providing unparalleled optical access to the underbody of the car. The on-site measurement setup and the interaction between car model and ground enhance the realism and fidelity of the experiments, while potentially reducing testing costs associated with wind tunnel operation. The setup is shown to be a valid alternative to conventional testing approaches to capture flow separation, 3D flow evolution and differences in the flow field between the four tested configurations, whereby the diffuser angle was varied in the range between 5° and 20°. The 15° diffuser led to the largest velocity and pressure peaks under the car, whereas the 10° diffuser produced the most downforce thanks to the diffuser “pumping” effect, leading to a large region of low pressure under the vehicle. Notably, the 20° diffuser featured the most prominent flow separation at the diffuser’s leading edge, heavily affecting its ability to sustain low pressures under the car. The results show that the wide tyres have a major impact on the underbody flow, because their large wakes induce mass flow leakage through the sides of the car, thus disrupting the mechanism of downforce generation and impairing the generation of streamwise vortices.

Feasibility Study For Large Scale Thermal Convective Flow Measurements In Building Physics

The Department of Building Physics / Energy-efficient Buildings at the Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau is about to put a novel research-building into commission, the “Small House III”. Among other measurement equipment, a system for volumetric, large-scale, high-resolution flow velocity measurement should be utilized. In this paper, requirements for such a system are detailed, a suitable measurement system is proposed and a feasibility study for the verification of the system requirements is conducted. To this end, a tailored system for large-scale Lagrangian particle tracking (“Shake-the-Box”) is applied to thermal convective flow measurements above an electric radiator close to a wall. As a result, it is found that the designed volumetric velocity measurement system is capable of successfully operating in the design environment without minimal disturbance of the low-speed convection flow. . After a relatively short setup time (about 5 hours, including camera setup, calibration and self-calibration) up to 10000 images at 50 Hz (200 seconds) have been recorded continuously. Shake-the-Box results show a decline of the number of tracked particles from initially 48000 to about 8000 (with a half-life span of about 100 seconds for the helium filled soap bubbles used for seeding). Applying fine scale reconstruction (data assimilation), a vector spacing of 4 mm could be achieved for instantaneous volumetric velocity snapshots. Averaging resulted in a 2 mm vector spacing with an average of 3300 particles per bin and 410 particles per bin for 1 mm vector spacing (with 75% bin overlap). Weaker particles could only be detected in front of a black background. Using a white background (default background for later applications), weak particles could not be detected as well, so the number of detected particles and the measurement volume decreased slightly compared to the black background. Overall, the feasibility study successfully confirmed the readiness of the measurement system for the intended use for “Small House III” measurements.

Object Registration Techniques For 3D Particle Tracking

Image based 3D particle tracking is currently the most widely used technique for volumetric velocity measurements. Inspecting the flow-field around an object is however, hampered by the latter, obstructing the view across it. In this study, the problem of measurement limitations due to the above is addressed. The present work builds upon the recent proposal from Wieneke and Rockstroh (2024), whereby the information of the occluded lines of sight can be incorporated into the particle tracking algorithm. The approach, however, necessitates of methods that accurately evaluate the shape and position of the object within the measurement domain. Methods of object marking and the following 3D registration of a digital object model (CAD) are discussed. For the latter, the Iterative Closest Point (ICP) registration algorithm is adopted. The accuracy of object registration is evaluated by means of experiments, where marking approaches that include physical and optically projected markers are discussed and compared. Three objects with growing level of geometrical complexity are considered: a cube, a truncated wing and a scaled model of a sport cyclist. The registered CAD representations of the physical objects are included in aerodynamic experiments, and the flow field is measured by means of large-scale particle tracking using helium filled soap bubbles. Three operating regimes are studied and compared: monolithic, partitioned and object-aware (OA) monolithic. The results indicate that object registration enables a correct reconstruction of particle tracers and strongly reduces the domain clipping typical of the monolithic approach. Furthermore, the dynamical use of all views in the OA monolithic method offers clear benefits compared to the partitioned approach, namely a lower occurrence of ghost particles. Finally, the combined visualization of the object and the surrounding flow pattern offers means of insightful data inspection and interpretation, along with posing a basis for PIV data assimilation at the fluid-solid interface.

Further Development of a High Pulse-Energy LED at 4 kHz for Volumetric Particle Tracking Velocimetry and a Demonstration Using 32 Such LED Units

In 2022, we reported at the 20th Lisbon symposium on the development of 460 nm LED specifically designed for illumination in volumetric Particle Tracking Velocimetry (PTV). At that time, our pulsed LED unit emitted light with a 6 ◦ divergence beam and a top-hat power cross section, producing 20 µ s pulses at a 4 kHz repetition rate and a 0.15 mJ pulse energy. Since then, we have been improving the efficiency of this LED. Currently, our LED unit emits a beam with similar specifications but with a pulse energy up to 0.65 mJ , which is 4.3 times more than the previous LED unit. We improved the efficiency of the electrical driver by further decreasing the footprint of the SMD circuitry and by using higher quality electronic components. Additionally, we replaced the aluminium pin fin heat sink with a copper pin fin heat sink and we characterized the thermal dissipation. Using SolidWorks, we integrated the electric driver, the copper heat sink and the collimating optics into a compact mechanical casing. These improvements resulted in an LED unit with greater overall efficiency, a larger pulse energy and a volume footprint that is half the the size of the previous design. Furthermore, we constructed four batteries of these LEDs, with each battery containing eight LED units. Here, we report on our improvements to the LED unit and our considerations in its development. Additionally, we describe preliminary results of a 3D-PTV experiment with Helium Filled Soap Bubbles (HFSB), which were illuminated by the four LED batteries.

Boiling induced atomization of liquid film produced by oblique jet impingement on superheated wall

For the thermal management of industrial devices, a reduction in the net coolant flow rate by droplet dispersion from a liquid film is important because it can cause unexpected thermal failure. To understand the process of droplet dispersion from a liquid film better, we experimentally and theoretically evaluated the characteristics of boiling-induced atomization in a liquid film formed by oblique jet impingement on a superheated wall. Atomization processes were visualized using magnified high-speed imaging using a backlight technique. In this study, two types of droplets were observed using high-speed-magnification imaging. These were large droplets that disintegrated from the ligament formed on a relatively high-temperature wall, and small droplets from the ligament formed via bubble bursting in the nucleate boiling regime. For the atomization induced by nucleate boiling, larger droplets were produced via bubble bursting further downstream from the impingement point because the bubble size and liquid film thickness increased. Finally, the total volume of the droplets produced by nucleate boiling was estimated from the frequency of bubble bursting and droplet size measured from the visualization results. The estimation results suggest that the ratio of the total volume flow rate of the ejected droplets to the injection flow rate of the liquid was negligible (2%). Thus, most of the injected liquid eventually reached the wetting front of the sheet, separating it from the wall before drying out.