Bubble Deformation Research Articles

Optical measurement of the shear stress and velocity distribution in an idealized deglutition process

The rheological properties of food have an impact on physical interaction with various haptic sensors in the mouth during the chewing and swallowing process. Therefore, the investigations on food rheology are dedicated to improving the texture or mouthfeel of a product. It is advantageous to perform such rheological measurements in geometries and under conditions that reflect the flow conditions during the food distortion in the mouth cavity. Such investigations have been limited primarily to viscous or lumpy foodstuffs. Our study is dedicated to the compression of liquid foams in an idealized deglutition process. To reflect the flow conditions in such a process, we developed an experimental setup consisting of a quasi-two-dimensional replica of the palate and a movable tongue. During the idealized deglutition process, the optical measurements of bubble displacement and deformation were performed. The deglutition process was modelled by varying the compression speed of the tongue towards the static palate. The variation in mean bubble size and liquid fraction of foam for two tongue geometries with different roughness are available. It is observed that the velocity distribution of bubble motion during the deglutition corresponds to a rigid body flow, notwithstanding the surface roughness. The resulting wall-shear stress, however, was higher for the rough tongue plate for all foam bubble sizes and liquid fraction. The resulting velocity and wall-shear stress distributions can provide information about the haptic perception in the mouth during the swallowing process.

Direct numerical simulation of bubble collision, bounce and coalescence in bubble-induced turbulence

A direct numerical simulation study has been carried out to better understand the dynamics of deformable bubbles in bubble-induced turbulence. A mathematical model for bubble collision, bounce and coalescence is developed based on the Volume-of-Fluid (VoF) method. A surface-tension-holding film thickness δc is introduced to determine whether the bubbles will coalesce or bounce after collision. Bubbly flows with the gas volume fractions αg=5.6% (low), 11.2% (medium) and 22.1% (high) are considered in the study. The DNS results show that the dissipation of turbulent kinetic energy in the cases under consideration takes place when the wavenumber κ is smaller than twice the wavenumber for the bubble diameter 2κd. The bubble-induced turbulence is anisotropic at the length scales close to the bubble diameter due to the elongated turbulent structures in the bubble-rising direction. The bubbles collide intensively with each other when they are in a cluster surrounded by the liquid with low pressure. Parallel clustering of bubbles is found when the gas volume fraction has a low or medium value. Three-dimensional clustering is found when the bubbles are densely populated. Two different mechanisms of bubble collision have been identified from the DNS results, termed parallel collision and vertical collision. Parallel collision is often observed when bubbles are sparsely populated. In a parallel collision, the relative velocity of the bubbles slows down as two bubbles approach each other due to the jet flow between them, while the relative velocity increases sharply after the bounce. In a vertical collision, by contrast, the relative velocity of bubbles accelerates as two bubbles approach each other, while it slows down during the collision. Vertical collisions occur when the bubbles are more densely populated. The numerical results also show the significant effects of δc on bubble coalescence.

Phase field simulation of single bubble behavior under magnetic field

By combining the continuum equation with the momentum equation, phase field and magnetic field, a three-dimensional multi-field coupled model of the single bubble rising dynamics in the gas–liquid two-phase flow is established. The phase field method is used to capture the two-phase interface and simulate the movement of the gas–liquid interface. Compare the model with the numerical simulation under the Level Set method, it turns out that the simulation effect of the model established by the phase field method is better. The effects of different magnetic field intensity on the rise velocity of bubble and bubble deformation under vertical and horizontal magnetic field are analyzed. The results show that the bubble stretches along the magnetic field line under the action of the magnetic field, and the degree of bubble deformation is proportional to the intensity of the magnetic field. The rising speed of the bubble is affected by the magnetic field, which speeds up the overall rising speed of the bubble in the vertical direction and slows down the rising speed of the bubble in the horizontal direction.

Investigation on interphase mass transfer coefficient of a deformable bubble with density contrast using phase-field lattice Boltzmann method

The gas–liquid mass transfer process with density contrast is modeled in this paper using a phase-field Lattice Boltzmann (LB) method. In this method, the phase-field model used to calculate the flow field and the continuous species transfer model used to calculate the concentration distribution are coupled by introducing the divergence condition of the velocity in the presence of mass transfer into the Allen-Cahn equation. For a deformable bubble rising in stagnant liquid, a two-dimensional parameter dependence study is conducted and the results indicate that an increase in initial diameter, as well as a decrease in liquid diffusion coefficient or liquid viscosity, can improve the steady-state value for the Sherwood number, whereas the distribution coefficient has a little impact on this steady-state value. Furthermore, a correlation originally proposed by Takemura and Yabe (1998) modified with a shape factor can be used to predict the steady-state Sherwood number in the numerical results.

A microfluidic hemostatic diagnostics platform: Harnessing coagulation-induced adaptive-bubble behavioral perception

Clinical viscoelastic hemostatic assays, which have been used for decades, rely on measuring biomechanical responses to physical stimuli but face challenges related to high device and test cost, limited portability, and limited scalability.. Here, we report a differential pattern using self-induced adaptive-bubble behavioral perception to refresh it. The adaptive behaviors of bubble deformation during coagulation precisely describe the transformation of viscoelastic hemostatic properties, being free of the precise and complex physical devices. And the integrated bubble array chip allows microassays and enables multi-bubble tests with good reproducibility. Recognition of the developed bubble behaviors empowers automated and user-friendly diagnosis. In a prospective clinical study (clinical model development [n= 273]; clinical assay [n= 44]), we show that the diagnostic accuracies were 99.1% for key viscoelastic hemostatic assay indicators (reaction time [R], kinetics time [K], alpha angle [Angle], maximum amplitude [MA], lysis at 30min [LY30]; n= 220) and 100% (n= 44) for hypercoagulation, healthy, and hypocoagulation diagnoses. This should provide fresh insight into existing paradigms and help more clinical needs.

А particle model of interaction between weakly non-spherical bubbles

A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed. It is a system оf the second order ODEs in the radii of bubbles, the position vectors of their centers and the amplitudes of their small deformations in the form of spherical harmonics. Compared to the available analogs, the proposed model equations are more accurate in terms of the ratio of the radii of bubbles to the distance between their centers. This allows one to study bubble-bubble interaction at smaller distances between the bubbles. The model equations are quite compact, which simplifies their theoretical analysis and construction of algorithms of their solution. Five problems (dynamics of a single bubble under harmonic excitation, bubble collapse near a plane rigid wall, interaction of three synchronized and nonsynchronized bubbles located in line, and interaction between sixteen bubbles with the centers located on a plane surface) are considered for validation. It is shown that in all cases the proposed model results well agree with the corresponding available experimental data and numerical solutions. For demonstration of the applicability, the proposed model is used to analyze radial oscillations, spatial movements and surface deformations of the bubbles in rectilinear, planar and spatial clusters under harmonic forcing. Initially 125, 121 and 125 bubbles of the clusters are located at the nodes of 1D, 2D and 3D uniform grids, respectively. It is found that the monotonically decaying radial oscillations of the 1D cluster bubbles during one period of forcing are quite similar to those of a single bubble. Unlike this, the attenuation of the radial oscillations of the central bubbles in the 2D and 3D clusters is essentially non-monotonic. The maximum pressures in the central bubbles of the 2D and 3D clusters are significantly higher than in the single and 1D cluster bubbles. In all clusters the maximum deformations of bubbles are in the form of the second spherical harmonics, except for the central bubble of the 3D cluster, the maximum deformations of which are in the form of the fourth harmonics.

Fate of bubble clusters rising in a quiescent liquid

We use experiments to study the evolution of bubble clusters in a swarm of freely rising, deformable bubbles. A new machine learning-aided algorithm allows us to identify and track bubbles in clusters and measure the cluster lifetimes. The results indicate that contamination in the carrier liquid can enhance the formation of bubble clusters and prolong the cluster lifetimes. The mean bubble rise velocities conditioned on the bubble cluster size are also explored, and we find a positive correlation between the cluster size and the rise speed of the bubbles in the cluster, with clustered bubbles rising up to $20\,\%$ faster than unclustered bubbles.

Large eddy simulations of bubbly flows and breaking waves with smoothed particle hydrodynamics

For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubbles are prohibitively expensive in the context of different natural phenomena. One example is breaking waves, where bubbles strongly influence wave impact loads, acoustic emissions and atmospheric-ocean transfer, but detailed simulations in all but the simplest settings are infeasible. An alternative approach is to resolve only large scales, and model small-scale bubbles adopting sub-resolution closures. Here, we introduce a large eddy simulation smoothed particle hydrodynamics (SPH) scheme for simulations of bubbly flows. The continuous liquid phase is resolved with a semi-implicit isothermally compressible SPH framework. This is coupled with a discrete Lagrangian bubble model. Bubbles and liquid interact via exchanges of volume and momentum, through turbulent closures, bubble breakup and entrainment, and free-surface interaction models. By representing bubbles as individual particles, they can be tracked over their lifetimes, allowing closure models for sub-resolution fluctuations, bubble deformation, breakup and free-surface interaction in integral form, accounting for the finite time scales over which these events occur. We investigate two flows: bubble plumes and breaking waves, and find close quantitative agreement with published experimental and numerical data. In particular, for plunging breaking waves, our framework accurately predicts the Hinze scale, bubble size distribution, and growth rate of the entrained bubble population. This is the first coupling of an SPH framework with a discrete bubble model, with potential for cost-effective simulations of wave–structure interactions and more accurate predictions of wave impact loads.

Study on the Dynamic Evolution of Bubbles in Oil/Pressboard Insulation

Power transformer may generate bubbles in the transformer oil due to various factors such as internal insulation winding vibration and pressure change. Bubbles distort the spatial electric field, which makes the discharge breakdown along the gas channel, accelerate the discharge breakdown of insulating medium. Therefore, in order to prevent the arc discharge induced by micro bubbles inside the transformer from increasing the risk of transformer combustion damage, it is necessary to conduct in-depth research on the dynamic law of suspended bubbles before insulation breakdown from the source by combining experiments and simulations. In this paper, the bubble dynamic model of needle plate electrode under the multi coupling physical field of transformer is established in terms of the migration and deformation of suspended bubbles in liquid phase. By comparing the migration trajectories of single suspended bubbles obtained from experiments and simulations, the reliability of the model is verified. The variation of velocity component of voltage amplitude and the change of shape stretching of single suspended bubble in power frequency period are simulated, and the fluctuation law of pressure formed by electrostriction force inside and outside the bubble during migration is analyzed. The capacity absorption process of multi bubbles in the strong field region near the needle electrode was simulated. The changes of the surrounding liquid pressure and the spatial electric field distribution during the formation of the gas channel were analyzed, and the internal relationship between the gas channel and the formation of the discharge breakdown was revealed.

Type of pectin determines structuring potential of soy proteins into meat analogue applications

The addition of pectin to soy protein isolate (SPI) is a route to create fibrous products using shear cell technology. In this study, we investigated pectins derived from soybean, sugar beets, and citrus (two variants) that vary in sugar composition, degree of methylation and acetylation. The objective was to examine how these different pectins impact the functional properties of the SPI dispersions. The SPI-pectin blends were shear structured and their visual appearance, microstructural, rheological, and mechanical properties were analyzed. The addition of pectins from citrus (the highly methyl-esterified form) and soybean resulted in fibrous products when mixed with SPI. The addition of the low methyl-esterified pectin derived from citrus led to less pronounced fibrous product, and pectin from sugar beet did not lead to fibrous products. To explain the effect, several properties of the blends and products were tested. It was found that the fibrous products contained more air (i.e. higher void fraction) than products that were not fibrous, and that air bubbles were deformed in the shear direction. The rheological measurements of the blends revealed that the pectins lowered the yield and flow point of SPI, and the flow transition index. The blend with the highest elasticity after heating also had the highest deformation of air bubbles. Based on all results it was concluded that pectin influenced the structure formation in two ways: 1) affecting the ability to facilitate air inclusion and 2) influencing the storage modulus and elasticity of the matrix.

Competitive methane bubble growth in aquatic muds

Methane (CH4) bubbles residing in shallow aquatic muds pose a significant threat to the environment. Impeded by the muddy sediment opacity and insufficient resolution for their characterization, past studies overlooked bubble interactions as they grow. Here, the competitive fracture-driven growth of CH4 bubble pair with different initial sizes in the aquatic muds is simulated, using a mechanical/reaction-transport numerical model. Mechanical and solute transport interactions were found to dominate at the different stages of the bubble growth, both retarding the smaller competitive bubble growth. The stress from large competitive bubble affects the inner pressure and diffusive CH4 flux to the smaller bubble, causing its slower initial growth (at t < 40 s). The large competitive bubble also diverts CH4 from the smaller one later on, thus inhibiting its growth even more. Bubble stress interactions may produce more laterally oriented smaller bubble and significant deformations of the larger one, both amplified under the decreasing distance between the growing bubble pair. Competitive bubble growth may shape a bubble size distribution pattern observed in the lab experiments and in situ, which may promote muddy sediment CH4 gas retention and produce gas domes. The latter acts as pockmark precursors whose formation induces a violent gas release to the water column and potentially to the atmosphere. Our study presents a basis for a proper upscaling to various effective gassy muddy sediment characteristics and gas retention evolution transient models, while preserving the single bubble growth descriptors. It contributes to evaluation and even reduction of a long-persisting uncertainty related to CH4 flux from the shallow aquatic sediments.

Numerical Simulation on Insoluble Surfactant Mass Transfer on Deformable Bubble Interface in a Couette Flow by Phase-Field Lattice Boltzmann Method-Finite-Difference Method Hybrid Approach.

Elaborate management on bubble shape and transportations depends on the balance between multiple physical behaviors for two-phase flow with Marangoni stress and the interface mass transfer. In this paper, a new model combining PFLBM (phase-field lattice Boltzmann method) and FDM ( finite-difference method) coupling with the ghost-cell method was built. The PFLBM-FDM was validated for the high accuracy, less computational cost, and low mass loss compared to other methods. Based on the PFLBM-FDM, a surfactant-laden bubble deformed and transported in a laminar Couette flow was investigated. The deformation ratio and transportation velocity were explored with different density ratios, surface tensions, shear velocities, and diffusion coefficients. The numerical results showed that the equilibrium state of the bubble deformation was decided only by the dimensionless numbers when the Sh number was higher than 100. Moreover, the transportation velocity of the bubble can be controlled by the balance between the Marangoni stress and shear velocity. When the Sh is lower than 100, the Marangoni stress from the surfactant is not a long-range force, which only works at the early flow. Otherwise, the Marangoni stress will be a long-range force that provides a persistent force to accelerate the bubble by ∼10%. Increasing ReH will further intensify the effect. Based on all the data, a correlation of the bubble deformation including with the densities of two fluids was obtained and the error range is less 5%.

Impact of surfactants on the rise of deformable bubbles and interfacial gas–liquid mass transfer

Axisymmetric numerical simulations of the hydrodynamics around rising bubbles are performed in order to investigate the impact of surfactants on the bubble dynamics. Surfactants are assumed to be insoluble. The transport of the adsorbed surfactants is computed along the deforming surface at large surface Péclet number, and Marangoni stresses are taken into account. This simulation model leads to the stagnant-cap regime, with partially immobile interfaces. A parametric study is performed on cases at given Archimedes number, by varying the degree of contamination (Marangoni number) but maintaining a nearly constant Eötvös number. The presence of surfactants affects the rise velocity for oblate bubbles less than for spherical bubbles: the increase of the drag coefficient, due to interface contamination, is mitigated by a lower bubble deformation. When the cap angle $\theta _{cap}$ belongs to the southern hemisphere, the aspect ratio $\chi$ is found to decrease with contamination: the dynamic pressure responsible for the bubble distortion is lowered, related to the decline of kinetic energy. As soon as $\theta _{cap}$ lies in the northern hemisphere, the pressure stress causing distortion becomes independent on $\theta _{cap}: \chi$ no longer evolves with contamination, and already matches the prediction for fully immobile interfaces. Mass transfer of a passive scalar across the contaminated interface is also analysed. Surprisingly, the Sherwood number $Sh$ is found to follow the same law as for spherical shapes (Kentheswaran et al., Intl J. Heat Mass Transfer, vol. 198, 2022, 123325), allowing us to predict the decrease in $Sh$ due to contamination. These results reveal the couplings between interface immobilisation, bubble deformation, rise velocity and interfacial mass transfer.

Analysis of Bubble Motion Characteristics in Oil Based on Level Set Method

At present, transformer oil is the primary insulation method for large power transformers, and the dynamic behavior of bubbles in transformer oil can impact the insulation performance of transformer oil. Therefore, based on the level set method in this paper, the motion characteristics of bubbles in two structures, a horizontal oil channel and a vertical oil channel, under various conditions of different bubble numbers, different flow velocities, and different bubble sizes are studied using finite element simulation. The simulation results show that the kinetic behavior of bubbles becomes more complicated as the radius increases, the number of bubbles increases, and the flow velocity increases. At the same time, the bubble expansion and deformation is a cyclic process due to the electric field force, laminar flow and surface tension in the bubble suspension process.

Application of PIV for Virtual Mass Coefficient Measurement

The particle image velocimetry (PIV) technique is employed for the measurement of the virtual mass of a submerged object, an important parameter in the two-fluid model, particularly so for reactor thermal-hydraulic and safety analyses. Instead of carrying out the measurement through traditional transient processes that mix steady-state drag, virtual mass force, and Basset force, a new PIV approach is developed for steady-state flows through the integration of the fluid kinetic energy around the object. The Basset force, an inseparable transient force in viscous flows, is eliminated in the new approach, making virtual mass quantification possible. This new method has been applied to the virtual mass measurement of a solid cylinder, and although the measurement uncertainty from the flow’s random fluctuations is substantial, the results are very encouraging. The results suggest that the existence of drag force in viscous flow affects the virtual mass, as the flow field is different from the ideal potential flow. When the measurement method was applied to the quantification of air bubbles, no reliable data were obtained due to complications from bubble lateral motions and deformation. Further study is needed for the PIV method to be employed for bubble virtual mass force measurements under steady-state flow conditions.

Single-Bubble Rising in Shear-Thinning and Elastoviscoplastic Fluids Using a Geometric Volume of Fluid Algorithm.

The motion of air bubbles within a liquid plays a crucial role in various aspects including heat transfer and material quality. In the context of non-Newtonian fluids, such as elastoviscoplastic fluids, the presence of air bubbles significantly influences the viscosity of the liquid. This study presents the development of an interface-capturing method for multiphase viscoelastic fluid flow simulations. The proposed algorithm utilizes a geometric volume of fluid (isoAdvector) approach and incorporates a reconstructed distance function (RDF) to determine interface curvature instead of relying on volume fraction gradients. Additionally, a piecewise linear interface construction (PLIC) scheme is employed in conjunction with the RDF-based interface reconstruction for improved accuracy and robustness. The validation of the multiphase viscoelastic PLIC-RDF isoAdvector (MVP-RIA) algorithm involved simulations of the buoyancy-driven rise of a bubble in fluids with varying degrees of rheological complexity. First, the newly developed algorithm was applied to investigate the buoyancy-driven rise of a bubble in a Newtonian fluid on an unbounded domain. The results show excellent agreement with experimental and theoretical findings, capturing the bubble shape and velocity accurately. Next, the algorithm was extended to simulate the buoyancy-driven rise of a bubble in a viscoelastic shear-thinning fluid described by the Giesekus constitutive model. As the influence of normal stress surpasses surface tension, the bubble shape undergoes a transition to a prolate or teardrop shape, often exhibiting a cusp at the bubble tail. This is in contrast to the spherical, ellipsoidal, or spherical-cap shapes observed in the first case study with a bubble in a Newtonian fluid. Lastly, the algorithm was employed to study the buoyancy-driven rise of a bubble in an unbounded elastoviscoplastic medium, modeled using the Saramito-Herschel-Bulkley constitutive equation. It was observed that in very small air bubbles within the elastoviscoplastic fluid, the dominance of elasticity and capillary forces restricts the degree of bubble deformation. As the bubble volume increases, lateral stretching becomes prominent, resulting in the emergence of two tails. Ultimately, a highly elongated bubble shape with sharper tails is observed. The results show that by applying the newly developed MVP-RIA algorithm, with a tangible coarser grid compared to the algebraic VOF method, an accurate solution is achieved. This will open doors to plenty of applications such as bubble columns in reactors, oil and gas mixtures, 3D printing, polymer processing, etc.

The Shock-Induced Deformation and Spallation Failure of Bicrystal Copper with a Nanoscale Helium Bubble via Molecular Dynamics Simulations.

Both the nanoscale helium (He) bubble and grain boundaries (GBs) play important roles in the dynamic mechanical behavior of irradiated nanocrystalline materials. Using molecular dynamics simulations, we study the shock-induced deformation and spallation failure of bicrystal copper with a nanoscale He bubble. Two extreme loading directions (perpendicular or parallel to the GB plane) and various impact velocities (0.5-2.5 km/s) are considered. Our results reveal that the He bubble shows hindrance to the propagation of shock waves at lower impact velocities but will accelerate shock wave propagation at higher impact velocities due to the local compression wave generated by the collapse of the He bubble. The parallel loading direction is found to have a greater effect on He bubble deformation during shock compression. The He bubble will slightly reduce the spall strength of the material at lower impact velocities but has a limited effect on the spallation process, which is dominated by the evolution of the GB. At lower impact velocities, the mechanism of spall damage is dominated by the cleavage fracture along the GB plane for the perpendicular loading condition but dominated by the He bubble expansion and void growth for the parallel loading condition. At higher impact velocities, micro-spallation occurs for both loading conditions, and the effects of GBs and He bubbles can be ignored.

Prediction of bubble shape deformation in aqueous solutions of short-chain alcohols

The behaviour of bubbles in aqueous solutions of short-chain alcohols depends significantly on the alcohol concentration. At low concentrations, alcohols act as surfactants and slow the rising velocity of the bubble, whereas at higher concentrations, primarily due to the internal arrangement at the molecular level, the desorption of molecules from the bubble surface is facilitated and the mobility of the bubble surface is increased. These factors significantly affect both bubble velocity and deformation. On the basis of experimental data (aqueous solutions of ethanol and propanol in the entire concentration range), two relations were proposed for the estimation of bubble deformation depending on the dimensionless Weber number. The model was successfully verified on an independent data set of the velocity and deformation of bubbles that rise in a stationary liquid.

Experimental and numerical analysis on electrolytic bubble group dynamics in the aluminum electrolysis process using the slotted anode

The CuSO4 aqueous solution electrolysis experiment is conducted to investigate the electrical bubble dynamics using the slotted anode to reveal the gas removal mechanism. A three-dimensional transient mathematical model coupled discrete phase model (DPM) − discrete-continuum transition model (DCTM) − volume of fluid (VOF) method is developed to track the dispersed bubble trajectory, bridge the dispersed bubble to continuous gas, and resolve the deformed bubble surface, respectively. The slotted anode decreases the bubble diameter compared with the traditional anode because the slot shortens the bubble motion distance to decrease the bubble residence time. The slot width smaller than the detached bubble diameter can limit the bubble deformation. Increasing current plays a dual role in bubble motion in the experiment: it accelerates the bubble coalescence process but decreases the bubble collision probability. The longitudinal slot is more conducive to reducing the maximum bubble coverage and increasing the bubble release frequency than the transverse slot.

Numerical investigation of shock Mach number effects on Richtmyer–Meshkov instability in a heavy square bubble

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: Ms=1.12, 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated.