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In this study, an incompressible and immiscible two-phase flow solver was employed to assess the accuracy of phase-interface capturing methods in simulating two-phase flows. Three benchmark investigations were conducted involving two dam break flows with deformable free surfaces and the upward motion of a gas bubble through a liquid column. Four phase-interface capturing schemes, namely, MULES, HRIC and CICSAM from the Color Function Volume of Fluid (CF-VoF), and Interface Reconstruction Volume of Fluid (IR-VoF), were utilized. Comparative analysis of the phase interfaces indicated that CICSAM and IsoAdvector consistently provided sharp interfaces across all cases when compared to MULES and HRIC. The mass conservation performance of all schemes excelled in the dam-break case with relatively simple free-surface development and the rising bubble case. An examination of the local pressure distribution over time revealed that methods yielding diffusive interfaces produced inaccurate results. Thus, the importance of employing denser grids or schemes that yield sharper interfaces, such as CICSAM and IsoAdvector, to enhance simulation accuracy was underscored. Overall, the results of this analysis confirm that the IsoAdvector scheme, which provides sharp interfaces, is a reliable option for simulating incompressible immiscible two-phase flows. [ABSTRACT FROM AUTHOR]

In this paper, we perform direct numerical simulation of the ascent of an initially resting air bubble in water without a current. For comparison with the experiment, a complicated initial bubble shape corresponding to the experimental one is taken. Changes in the shape of the bubble during the ascent process that are obtained as a result of numerical modeling are close to experimental changes in the shape of the bubble. For comparison with the results of numerical simulations available in publications, a rising bubble with an initially spherical shape is simulated. During the ascent process, the shape of the bubble is found to be at first close to elliptical and experiences oscillations. However, then it becomes more complex: a "tail" appears in the lower part of the bubble. This mode of rising-bubble dynamics is confirmed by published results of numerical simulations. [ABSTRACT FROM AUTHOR]

This study implements a new solver (reactiveInterFoam) to simulate the component mass transfer alongside deformable gas–liquid interfaces. Mass transfer from the rising bubble in a quiescent Newtonian fluid is simulated. An effect of bubble hydrodynamics on the simultaneous diffusion reaction and selectivity of the cyclohexane oxidation process is investigated on a two-dimensional axisymmetric domain. The color function volume of fluid (CF-VoF) technique is applied to capture the deformable interface, and the continuous species transfer method is used to monitor the gas–liquid mass transfer behavior. Several simulations have been conducted to validate the model reliability to forecast component mass transfer from the bubble to the liquid phase, bubble shape, and flow field. Simulation findings approved that the rate of mass transfer is a function of boundary's concentration, layer thickness, and bubble surface area. Furthermore, the selectivity increases by decreasing bubble diameter in both spherical and ellipsoidal regimes. The small bubbles with a lower Reynolds number have higher average selectivity. Comparing the simulated bubble shape and the grace chart indicates that the suggested numerical method can perfectly predict bubble regimes. The absolute average relative deviation (AARD%) of 14.59% has been observed between the terminal velocities predicted by the numerical simulation and six experimental measurements. [ABSTRACT FROM AUTHOR]

This study is dedicated to comparison of the results of two-dimensional (2D) and three-dimensional (3D) numerical modeling of dynamics of a single bubble rising in stagnant viscous liquid. The volume of fluid method is used to track the moving interface. This method makes it possible to take into account all the forces acting on the interface in a natural way without using empirical data. The solution of the continuity equation, Navier–Stokes equation, and equation for determining the position of interface is based on the finite volume method. When carrying out numerical experiments, the bubble diameter at the initial time is fixed. It is shown that the shape of the bubbles in the vertical section of the computational domain is different in the case of 2D and 3D simulations. It has been established that the rising velocity of bubble in 3D simulation is greater than in 2D simulation. [ABSTRACT FROM AUTHOR]

Liquid‐liquid interfacial tension is an important parameter in gas‐liquid‐liquid multiphase flows. Here, bubble passage through an immiscible liquids interface was used for determining the interfacial tension. The method is based on measuring the volume of the heavy liquid entrained into the light one. Two different semi‐empirical models were developed for determining the entrainment ratio. The results are in good agreement with experiments covering a wide range of physical properties of the liquids. Each model is extended to build a master curve that can be used for predicting the interfacial tension. The models and master curves are obtained based on experimental data for gas‐phase motion through the interface between immiscible liquids, which makes the modeling results more reliable for gas‐liquid‐liquid systems. [ABSTRACT FROM AUTHOR]

Evaluation of the behavior of adsorbed layers of the protein-surfactant mixture at air-water interfaces has recently received great attention due to their many applications in food and pharmaceutical industries. This research study employs rising bubble method to investigate the qualitative study of surface activities of two kinds of proteins, i.e., Beta-Lactoglobulin (BLG) and Beta-Casein (BCS), non-ionic surfactant of C10DMPO, and the mixtures of them at different concentrations at the air-water interface. The similarity between measured local velocity profiles results from the fact that all the mentioned materials are surface-active, can create the Marangoni effect, and develop a dynamic adsorption layer. Given the insignificant interaction between the protein and surfactant molecules, stable complex structures cannot be formed in the protein-C10DMPO mixture. The mixture velocity profile is more similar to that of the surfactant resulting from the replacement of protein molecules or complexes with free surfactant at the bubble interface. It is found that the mixture of non-ionic surfactant and BCS has minor synergetic effect, while for its mixture with BLG, a negative synergy resulting from the shape of protein is observed. [ABSTRACT FROM AUTHOR]

Rising bubbles in liquid metals in the presence of magnetic fields is an important phenomenon in many engineering processes. The nonlinear behavior of the terminal rise velocities of the bubbles as a function of increasing field strength has been observed experimentally, but it remains poorly understood. We offer an explanation of the phenomenon through numerical calculations. A single rising bubble in stagnant liquid metal in the presence of an applied horizontal magnetic field is simulated. The observed nonlinear behavior is successfully reproduced; the terminal velocity increases with the increase in the magnetic field strength in the lower magnetic field regions but decreases in higher regions. It is shown that, in the lower region, the increase in the average bubble rise velocity results from the suppression of the fluctuations in the bubble trajectory in the vertical plane perpendicular to the magnetic field, as a consequence of the Lorentz force resulting from the component of induced electric current due to the magnetic field, which (approximately) acts in the opposite direction to that of the flow velocity. For higher magnetic field strengths, the Lorentz force induces a broadened wake in the vertical plane parallel to the applied magnetic field, resulting in a decrease in the rise velocity. [ABSTRACT FROM AUTHOR]

In the present work, the problems of oil-water dam-break flow interaction with porous structures are numerically investigated using the coupled Volume-Of-Fluid model (VOF) and non-linear Darcy-Brinkman-Forchheimer model. The accuracy of the developed model is verified through rigorous validation against various demanding benchmark scenarios. These included mixed convection heat transfer in a square porous cavity, the ascent of a single bubble in both fully and partially filled containers, and the interaction of waves with porous structures. Comparative evaluation against existing literature confirmed the reliability and effectiveness of the numerical approach in accurately simulating intricate fluid dynamics within porous media. Subsequently, the validated numerical model is utilized to examine the hydrodynamic behaviour of oil-water dam-break flows through porous media. In the first scenario, a rectangular oil column is positioned atop a rectangular water column. In the second scenario, the two columns are arranged sequentially beside each other. The effects of these arrangements on the resultant pressure shock and hydrodynamic behavior have been investigated. The findings results vividly reveal that the morphology and hydrodynamic characteristics of the dam-break flow are significantly influenced by the presence of the porous matrix. Furthermore, the results showed that the resultant shock pressure is considerably affected by the initial positions of oil and water. The obtained results are depicted in forms of contours of pressure and volume fraction fields and are discussed in details. [Display omitted] • A hybrid VOF and Darcy-Brinkman-Forchheimer model has been developed for simulating multiphase flows inside enclosures containing porous structure. • The hydrodynamic behavior of oil-water dam break flow through porous structures is investigated numerically. • The effects of the arrangement of the oil and water columns on the resultant pressure shock are examined. • The governing equation for the VOF-Darcy-Brinkman-Forchheimer has been thoroughly explained. [ABSTRACT FROM AUTHOR]

The integrated behavior of the fluid flow, encompassing variation of some specific response, has received more attention than mere examination of velocity and pressure distributions. A machine learning framework is introduced for the first time to elucidate and predict the complex fluid dynamic responses across varying time scales. For the same class of fluid processes, the dynamic response curves with varying time durations can be defined in terms of time scales and curve shapes. The former is predicted by a single-objective regression model, and the curves are normalized and recovered using time scaling and uniform interpolation. The latter are downscaled by Principal Component Analysis (PCA) and then predicted by a multi-objective regression model. As a novel application, this framework is employed to analyze small bubbles in a Newtonian fluid as they impact a horizontal wall, predicting the velocity, aspect ratio, and position dynamic response of the bubbles. Both Random Forest and Gaussian Process models, based on PCA-driven data processing, exhibit remarkable accuracy in describing and predicting complex dynamics of rising bubbles. Notably, PCA's principal components demonstrate independence and are set through rigorous cross-validation of the training set, rather than dependence on the Cumulative Variance Explained (CVE) values. Furthermore, our framework adeptly extends to predict the complex behavior of multiple bubble bounces by concatenating individual bounce predictions with high efficiency and precision. The proposed framework proves to be a catalyst for comprehending the dynamic response of fluids. [ABSTRACT FROM AUTHOR]

Pressure and viscous drags acting on a bubble rising in a viscous fluid are numerically estimated to obtain the corresponding drag coefficients that are rarely reported in the existing papers. The numerical method has been successfully validated by solving the existing benchmark problems of a bubble rising in a quiescent liquid at various flow regimes. For spherical cap bubbles, the formula of total drag coefficient is proposed in a similar form to that by viscous potential flow theory expressed by the Reynolds number, and the corresponding formulas for pressure and viscous drag coefficients are derived. Furthermore, the effect of the density ratio of a bubble and the surrounding liquid on terminal velocity is also investigated for fixed Morton and Eotvos numbers: the lighter bubble has a higher terminal velocity having an asymptotic value as the density ratio increases although the Reynolds numbers based on the terminal velocity are nearly constant. [ABSTRACT FROM AUTHOR]

The passage of a rising air bubble through a stratified horizontal interface between two Newtonian liquids is studied numerically. A ternary phase‐field model has been utilized for capturing the interface between three immiscible fluids. According to the previous studies, the density, viscosity, and surface tension of the two liquids, in addition to the bubble diameter, are the effective parameters of bubble interaction with the interface. By changing these variables, three main flow patterns are identified in numerical simulations. Penetration flow regime is observed when the bubble enters the upper liquid alone and does not raise the lower liquid. Entrainment flow regime occurs when the bubble lifts some of the heavier liquid to the lighter liquid but still rises alone. If the bubble holds a film of the denser liquid when it rises in the upper liquid, envelopment flow regime takes place. A flow regime map is represented to distinguish the aforementioned flow patterns using Weber and Morton numbers and determine regime transition criteria based on these two dimensionless parameters. For Weber numbers lower than 30, or Morton numbers higher than 1.7 × 10−2, the penetration regime is observed. On the contrary, when the Weber number is higher than 65 and the Morton number is lower than 7 × 10−5, the envelopment regime occurs. The entrainment pattern happens between these ranges and two additional limiting relations of 320Mo0.18 < We < 1500Mo0.23. [ABSTRACT FROM AUTHOR]

Rising bubbles in liquid metals in the presence of magnetic fields is an important phenomenon in many engineering processes. The nonlinear behavior of the terminal rise velocities of the bubbles as a function of increasing field strength has been observed experimentally, but it remains poorly understood. We offer an explanation of the phenomenon through numerical calculations. A single rising bubble in stagnant liquid metal in the presence of an applied horizontal magnetic field is simulated. The observed nonlinear behavior is successfully reproduced; the terminal velocity increases with the increase in the magnetic field strength in the lower magnetic field regions but decreases in higher regions. It is shown that, in the lower region, the increase in the average bubble rise velocity results from the suppression of the fluctuations in the bubble trajectory in the vertical plane perpendicular to the magnetic field, as a consequence of the Lorentz force resulting from the component of induced electric current due to the magnetic field, which (approximately) acts in the opposite direction to that of the flow velocity. For higher magnetic field strengths, the Lorentz force induces a broadened wake in the vertical plane parallel to the applied magnetic field, resulting in a decrease in the rise velocity.

[Display omitted] The shear stress of the axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap. The formation of the stagnant cap gives rise to Marangoni stresses that reduce the mobility of the interface, which in return reduces the rising velocity. However, the conditions in technological processes usually deviate from the linear rise of a single bubble in a quiescent unbounded liquid. Asymmetric shear can act on the bubble surface e.g. due to the vorticity in the surrounding flow, bubble–bubble interactions, or influence of the reactor wall. A different surfactant distribution at the interface is expected under asymmetric shear, which can change the hydrodynamic behavior of the interface drastically. Here we conduct model experiments with a bubble or a drop at the tip of a capillary placed in a defined flow field. Thereby we investigate the influence of asymmetric shear forces on the interface in the presence of surfactants. Microscopic particle tracking velocimetry is employed to measure the velocity of the surfactant-laden interface for different degrees of asymmetry in the surrounding liquid flow. We show a direct experimental observation of the circulating flow at the interface under asymmetric shear, which prevents the formation of the typical stagnant cap. Additionally, we reveal that the interface remains mobile regardless of the surfactant concentration. Our results confirm that increasing the degree of asymmetry increases the shear forces and thus the interfacial velocity. [ABSTRACT FROM AUTHOR]

Industrial processes do not often deal with a pure fluid. Impurities can affect physical properties of gas-liquid systems, resulting in change of gas bubbles velocity. Purpose of the study was to determine drag coefficient of a bubble rising through a contaminated fluid. As well as, a comparison was done between conditions of a free rising bubble and a rising bubble in wall-bounded flow. Thus, the behavior of a single air bubble rises in aqueous rhamnolipid solutions within two columns with different dimensions was studied experimentally. The experiments were conducted at high Reynolds numbers compared to other researches. The results revealed that effect of the surfactant in wall-bounded flow was much less than free flow whereas bubble terminal velocity was close to the one in a pure fluid and independent of concentration. Moreover, terminal velocity of the free rising bubble decreased as the solution concentration increased for the one less than critical micelle concentration. After that, it kept constant. Furthermore, resulted drag coefficient did not change significantly in different biosurfactant concentrations. The results showed that in high Reynolds number, drag coefficient was a function of Eötvös number and independent of Reynolds and Morton numbers. Consequently, two empirical correlations were presented to predict the terminal velocity and drag coefficient based on surface tension and Eötvös number, respectively. [ABSTRACT FROM AUTHOR]

A multi-level adaptive mesh refinement technique for an integrated finite element/level set formulation was implemented to simulate the incompressible interfacial flows with surface tension by using unstructured P2P1 triangular and tetrahedral meshes. Linear/quadratic elements near the interface were dynamically refined as an interface evolves in order to produce an accurate solution with a lower computational cost. An adaptive mesh refinement algorithm for a linear element has been extended to a quadratic element by using a node-reordering. The proposed algorithm was successfully validated by solving several benchmark problems. Simulation of a static bubble problem was found to give an accurate solution with negligible spurious currents compared with existing results. Simulation results of rising bubble problems in 2D and 3D were also compared against existing numerical and experimental results in terms of terminal rising speed and terminal bubble shape. We have found that the present algorithm provided stable and accurate solutions even for a high density-ratio and that the solution accuracy strongly depended on the mesh resolution near the interface. Further, the present algorithm was shown to be very efficient because the computational overhead by mesh-refinement algorithm was very small compared to the elapsed times consumed for solving the incompressible Navier–Stokes equations and the advection/re-initialization equations of level set method. Lastly, the coalescence scenario of two oblique bubbles was well reproduced by the present 3D simulation. [ABSTRACT FROM AUTHOR]

For numerical analysis of multiphase flow, each interface boundary should be captured, and the geometric deformation of the interface needs to be predicted. To predict the interface, the singular interface model and diffusion interface model can be used. Among them, free energy based lattice Boltzmann method has adopted the diffusion interface model, with which it is easy to simulate complex multiphase flow phenomena such as bubble collapse, droplet collision, and moving contact lines. A new lattice Boltzmann method for the simulation of multiphase flows is described, and test results for the validation are presented. Finally, some simulations were carried out for the investigation of dynamic behavior of multiple rising bubbles. [ABSTRACT FROM AUTHOR]

• An extended volume of fluid (VoF) method for systems with one viscoelastic and one Newtonian phase is developed. • A volume-averaged VoF formulation is derived which comprises an additional interfacial stress term. • We propose a novel numerical scheme for the finite-volume discretization of the additional interface stress term. • Transient direct numerical simulations of single bubbles rising in a quiescent viscoelastic fluid are performed in 3D. • The jump discontinuity in the terminal rise velocity at critical bubble volume is quantitatively captured by the method. • The extended VoF method is stable for both sub- and supercritical bubble volumes. An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume averaging the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • The velocity and aspect ratio of rising particle-laden bubbles was investigated. • The buoyancy force and drag force exerted on the bubbles and the effect of particles were calculated. • Particles attached strongly dampen the oscillations observed in bubble velocity and aspect ratio. • A drag modification factor was identified to quantify the drag influence of particles on bubble velocity. • A modified drag coefficient for uncoated and particle-laden bubbles was introduced for the first time. Abstract A systematic investigation of the influence of particle coverage on the dynamics of rising bubbles was carried out using high-speed photography and image analysis techniques to study bubble behavior in terms of changes in velocity and aspect ratio. The buoyancy force and drag force exerted on the bubbles and the effect of particles were calculated to further understand their behavior. Results show that particles attached on the bubbles strongly dampen the oscillations observed in bubble aspect ratio and decrease its velocity and acceleration. The particles also render the bubbles more spherical and slow their velocity. It was found that the overall velocity of a bubble is directly correlated to its aspect ratio and inversely correlated to its particle coverage, while the acceleration and the aspect ratio and its change are inversely correlated. Interestingly, the trend observed in the oscillation and the oscillation period of particle-laden bubbles is similar for different levels of particle coating. A drag modification factor η p , which quantifies the drag influence of particles on bubble velocity, was identified from force analysis. A modified drag coefficient for uncoated and particle-laden bubbles was introduced, which allows, for the first time, to predict the behavior of rising bubbles in gas-liquid-particle systems. [ABSTRACT FROM AUTHOR]

Abstract In this study, rising and deformation of a single bubble in a viscoelastic fluid obeying the Giesekus model are numerically simulated by a modified version of weakly compressible smoothed particle hydrodynamics (WC-SPH). It is shown that the developed algorithm is robust enough to simulate two-phase flow with large density and viscosity ratios (up to 1000 and 100, respectively) not only in Newtonian cases but also in viscoelastic ones. After quantitative and qualitative verification of the developed code against previously published results, it is applied for simulating the rising bubble in the Giesekus fluid as a realistic model for polymeric solutions. Several simulations are performed to investigate the effects of mobility factor (0 ≤ α ≤ 1), polymer concentration (2.5 ≤ c l ≤ 20), relaxation time (1.14 ≤ De ≤ 114), density ratio (10 ≤ ρ l ∕ ρ b ≤ 1000) as well as domain width (6.6 ≤ W/D 0 ≤ 16.6). It is found that in contrast to relaxation and polymer concentration parameters which have dramatic effects on the rising bubble, the mobility factor has no significant effect on the rising bubble in high viscous polymeric solution. Also, the cusp trailing edge is postponed by decreasing the domain width. [ABSTRACT FROM AUTHOR]

Bubbles have very important applications in many fields such as shipbuilding engineering, ocean engineering, mechanical engineering, environmental engineering, chemical engineering, medical science and so on. In this paper, the research status and the development of the bubble dynamics in terms of theory, numerical simulation and experimental technique are reviewed, which cover the underwater explosion bubble, airgun bubble, spark bubble, laser bubble, rising bubble, propeller cavitation bubble, water entry/exit cavitation bubble and bubble dynamics in other fields. Former researchers have done a lot of researches on bubble dynamics and gained fruitful achievements. However, due to the complexity of the bubble motion, many tough mechanical problems remain to be solved. Based on the research progress of bubble dynamics, this paper gives the future research direction of bubble dynamics, aiming to provide references for researches related to bubble dynamics. [ABSTRACT FROM AUTHOR]

The buoyancy-driven rise of a small single fluid inclusion in a viscous liquid that is enclosed in a container of the cylindrical shape is numerically modelled. It is additionally assumed that the inclusion is slowly absorbed by the surrounding liquid. The phase-field approach is used as a physics-based model for the description of the thermo- and hydrodynamic evolution of a miscible heterogeneous binary mixture. The interplay of the effects of absorption and inclusion’s motion are investigated. We found that the dissolution of a nearly spherical inclusion does not occur evenly over its surface. The interfacial diffusion is stronger at the inclusion’s top cap. The matter absorbed by the liquid does not quickly penetrate into the bulk of the ambient phase, it accumulates behind the inclusion forming a concentration wake. We found that during the rise the inclusion’s speed grows. The speed and the acceleration of the inclusion strongly depend on the absorption rate, so the inclusion rises faster at the higher absorption rates. This effect is explained by the action of the Marangoni stress that is developed due to non-uniform mixture composition along the inclusion’s surface. We also found that the rise of the inclusion in a closed container is accompanied by the recirculation flow that is developed near the inclusion and that rises upwards with the inclusion. In the limit of negligible absorption (higher Peclet numbers) the convergence to a constant terminal speed of an immiscible inclusion is observed. [ABSTRACT FROM AUTHOR]

A powerful two-phase lattice Boltzmann model with the ability of modeling high density ratio is applied to simulate a rising bubble striking a porous obstacle. This model is able to simulate immiscible two-phase flow with density ratio of 1000 and result in desirable mass conservation. In present research, a porous obstacle is posed in two-phase flow domain, bounce back and wetting boundary conditions at walls and corners is discussed and showed that after implementation of obstacle boundary conditions, mass conservation of the model is preserved. Accuracy and ability of the model firstly examined by some basic problems. Next, striking of a rising bubble with 1000 density ratio to a porous obstacle is simulated and the effect of contact angle, Eotvos number and porosity ratio in deformation and passing of the bubble from the obstacle is investigated systematically. Different porosity ratios and contact angles, result in different bubble behavior striking the porous obstacle; In low porosity ratios and low contact angles, the bubble remains below the obstacle. At high contact angles, the hydrophobicity of the obstacle surface draws the bubble into the porosities, and the bubble moves to the top of the obstacle and stays on the top surface of the obstacle. In other cases, the bubble completely passes through the obstacle and separates it. Mass conservation error of bubble passing the porous obstacle is of order of 10-11 which is completely desirable. [ABSTRACT FROM AUTHOR]

In this study, smooth bubble condensation that occurs in subcooled pool water was examined to understand condensation phenomena at the beginning of boiling. The behaviors of condensable and non-condensable bubbles were investigated with respect to various temperatures and bubble sizes. The experimental data were analyzed using visual and acoustic methods including Phase Interface Binarization (PIB), Tridimensional Reconstructing Assumption (TRA), and acoustic data conversion. For visual analyses, (1) the PIB method determined bubble departure frequency, condensation time, and rising distance, and (2) the TRA method determined departure bubble size and volume reduction rate. The bubble detached with smaller volume and occurred more frequently with a smaller nozzle and a higher subcooling degree. Because the condensation always occurred during the growth, necking, and detachment of a bubble, the bubble was detached before it grew sufficiently. Lower condensation time and rising distance were associated with higher subcooling degrees and smaller injected bubbles. With respect to the acoustic analysis, sound signals were measured using a hydrophone, and the obtained analog data were converted to sound pressure units. The results revealed that higher volume reduction rate resulted in stronger sound pressure. As a result, the condensation phenomena in the smooth bubble regime were visually observed, and the possibilities of acoustic monitoring for earlier boiling were investigated. [ABSTRACT FROM AUTHOR]

In this work, we provide a unified and comparative description of the most prominent phase field based two-phase flow models and present our numerical results of the application of Galerkin-based Isogeometric Analysis (IGA) to incompressible Navier–Stokes–Cahn–Hilliard (NSCH) equations in velocity–pressure–phase field-chemical potential formulation. For the approximation of the velocity and pressure fields, LBB compatible non-uniform rational B-spline spaces are used which can be regarded as smooth generalizations of Taylor–Hood pairs of finite element spaces. The one-step θ -scheme is used for the discretization in time. The static and rising bubble, in addition to the nonlinear Rayleigh–Taylor instability flow problems, are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme. [ABSTRACT FROM AUTHOR]

The modeling of moving objects has been the focus of many studies and has succeeded to attract sufficient attention by researchers. However, commonly used modeling approaches such as discrete element modeling (DEM), direct numerical simulations (DNS) lack simplicity and have been computationally intensive. In the present work, simple method of dynamic mesh in the framework of computational fluid dynamics has been employed. Eulerian-Eulerian simulations of a monodisperse solid-liquid fluidized bed (SLFB) have been carried out. A foreign particle (settling particle or rising bubble) was inserted in the system to study the effect of turbulence in SLFB on the motion of settling particle. The operating and geometrical parameters have been chosen based on the experiments performed by Ghatage et al. (2013). The results showed that the model can satisfactorily predict the settling velocity for low voidage fluidization in 2D as well as 3D simulations. Computational fluid dynamics (CFD) simulations at higher values of superficial liquid velocity showed liquid bubbles confirming the transition to heterogeneous regime. These liquid bubbles directed the settling particle to move zig-zag resulting in lower settling velocity. The size and number of the bubbles increase with an increase in the liquids velocity indicating increased heterogeneity. However, CFD predicted larger and higher number of bubbles than experimentally noted. This resulted in an increase in the deviation of predicted settling velocities from experimentally observed with an increase in superficial liquid velocity. In case of bubbles, it was observed that the dynamic mesh method is greatly dependent on the regime of operation in the column and works only in the range of low voidage when the fluidized bed is homogeneous and does not contain liquid bubbles. [ABSTRACT FROM AUTHOR]

As a Lagrangian meshless method, smoothed particle hydrodynamics (SPH) method is robust in modelling multi-fluid flows with interface fragmentations. However, the application for the simulation of a rising bubble bursting at a fluid surface is rarely documented. In this paper, the multiphase SPH model is extended and applied to simulate this challenging phenomenon. Different numerical techniques developed in different SPH models are combined in the present SPH model. The adoption of a background pressure determined based on the surface tension can help to avoid tensile instability and interface penetrations. An accurate surface tension model is employed. This model is suitable for bubble rising problems of small scales and high density ratios. An interface sharpness force is adopted to achieve a smoother bubble surface. A suitable formula of viscous force, which is proven to be able to accurately capture the bubble splitting and small bubble detachment, is employed. Moreover, a modified prediction-correction time-stepping scheme for a better numerical stability and allows a relatively larger CFL factor is adopted. It is also worthwhile to mention that the particle shifting technique, which helps to make the particle distribute in an arrangement of lower disorder, can significantly improve the numerical accuracy. Regarding the treatment of the fluid surface, particles of lighter phase are arranged above the free surface of the denser phase to avoid the kernel truncation in the density approximation. Furthermore, this technique also allows an accurate calculation of the surface tension on the fluid surface. A number of cases of bubbly flows are presented, which confirms the capability of the present multiphase SPH model in modelling complex bubble-surface interactions with the density ratio and viscosity ratio up to 1000 and 100 respectively. [ABSTRACT FROM AUTHOR]

In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations. [ABSTRACT FROM AUTHOR]

A typical process in many industrial applications is rising bubble dynamic in viscous liquids like two-phase reactors. Examining the physical behavior of bubbles may improve the understanding of systems regarding design and operation. This study focused on the splitting of bubbles resulting from their impact on solid obstacles. Fragmentation of the bubbles appears in many applications such as lab on a chip in small scale or slug bubbly flow moving upward in a tube in large scales. Using a new index-function model in Lattice Boltzmann technique proposed by “He”, we simulated the deformation and motion of a bubble in different regimes, through which, we accurately captured a sharp interface between the two phases. We extended the aforementioned technique from 2D to 3D modelling of buoyancy-driven motion of a single bubble in quiescent viscous liquid. It was demonstrated that there is a reasonable agreement in terms of terminal rising velocity as well as bubble shape. This was found by comparing it with other available experimental and numerical results in different regimes through varying the two non-dimensional numbers (Eotvos and Morton) to characterize the fluid regime behind the rising bubble. In addition, by applying Bounce-Back no slip boundary condition to the surface area of the tubes with circular cross sections, we simulated the impact of the bubble during its upward motion. Changing the distance between the tubes and their corresponding diameters causes different shapes in the bubbles. Our simulation demonstrated that the 3D model based on index-function model of LBM is a suitable tool for 3D numerical simulation of rising bubbles in the presence of obstacles. [ABSTRACT FROM AUTHOR]

Research topics I have been working for the last 27 years related to rising bubbles are reviewed with the emphasis of surfactant effect on the multiscale structure of bubbly flows. Small amounts of surfactant can drastically change single bubble behaviors. For example, a bubble in aqueous surfactant solution rises much slower than one in purified water. This phenomenon is explained by the so-called Marangoni effect caused by a non-uniform concentration distribution of surfactant along the bubble surface. More interestingly, this Marangoni effect influences not only the rising velocity, but also the lateral migration in the presence of mean shear. Furthermore, these phenomena influence the multiscale nature of bubbly flows and cause a drastic change in the bubbly flow structure. In this article, these interesting phenomena are reviewed for the celebration of 30th anniversary of the Japan Society of Multiphase Flow. [ABSTRACT FROM AUTHOR]

A weakly compressible sharp-interface framework for two-phase flows is presented. Special emphasis is on investigating its convergence properties. For this purpose a well-defined set of benchmark configurations is introduced. These may serve as future references for the verification of sharp-interface methods. Global mass and momentum conservation is ensured by the conservative sharp-interface method. Viscous and capillary stresses are considered directly at the interface. A low-dissipation weakly compressible Roe Riemann solver, in combination with a 5th-order WENO scheme, leads to high spatial accuracy. A wavelet-based adaptive multi-resolution approach permits to combine computational efficiency with physical consistency. The first test configuration is a Rayleigh–Taylor instability at moderate Reynolds number and infinite Eötvös number. A second group of benchmark cases are isolated air bubbles rising in water at high Eötvös numbers, and low to high Reynolds numbers. With these test cases, three distinct types of complex interface evolution, which are typical for a wide range of industrial applications, are realized. [ABSTRACT FROM AUTHOR]

The Bakken is one of the shale reservoirs that has been discovered to hold a vast amount of resource and is contributing to the production boom in the US. This unconventional reservoir, like most others, displays favorable initial production rates due to stimulation by hydraulic fracturing, but production rates quickly decline after few months. Due to the extremely low permeability and low recoveries, miscible gas injection is considered for improving the recovery of oil in the Bakken formation. Feasibility of miscible gas injection in the Bakken would depend on the analysis of minimum miscibility pressure (MMP) experiments. The Rising Bubble Apparatus (RBA) has been chosen for the purpose of these experiments. The RBA provides results in a short amount of time using small amounts of fluid samples. The RBA consists of a cell gage containing a flat glass tube where oil samples are placed and an injection needle where gas is injected into the flat glass tube. To simulate reservoir conditions, the glass tube is pressurized using de-ionized water, and heating plates surrounding the cell are used to regulate temperature. Visual observation of the injected gas bubble behavior is captured by a camera as it rises and moves upward along the oil column. By observing the shape and dissolution behavior of the bubble, the MMP can be determined. MMP results from a Bakken crude sample are shown to range from 2100 to 3500 psi at temperatures from 160 to 240 °F using CO 2 as the injection fluid. Other injection fluids such as nitrogen and hydrocarbon gases have been tested and also provided reasonable MMP values. MMP results from Bakken crude oil samples were compared to existing correlations, and the correlations were found to produce mostly unreliable MMP results for the Bakken oils evaluated in the study. On the other hand, an equation of state phase behavior program showed similarities with the RBA MMP results. The impact of different injection fluids, inclusive of CO 2 and enriched hydrocarbon gases is the subject of this study. MMP results are influenced by the choice of injection fluids, providing valuable information for economic production and increased recovery in the Bakken formation. The results from this study provide a range of MMP data that can be used in planning pilot tests for miscible gas injection in the Bakken. [ABSTRACT FROM AUTHOR]

The local velocity profile (LVP) of a rising bubble can serve as a fingerprint for the dynamic behavior of the adsorption/desorption processes going on at a solution/air interface. The LVP of bubbles in β-lactoglobulin (BLG) solutions proves to be extremely sensitive for the adsorption of BLG at low bulk concentrations. In addition, it can show the impact of pH and ionic strength on the dynamic surface properties of BLG at the solution/air interface. It is observed that the time for establishing an immobile rigid surface layer at the rising bubble surface becomes shorter with increasing pH from 3 to 7. A peculiar behavior is observed at the isoelectric point (IEP) where the LVPs show irregularities. Under dynamic conditions BLG does not exhibit highest surface active at the IEP within the range of BLG concentrations as measured by the rising bubble technique. [ABSTRACT FROM AUTHOR]

A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21] ) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin–Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a typical chaotic structure in the flow field is observed at a Reynolds number of 10000, which indicates that the proposed model is a promising tool for direct numerical simulation of two-phase flows. [ABSTRACT FROM AUTHOR]

The total energy balance of a system consisting of a bubble (radius 0.74 mm) freely rising in viscous liquid under the action of buoyancy was considered. Values of bubble acceleration, local and terminal velocities, and shape deformations calculated by numerically solving the Navier-Stokes equation are compared with experimentally determined values. Additionally, the energies of the system associated with bubble motion (kinetic, potential, and rate of viscous energy dissipation), obtained from simulations, are given. On the basis of energy balances obtained for the system, two independent relations describing the motion of a bubble (Lagrange and Joseph equations) were used to show that, for steady-state conditions, the constant (terminal) velocity of the bubble is a result of balance between buoyancy force and the drag originating from energy dissipation due to fluid viscosity. According to the calculations performed, the discrepancy between the expected and actual results of the Lagrange and Joseph equations for the system considered was ∼1 %. The estimated added mass coefficient was in close agreement with expected theoretical value for deformed spheres, and increased with decreasing tube radius. [ABSTRACT FROM AUTHOR]

This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen–Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capillary wave, (iii) an unconfined rising gas bubble in liquid, (iv) a Taylor bubble in a cylindrical tube, and (v) the vertical and (vi) oblique impact of a drop into a pool of liquid. Comparing the simulation results with either analytical models or experimental data from the literature, four major observations were made. Firstly, the PFLBM selected was able to simulate flows purely governed by surface tension with reasonable accuracy. Secondly, the FSLBM, a sharp interface model, generally requires a lower resolution than the PFLBM, a diffuse interface model. However, in the limit case of a standing wave, this was not observed. Thirdly, in simulations of a bubble moving in a liquid, the FSLBM accurately predicted the bubble's shape and rise velocity with low computational resolution. Finally, the PFLBM's accuracy is found to be sensitive to the choice of the model's mobility parameter and interface width. • The free-surface LBM (FSLBM) and conservative Allen-Cahn phase-field LBM (PFLBM) are compared in six numerical test cases. • The FSLBM with sharp interface generally required less computational resolution than the PFLBM with diffuse interface. • The PFLBM simulated flows purely governed by surface tension with reasonable accuracy. • The FSLBM accurately simulated flows driven by surface tension and body forces with moderate resolution. • The PFLBM was sensitive to the choice of its mobility parameter and interface width. [ABSTRACT FROM AUTHOR]

The numerical simulation of bubbly flows is challenging due to the unstable multiphase interfaces with large density ratios and viscous ratios. The multiphase Smoothed Particle Hydrodynamics (SPH) method is applied in this paper to simulate the phenomena of bubbles rising and coalescing in three dimensions. Firstly, the multiphase SPH model is introduced in detail, including the derivation of the discretized governing equations based on the principle of virtual work, the viscous force, the multiphase interface treatment, the time-stepping scheme, the boundary implementation, etc. Considering the expensive computational cost in three-dimensional (3-D) SPH simulations, the effects of the scale of the computational domain and the density ratio on the multiphase interface are numerically investigated in order to decrease the amount of calculation. Afterwards, several cases of single bubbles rising through viscous fluids are tested and the SPH results are validated by both the experimental data and other numerical results in the literature. Furthermore, the phenomena of bubbles coalescing in both vertical and horizontal directions are simulated and the results agree well with the experimental data. It is found that the background pressure in the equation of state is essential to keep the multiphase interface smooth and stable when the Bond number is relatively small. The fair agreements between the results of SPH and other reference results demonstrate that the present multiphase SPH model is robust and stable enough to accurately simulate the dynamic phenomena of rising bubbles in different conditions, which can give a reference for engineering applications. [ABSTRACT FROM AUTHOR]

Local velocities of rising bubbles decrease with the increasing concentration in solution of surface-active, water-soluble species. Therefore, it is possible to use this phenomenon to monitor products of enzymatic reactions, which meet such criteria. In this study, hydrolysis of 1,2-dilauroyl- sn -glycero-3-phosphatidylcholine (DLPC) catalyzed by calcium-dependent phospholipase A2 (PLA2) (EC3.1.1.4) from porcine pancreas was used as model reaction. The products of this reaction are lauric acid (LA) and 1-lauroyl-2-hydroxy- sn -glycero-3-phosphatidylcholine (Lyso-PC). DLPC was dispersed in a chloroform/methanol mixture that was spread on a free PLA2 solution surface. Air bubbles were then formed at a capillary orifice and the local velocity of rising bubbles as a function of the distance from the capillary tip was monitored. Local velocity profiles were compared with profiles recorded for solutions of pure enzymatic reaction products and their mixtures. Our experiments showed that the product, which had a dominating effect on bubble motion retardation, was lyso-phosphatidylcholine. This can be explained by differences in the kinetics of lauric acid and lyso-phosphatidylcholine transfer from the spread layer to the solution. [ABSTRACT FROM AUTHOR]