A model to estimate the size of aggregates formed in a Dissolved Air Flotation unit

In Dissolved Air Flotation (DAF) a solid phase is separated from a liquid phase with the aid of air bubbles. The solid phase is usually coagulated into larger particles termed flocs. The air bubbles and flocs form aggregates, which rise to the surface of the flotation unit where they are removed. In this paper we propose a model that estimates the size of the formed aggregates. The estimation is based on the local balance of forces describing the approach and attachment of flocs to air bubbles. The interaction of flocs and bubbles is described by surface forces, hydrodynamic forces and the buoyancy force. The model is validated with available experimental results and the obtained aggregate sizes agree reasonable with those obtained by the experiments. The approach proposed here is intended for water treatment applications, but can be modified for other flotation processes.     

金融摩擦、资本配置与资产泡沫的演化机理——基于微观群体行为的演化博弈分析

构建企业家和贷款人的非对称演化搏弈模型,分析金融摩擦约束下代理人群体决策与资产泡沫的联系,探索资产泡沫产生的微观机理。研究发现:金融摩擦对代理人群体的影响是异质的,但都会导致资本配置扭曲;资产泡沫产生是代理人在金融摩擦冲击下,个体短期非理性在羊群效应和传染效应作用下引致的群体非理性;贷款人对资本高租金追求是资本泡沫产生的根源,但企业家为资产泡沫膨胀提供了资本支持;资产泡沫产生源于经济个体的最大化目标与宏观经济发展目标的背离。金融摩擦为资产泡沫产生提供了外生条件,切断资产泡沫产生路径的有效方式是提高金融市场效率和完善金融市场功能。     

The dynamics of the growth of vapour bubbles in a superheated liquid

The boiling of a superheated liquid is investigated assuming that, in the initial state, the liquid and a vapour bubble (or a system of vapour bubbles) are in mechanical and thermal equilibrium. It is shown that the state of a mixture of a liquid and bubbles is unstable due to the action of capillary forces. Linear and non-linear solutions are constructed describing the emergence of the system from the unstable state and also the unbounded growth of a single bubble and the transition into a stable vapour-liquid state when there are bubbles distributed throughout the volume in the initial state.     

Particle simulation of large carbon dioxide bubbles in water

A method that can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, the motion of carbon dioxide bubbles in water. The mathematical formulation uses classical molecular dynamics type formulas and results in an n-body problem that is solved numerically. The rise of the bubbles is described, as is the motion of the water near the bubbles. For variety, both H₂O water and D₂O heavy water are considered. Only workstation computer capabilities are required.     

网络股泡沫大小测度研究

网络股泡沫是最能反映网络泡沫本质的表现形式，本文利用理性预期理论，构建了网络股泡沫大小的测度模型，说明网络股泡沫的存在，在此基础上确定了网络股泡沫大小的测度指标，并以雅虎公司股票为例对泡沫的大小进行了测度，结果符合网络泡沫的实际情况。     

Numerical simulation of single gas bubbles under shear flow conditions

Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break-up or coalescence in different systems can be crucial for the process design. Usually the flow experienced by bubbles is not uniform but sheared. Under shear-flow conditions bubbles develop a lift force perpendicular to the flow direction. In the present work direct numerical simulations are applied to examine the dependency of the lift force on the shear rate for bubbles in pure liquids. A level-set based volume-tracking method is implemented into the CFD-code OpenFOAM, to follow the free interface of the gas bubble. Results show good agreement with available experimental results from single bubbles in a rotating chamber. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of inviscid bubble dynamics in a centrally symmetric gravitational field

The motion of bubbles in a centrally symmetric gravitational field is numerically simulated using two-dimensional conservation laws (Euler equations). The dynamics of bubbles with various numbers of modes in the initial perturbation are studied. The numerical results reveal features that are substantially different from the plane case in a homogeneous gravitational field. Bubble perturbations nearly do not interact at the formation stage. The lowest modes are amplified in the course of the bubble evolution.     

Receptivity of the boundary layer with separation bubble to external sound waves

The receptivity problem of laminar separated two-dimensional boundary-layer under influence of external acoustic waves is considered. Basic features of this theory were formulated by Ruban (1984) and then Goldstein (1985), but these investigations were limited by small perturbations of steady parallel flow only. The current paper takes into account essentially nonparallel regimes of base flow, including attached flows, flow with separated bubbles and the base flow at marginal value of parameter. The steady flow near a corner point of profile is of considerable interest and a question naturally arises about the sensitivity of separation bubble inside the boundary layer to external disturbances such as sound waves. Another question arises about the sensitivity of near critical base flow, namely if corner is concave there is a marginal angle which limits existence of such base flow. This fact usually is linked with sudden reconstruction of full flow pattern past a profile. Development of perturbations inside the interaction region may give some answers about the appearance of turbulence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration

Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions of nonlinear evolution equation of the fourth order are found by means of the simplest equation method. Properties of nonlinear waves in a liquid with gas bubbles are discussed.     

基于自组织理论的房地产泡沫动态演化过程研究

主要利用自组织行为理论,对非线性系统中房地产泡沫产生、形成、发展以及破灭的动态演化过程加以描述与分析.对自组织理论进行了简要介绍,并把这一理论应用于房地产市场,说明了房地产泡沫的动态演化过程就是一个不确定行为本质特征的复杂系统的自组织行为.在此基础上,对中国房地产泡沫的防范给出了政策建议.     

Numerical simulation of the interaction between vortex ring and bubble plume

In present paper a three-dimensional Vortex-In-Cell method with two-way coupling effect was developed to study the bubble plume entrainment by a vortex ring. In this method the continuous flow was calculated by the three-dimensional Vortex-In-Cell method and the bubbles are tracked through bubble motion equation. Two-way coupling effect between continuous flow and dispersed bubbles is considered by introducing a vorticity source term, which is induced by the change of void fraction gradient in each computational cell. After validated by the comparison between experimental measurements and simulation results for the motion of vortex rings and the rising velocity of bubble plume, present method is implemented to simulate the interaction between an evolving vortex ring and a rising bubble plume. It was found that there is little effect of the bubble entrainment to the total circulation of vortex ring while the effect of bubble entrainment to the vortex ring structure is quite obvious. The bubble entrainment by the vortex ring not only changed the vorticity distribution in the vortex structure, but also displaced the positions of the vortex cores. The vorticity in the lower vortex core of the vortex ring decreases more than that in the upper vortex core of the vortex ring while the vortex core in the upper part of the vortex ring is displaced to the center of vortex ring by the entrained bubbles. Smaller bubbles are easier to be entrained by the large scale vortex structure and the transportation distance is in inverse proportion to bubble diameter.     

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.     

On the effective viscosity of a dilute emulsion of gas bubbles

The problem of the motion of a rigid spherical body in a homogeneous emulsion of gas bubbles is considered in the Stokes approximation, using the self-consistent field method. An expression is obtained for the correction factor in the Stokes formula for the drag of the body in the first approximation with respect to the volume concentration of the dispersed phase. An analytical relation between the correction factor and the ratio of the sizes of the bubbles and the body is found. It is shown that, in the limit when this ratio tends to zero, the correction factor obtained is identical to Taylor's result for the effective viscosity of an emulsion of gas bubbles. In the case of non-point bubbles, the coefficient on the volume concentration in the expression for the effective viscosity of the emulsion can be considerably different from Taylor's result. A similar conclusion was also obtained in the case of the problem of the motion of a spherical bubble of arbitrary size in an emulsion of gas bubbles.     

The lifetime of a financial bubble

We combine both a mathematical analysis of financial bubbles and a statistical procedure for determining when a given stock is in a bubble, with an analysis of a large data set, in order to compute the empirical distribution of the lifetime of financial bubbles. We find that it follows a generalized gamma distribution, and we provide estimates for its parameters. We also perform goodness of fit tests, and we provide a derivation, within the context of bubbles, that explains why the generalized gamma distribution might be the natural one to expect for the lifetimes of financial bubbles.     

Modelling and Simulation of Food Foams

The rheological behaviour of protein solutions containing bubbles at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. Protein foams have a great importance in food production because of their special sensory properties. A suspension that contains bubbles in a Newtonian liquid exhibits inherently a complex rheological behaviour, such as elastic effects, a shear- and time-dependent viscosity and normal stress differences. The deformation state of the bubbles in a suspension subjected to a steady shear is a function of the gas volume fraction ϕ and the capillary number N_Ca. In the present article, material equations for protein solutions with gas volume fractions ϕ ≤ 0.75 and small bubble deformations, i. e. N_Ca ≪ 1, are analysed and further developed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

VLES turbulence model for an Eulerian–Lagrangian modeling concept for bubble plumes

Traditional Reynolds-averaged Navier–Stokes (RANS) approaches to turbulence modeling, such as the k-ϵ model, have some well-known shortcomings when modeling transient flow phenomena. To mitigate this, a filtered URANS model has been derived where turbulent structures larger than a given filter size (typically grid size) is captured by the flow equations and smaller structures are modeled according to a modified k-ϵ model. This modeling approach is also known as a VLES model (Very Large Eddy Scale model), and provides more details of the transient turbulence than the k-ϵ model at little extra computational cost.In this study a two-phase extension to the VLES model is described. A modeling concept for bubble plumes has been developed in which the bubbles are tracked as particles and the flow of liquid is solved by the Navier–Stokes equations in a traditional mesh based approach. The flow of bubbles and liquid is coupled in an Eulerian–Lagrangian model. Turbulent dispersion of the bubbles is treated by a random walk model. The random walk model depends on an estimation of the eddy life time. The eddy life time for the VLES model differs from a k-ϵ model, and its mathematical expression is derived.The model is applied to ocean plumes emanating from discharge of gas at the ocean floor. Validation with experiments and comparison with k-ϵ model are shown.     

Measurement of surface and interfacial tension from the maximum pressure in sessile and pendant bubbles and drops

The measurement of surface and interfacial tension from the maximum pressure in sessile and pendant bubble and drops is, described. New theoretical data are presented which enable the surface and interfacial tension to be calculated without iteration. Although the maximum pressure in pendant bubbles is less than that in sessile bubbles, they retain their symmetry during detachment from the capillary tip and so havt experimental advantages. Reproducible results in good agreement with literature values are obtained for the surface and interfacial tension of several liquids and immiscible liquid pairs.     

BUBBLES OF LANDAU-LIFSHITZ EQUATIONS WITH APPLIED FIELDS

In this paper, we discuss the Landau-Lifshitz equations with applied magnetic fields. The equations describing the bubbles in the ferromagnets and the behaviors of the solutions near the singularities are given. We found that the applied fields do not affect the bubbles and we have the same conclusions as in reference [1].     

A Quantitative Visualization Method for Wind Tunnel Experiments Based on 3D Particle Tracking Velocimetry (3D‐PTV)

The development of a measurement system to visualize, classify (based on topological features) and quantify complex flows in wind tunnel experiments is described. The basic idea is to extract topological features directly instead of postprocessing large sets of raw data (as generated by conventional PIV or PTV systems). As a particular aspect, the seeding methods in industrial wind tunnels are discussed. While helium filled soap bubbles are well suited because of their neutral buoyancy, there is a problem with their visibility, especially when reflecting model surfaces are being imaged at the same time. Various methods were evaluated in order to enhance the visual contrast of the bubbles.     

Numerical study of dynamics of single bubbles and bubble swarms

A systematic computational study of the dynamics of gas bubbles rising in a viscous liquid is presented. Two-dimensional simulations are carried out. Both the dynamics of single bubbles and small groups of bubbles (bubble swarms) are considered. This is a continuation of our previous studies on the two-bubble coalescence and vortex shedding [A. Smolianski, H. Haario, P. Luukka, Vortex shedding behind a rising bubble and two-bubble coalescence: a numerical approach, Appl. Math. Model. 29 (2005) 615–632]. The proposed numerical method allows us to simulate a wide range of flow regimes, accurately capturing the shape of the deforming interface of the bubble and the surface tension effect, while maintaining the mass conservation. The computed time-evolution of bubble’s position and rise velocity shows a good agreement with the available experimental data. At the same time, the results on the dynamics of bubble interface area, which are, up to our knowledge, presented for the first time, show how much the overall mass transfer would be affected by the interface deformation in the case of the bubble dissolution. Another set of experiments that are of interest for chemical engineers modelling bubbly flows concerns the bubble swarms and their behavior in different bubble-shape regimes. The ellipsoidal and spherical shape regimes are considered to represent, respectively, the coalescing and non-coalescing bubble swarms. The average rise velocities of the bubble swarms are computed and analyzed for both regimes.