scholarly journals RePBubLik: Reducing Polarized Bubble Radius with Link Insertions

2021 ◽  
Author(s):  
Shahrzad Haddadan ◽  
Cristina Menghini ◽  
Matteo Riondato ◽  
Eli Upfal
Keyword(s):  
Bubble Radius

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

Magnetohydrodynamic Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

1999 ◽  
Vol 66 (4) ◽  
pp. 1021-1023 ◽  
Author(s):  
R. Usha ◽  
P. Vimala
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Bubble Radius ◽  
Fluid Film ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Circular Plates ◽  
Air Bubble ◽  
Approximate Analytical Solutions

In this paper, the magnetic effects on the Newtonian squeeze film between two circular parallel plates, containing a single central air bubble of cylindrical shape are theoretically investigated. A uniform magnetic field is applied perpendicular to the circular plates, which are in sinusoidal relative motion, and fluid film inertia effects are included in the analysis. Assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained by approximating the momentum equation governing the magnetohydrodynamic squeeze film by the mean value averaged across the film thickness. Approximate analytical solutions for the air bubble radius, pressure distribution, and squeeze film force are determined by a perturbation method for small amplitude of sinusoidal motion and are compared with the numerical solution obtained by solving the nonlinear differential equation. The combined effects of air bubble, fluid film inertia, and magnetic field on the squeeze film force are analyzed.

scholarly journals Bubble Dynamics in a Two-Phase Bubbly Mixture

2010 ◽  
Author(s):  
Arvind Jayaprakash ◽  
Sowmitra Singh ◽  
Georges Chahine
Keyword(s):  
Void Fraction ◽  
High Speed ◽  
Bubble Dynamics ◽  
Bubble Radius ◽  
Discharge Voltage ◽  
Large Bubble ◽  
Water Mixture ◽  
Two Phase ◽  
Mixture Density ◽  
Bubbly Medium

The dynamics of a primary relatively large bubble in a water mixture including very fine bubbles is investigated experimentally and the results are provided to several parallel on-going analytical and numerical approaches. The main/primary bubble is produced by an underwater spark discharge from two concentric electrodes placed in the bubbly medium, which is generated using electrolysis. A grid of thin perpendicular wires is used to generate bubble distributions of varying intensities. The size of the main bubble is controlled by the discharge voltage, the capacitors size, and the pressure imposed in the container. The size and concentration of the fine bubbles can be controlled by the electrolysis voltage, the length, diameter, and type of the wires, and also by the pressure imposed in the container. This enables parametric study of the factors controlling the dynamics of the primary bubble and development of relationships between the bubble characteristic quantities such as maximum bubble radius and bubble period and the characteristics of the surrounding two-phase medium: micro bubble sizes and void fraction. The dynamics of the main bubble and the mixture is observed using high speed video photography. The void fraction/density of the bubbly mixture in the fluid domain is measured as a function of time and space using image analysis of the high speed movies. The interaction between the primary bubble and the bubbly medium is analyzed using both field pressure measurements and high-speed videography. Parameters such as the primary bubble energy and the bubble mixture density (void fraction) are varied, and their effects studied. The experimental data is then compared to simple compressible equations employed for spherical bubbles including a modified Gilmore Equation. Suggestions for improvement of the modeling are then presented.

Collective Effects on the Growth of Vapor Bubbles in a Superheated Liquid

1984 ◽  
Vol 106 (4) ◽  
pp. 486-490 ◽  
Author(s):  
G. L. Chahine ◽  
H. L. Liu
Keyword(s):  
Collective Behavior ◽  
Bubble Growth ◽  
Theoretical Study ◽  
Pressure Field ◽  
Bubble Radius ◽  
Significant Inhibition ◽  
Collective Effects ◽  
Superheated Liquid ◽  
Vapor Bubbles ◽  
Bubble Interaction

The problem of the growth of a spherical isolated bubble in a superheated liquid has been extensively studied. However, very little work has been done for the case of a cloud of bubbles. The collective behavior of the bubbles departs considerably from that of a single isolated bubble, due to the cumulative modification of the pressure field from all other bubbles. This paper presents a theoretical study on bubble interaction in a superheated liquid during the growth stage. The solution is sought in terms of matched asymptotic expansions in powers of ε, the ratio between rb0, a characteristic bubble radius and l0, the interbubble distance. Numerical results show a significant inhibition of the bubble growth rate due to the presence of interacting bubbles. In addition, the temperature at the bubble wall decreases at a slower rate. Consequently, the overall heat exchange during the bubble growth is reduced.

Analysis of the Motion and Deformation of a Bubble Rising in a Viscoelastic Fluid

2006 ◽  
Author(s):  
Shriram Pillapakkam ◽  
Pushpendra Singh ◽  
Denis L. Blackmore ◽  
Nadine Aubry
Keyword(s):  
Velocity Field ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Bubble Radius ◽  
Polymer Concentration ◽  
Deborah Number ◽  
Two Phase ◽  
Bubble Volume ◽  
Recirculation Zones ◽  
Bubble Rising

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid and both transient and steady state shapes of bubbles in viscoelastic buoyancy driven flows are studied. The influence of the governing dimensionless parameters, namely the Capillary number (Ca), the Deborah Number (De) and the polymer concentration parameter c, on the deformation of the bubble is also analyzed. Our simulations demonstrate that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on the parameter c and the bubble radius. Simulations also show that there is a critical bubble volume at which there is a sharp increase in the bubble terminal velocity as the increasing bubble volume increases, similar to the behavior observed in experiments. The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Interestingly, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of the motion of the bubble, thus creating a “negative wake”. In this paper, the velocity field in the wake of the bubble, the effect of the parameters on the velocity field and their influence on the shape of the bubble are also investigated.

Critical bubble radius for expansion in extrusion cooking

1993 ◽  
Vol 20 (4) ◽  
pp. 325-338 ◽  
Author(s):  
Hitomi Kumagai ◽  
Hitoshi Kumagai ◽  
Toshimasa Yano
Keyword(s):  
Bubble Radius ◽  
Extrusion Cooking ◽  
Critical Bubble

scholarly journals Designing key parameters of bubble plumes to restore water quality by using conceptual models: a case study in a sub-deep reservoir

2020 ◽  
Vol 20 (7) ◽  
pp. 2915-2927
Author(s):  
Chen Lan ◽  
Jingan Chen ◽  
Jianyang Guo ◽  
Jingfu Wang
Keyword(s):  
Flow Rate ◽  
Bubble Size ◽  
Gas Flow ◽  
Bubble Radius ◽  
Bubble Plume ◽  
Gas Flow Rate ◽  
Empirical Formulas ◽  
Bubble Plumes ◽  
Deep Reservoir ◽  
First Time

Abstract Bubble plumes are a popular hypolimnetic reaeration technique in deep-water reservoirs since they have the advantage of delivering direct reaeration to the hypolimnion. Improving the understanding of the integrated reaeration processes is beneficial to optimize the reaeration capacity of the aeration or oxygenation system. In this study, the discrete bubble model was first employed to design an oxygenation system for a sub-deep reservoir (the Aha Reservoir, southwest China, with water depths of 10–30 m). A new approach involving the discrete bubble model was used to determine the initial bubble size of the bubble plume applied. The intrusion models were demonstrated to be useful for designing the gas flow rate of the reaeration system. Using the intrusion models, we predicted the intrusion thickness and intrusion distance during operation for the first time. Subsequently, we verified the predictions and produced more realistic empirical formulas. At present, reports about recommendations on initial bubble size and gas flow rate are rare, and practical verification is absent. Taking the Aha Reservoir as an example, the initial bubble radius of 1 mm and the gas flow rate of 20 m3·h−1 were recommended for bubble plume oxygenation and were found to be successful in the field. Our understanding of the reaeration processes during the operation of the bubble plume system is far from comprehensive, but this study serves to highlight the potential of the discrete bubble model and the intrusion models for designing a bubble plume system in an individual lake.

The initial motion of a gas bubble formed in an inviscid liquid Part 1. The two-dimensional bubble

1962 ◽  
Vol 12 (3) ◽  
pp. 408-416 ◽  
Author(s):  
J. K. Walters ◽  
J. F. Davidson
Keyword(s):  
Constant Pressure ◽  
Bubble Radius ◽  
Steady Motion ◽  
Two Dimensional ◽  
Spherical Cap ◽  
Liquid Part ◽  
Irrotational Motion ◽  
Acceleration Of Gravity ◽  
Small Bubbles ◽  
Initial Motion

The paper deals with the initial motion of a two-dimensional bubble starting from rest in the form of a cylinder with its axis horizontal. The theory is based on the assumptions of irrotational motion in the liquid round the bubble, constant pressure within the bubble, and small displacements from the cylindrical form. This theory predicts that the bubble should rise with the acceleration of gravity, over a distance of at least the initial bubble radius, and that a tongue of liquid should be projected up from the base of the bubble into its interior. These predictions are confirmed by experiments which also show how the vorticity necessary for steady motion in the spherical-cap form is generated by the detachment of two small bubbles from the back of the main bubble.

Behavior of Inert Gas Bubbles in Forced Convective Liquid Metal Circuits

1976 ◽  
Vol 98 (1) ◽  
pp. 5-11 ◽  
Author(s):  
W. J. Minkowycz ◽  
D. M. France ◽  
R. M. Singer
Keyword(s):  
Liquid Metal ◽  
Bubble Dynamics ◽  
Bubble Radius ◽  
Gas Bubbles ◽  
Inert Gas ◽  
Liquid Sodium ◽  
Gas Bubble ◽  
Flowing Liquid ◽  
Argon Gas ◽  
The Core

Conservation equations are derived for the motion of a small inert gas bubble in a large flowing liquid-gas solution subjected to large thermal gradients. Terms which are of the second order of magnitude under less severe and steady-state conditions are retained, thus resulting in an expanded form of the Rayleigh equation. The bubble dynamics is a function of opposing mechanisms tending to increase or decrease bubble volume while being transported with the solution. Diffusion of inert gas between the bubble and the solution is one of the most important of these mechanisms included in the analysis. The analytical model is applied to an argon gas bubble flowing in a weak solution of argon gas in liquid sodium. Calculations are performed for these fluids under conditions typical of normal and abnormal operation of a liquid metal fast breeder reactor (LMFBR) core and the resulting bubble radius, internal gas pressure, and mass of inert gas are presented in each case. An important result obtained indicates that inert gas bubbles reaching the core inlet of an LMFBR will always grow as they traverse the core under normal and extreme abnormal conditions and that the rate of growth is quite small in all cases.

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