Critical bubble radius in solvent sublation

The deflection of an infinite ice sheet by a submerged gas source, as would result from an undersea gas or oil well blowout is analysed utilizing an elastic thin plate model. The results show that fracture may occur either at the bubble center or just beyond the bubble edge, depending upon the bubble depth, the ice thickness, and the material properties assumed for the ice sheet. For ice one meter in thickness and a trapped gas depth greater than 100 mm, fracture at the bubble edge is probable. The critical bubble radius for failure varies rapidly with ice thickness, bubble depth, and the ice properties, which in view of the variability of the latter, makes the prediction of actual bubble radii to cause failure subject to a large degree of uncertainty.

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Growth of Microcellular Foams in Viscoelastic Mediums

Materials ◽

10.1115/imece2004-59490 ◽

2004 ◽

Author(s):

Ki Young Kim ◽

Sung Lin Kang ◽

Ho-Young Kwak

Keyword(s):

Integral Method ◽

Close Agreement ◽

Bubble Radius ◽

Saturation Pressure ◽

Polymer Processing ◽

Governing Equations ◽

Concentration Boundary ◽

First Order ◽

Microcellular Foams ◽

Critical Bubble

The growing of the critical bubble by diffusion process in visco-elastic medium was treated by an integral method for the concentration boundary layer. In this study, we obtained a set of the first order time dependent equations to obtain bubble radius and gas pressure inside the bubble simultaneously. The calculated final cell sizes depending on the initial saturation pressure are in close agreement with the observed ones. The governing equations developed in this study may be used in polymer processing of microcellular foams.

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

Advances in Difference Equations ◽

10.1186/s13662-020-03054-5 ◽

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.

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Critical bubble diameters and Plateau border dimensions for drainage in aqueous xanthan foams

Colloids and Surfaces A Physicochemical and Engineering Aspects ◽

10.1016/j.colsurfa.2020.125682 ◽

2021 ◽

Vol 612 ◽

pp. 125682

Author(s):

Loïc Desbordes ◽

Agnès Grandjean ◽

Fabien Frances ◽

Hélène Lorcet ◽

Sylvain Faure

Keyword(s):

Plateau Border ◽

Critical Bubble

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

Journal of Applied Mechanics ◽

10.1115/1.2791773 ◽

1999 ◽

Vol 66 (4) ◽

pp. 1021-1023 ◽

Cited By ~ 7

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.

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Bubble Dynamics in a Two-Phase Bubbly Mixture

Volume 7: Fluid Flow, Heat Transfer and Thermal Systems, Parts A and B ◽

10.1115/imece2010-40509 ◽

2010 ◽

Cited By ~ 2

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.

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A Model of Bubble Nucleation on a Micro Line Heater

Journal of Heat Transfer ◽

10.1115/1.2825950 ◽

1999 ◽

Vol 121 (1) ◽

pp. 220-225 ◽

Cited By ~ 9

Author(s):

S.-D. Oh ◽

S. S. Seung ◽

H. Y. Kwak

Keyword(s):

Bubble Formation ◽

Three Dimensional ◽

Bubble Nucleation ◽

Heat Diffusion ◽

Nucleation Theory ◽

Molecular Cluster ◽

Heater Surface ◽

Calculation Results ◽

Critical Bubble ◽

Superheat Limit

The bubble nucleation mechanism on a cavity-free micro line heater surface was studied by using the molecular cluster model. A finite difference numerical scheme for the three-dimensional transient conduction equation for the liquid was employed to estimate the superheated volume where homogeneous bubble nucleation could occur due to heat diffusion from the heater to the liquid. Calculation results revealed that bubble formation on the heater is possible when the temperature at the hottest point in the heater is greater than the superheat limit of the liquid by 6°C–12°C, which is in agreement with the experimental results. Also it was found that the classical bubble nucleation theory breaks down near the critical point where the radius of the critical bubble is below 100 nm.

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

Journal of Fluids Engineering ◽

10.1115/1.3243155 ◽

1984 ◽

Vol 106 (4) ◽

pp. 486-490 ◽

Cited By ~ 3

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.

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