The Behavior of a Spherical Bubble in the Vicinity of a Solid Wall

1968 ◽  
Vol 90 (1) ◽  
pp. 75-89 ◽  
Author(s):  
A. Shima
Keyword(s):  
Surface Tension ◽  
Flow Velocity ◽  
Solid Wall ◽  
Bubble Surface ◽  
Bubble Collapse ◽  
Theoretical Treatment ◽  
Bubble Shape ◽  
Spherical Bubble ◽  
Numerical Examples ◽  
Impulse Pressure

The behavior of a spherical bubble as it collapses in the vicinity of a solid wall was theoretically analyzed, in terms of the effect of compressibility, viscosity, surface tension, and gravity being ignored, and the gas in the bubble following the adiabatic law of compression assumed. Numerical examples obtained by applying the theoretical treatment are given for the change in time of bubble shape as it collapses, the impulse pressure occurring during bubble collapse, and the flow velocity at the bubble surface.

scholarly journals Bubble Rise Velocity and Surface Mobility in Aqueous Solutions of Sodium Dodecyl Sulphate and n-Propanol

Minerals ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 743
Author(s):  
Pavlína Basařová ◽  
Yuliya Kryvel ◽  
Jakub Crha
Keyword(s):  
Surface Tension ◽  
Aqueous Solutions ◽  
Sodium Dodecyl Sulphate ◽  
Sodium Dodecyl ◽  
Bubble Surface ◽  
Rise Velocity ◽  
Bubble Rise ◽  
Spherical Bubble ◽  
Surface Mobility ◽  
Bubble Rise Velocity

Aqueous solutions of simple alcohols exhibit many anomalies, one of which is a change in the mobility of the bubble surface. This work aimed to determine the effect of the presence of another surface-active agent on bubble rise velocity and bubble surface mobility. The motion of the spherical bubble in an aqueous solution of n-propanol and sodium dodecyl sulphate (SDS) was monitored by a high-speed camera. At low alcohol concentrations (xP < 0.01), both the propanol and SDS molecules behaved as surfactants, the surface tension decreased and the bubble surface was immobile. The effect of the SDS diminished with increasing alcohol concentrations. In solutions with a high propanol content (xP > 0.1), the SDS molecules did not adsorb to the phase interface and thus, the surface tension of the solution was not reduced with the addition of SDS. Due to the rapid desorption of propanol molecules from the bottom of the bubble, a surface tension gradient was not formed. The drag coefficient can be calculated using formulas for the mobile surface of a spherical bubble.

The problem of stability of the spherical shape of a bubble during its supercompression

2010 ◽  
Vol 7 ◽  
pp. 19-37
Author(s):  
R.I. Nigmatulin ◽  
M.A. Ilgamov ◽  
A.A. Aganin
Keyword(s):  
Shock Wave ◽  
Spherical Harmonics ◽  
Nonlinear Interaction ◽  
Solid Wall ◽  
Spherical Shape ◽  
Bubble Collapse ◽  
Bubble Shape ◽  
Main Attention ◽  
The Law

Deviation of the bubble shape from the spherical one during supercompression of a bubble in liquid is considered. The main attention is focused on determining the law of the initial bubble nonsphericity distribution in the spherical harmonics. The most probable one is that with the amplitude reducing as the harmonics number increases. Such distribution is confirmed by the analysis of the bubble sphericity perturbation evolution at the bubble collapse near a solid wall and at coalesce of two identical bubbles. The influence of the bubble sphericity distortion during bubble compression on the deformation of a shock wave arising in the bubble and the dependence of the bubble nonsphericity evolution on the nonlinear interaction between the distortions in the form of different harmonics are also discussed.

Influence of Physical Parameters on the Collapse of a Spherical Bubble

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Surface Tension ◽  
Physical Parameter ◽  
Pressure Difference ◽  
Bubble Formation ◽  
Bubble Collapse ◽  
Physical Parameters ◽  
Liquid Environment ◽  
Spherical Bubble ◽  
Maple Code ◽  
Surrounding Liquid

This paper examines the influence of physical parameters on the collapse dynamics of a spherical bubble filled with diatomic gas ($\kappa=7/5$). The present numerical investigation shows that each physical parameter affects the bubble collapse dynamics differently. After comparing the contribution of each physical parameter, it appears that, of all the parameters, the surrounding liquid environment affects the bubble collapse dynamics the most. Meanwhile, surface tension has the weakest influence and can be ignored in the bubble collapse dynamics. However, surface tension must be retained in the initial analysis since this, as well as the pressure difference jointly control initial bubble formation. As an essential part of this study, a general Maple code is provided.

Deformation of a bubble or drop in a uniform flow

1980 ◽  
Vol 101 (4) ◽  
pp. 673-686 ◽  
Author(s):  
Jean-Marc Vanden-Broeck ◽  
Joseph B. Keller
Keyword(s):  
Surface Tension ◽  
Liquid Drop ◽  
Pressure Ratio ◽  
Bubble Surface ◽  
Stagnation Pressure ◽  
Two Dimensional ◽  
Bubble Shape ◽  
Fluid Density ◽  
Circular Arc ◽  
Steady Potential

Steady potential flow around a two-dimensional bubble with surface tension, either free or attached to a wall, is considered. The results also apply to a liquid drop. The flow and the bubble shape are determined as functions of the contact angle β and the dimensionless pressure ratio γ = (pb − ps)/½ρU2. Here pb is the pressure in the bubble, ps = p∞ + ½ρU2 is the stagnation pressure, p∞ is the pressure at infinity, ρ is the fluid density and U is the velocity at infinity. The surface tension σ determines the dimensions of the bubble, which are proportional to 2σ/ρU2. As γ tends to ∞, the bubble surface tends to a circle or circular arc, and as γ decreases the bubble elongates in the direction normal to the flow. When γ reaches a certain value γ0(β), opposite sides of the bubble touch each other. The problem is formulated as an integrodifferential equation for the bubble surface. This equation is discretized and solved numerically by Newton's method. Bubble profiles, the bubble area, the surface energy and the kinetic energy are presented for various values of β and γ. In addition a perturbation solution is given for γ large when the bubble is nearly a circular arc, and a slender-body approximation is presented for β ∼ ½π and γ ∼ γ0(β), when the bubble is slender.

scholarly journals Pressure Field Generated by Nonspherical Bubble Collapse

1983 ◽  
Vol 105 (3) ◽  
pp. 356-362 ◽  
Author(s):  
G. L. Chahine ◽  
A. G. Bovis
Keyword(s):  
Velocity Potential ◽  
Pressure Field ◽  
Solid Wall ◽  
Bubble Radius ◽  
Computer Time ◽  
Gas Content ◽  
Bubble Collapse ◽  
System Of Differential Equations ◽  
Spherical Bubble ◽  
Complex Cases

The method of matched asymptotic expansions is used to investigate the behavior of a collapsing bubble near a solid wall. Cases are studied in which the ratio ε between the initial spherical bubble radius and its distance from the wall is small. Expansions in powers of ε lead to a simple system of differential equations which is solved numerically. The bubble shape, the velocity potential and the pressure field are determined as functions of time. The deformation of the bubble is a singular perturbation of the pressure field around it. An increase in the value of ε augments the pressure on the solid wall by orders of magnitude. The influence of surface tension and the proximity of the wall, gas content and its law of compression, are investigated. The results are compared to previous investigations. One advantage of the method employed is the fact that it leads to a numerical solution which costs very little computer time. In addition, it can be extended very easily to more complex cases such as multibubble configurations or to walls coated with elastomeric coatings.

The nucleation of cavities at grain boundaries

1987 ◽  
Vol 45 ◽  
pp. 288-291
Author(s):  
P. J. Goodhew
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Grain Boundaries ◽  
Radiation Damage ◽  
Impurity Concentration ◽  
Driving Force ◽  
Nucleation And Growth ◽  
Phase Boundaries ◽  
Cavity Nucleation ◽  
Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

Study on bubble collapse near a solid wall under different hypergravity environments

2021 ◽  
Vol 221 ◽  
pp. 108563
Author(s):  
Liangtao Liu ◽  
Ning Gan ◽  
Jinxiang Wang ◽  
Yifan Zhang
Keyword(s):  
Solid Wall ◽  
Bubble Collapse

Gas diffusion from ascending gas bubbles

1969 ◽  
Vol 35 (4) ◽  
pp. 711-719 ◽  
Author(s):  
Paul H. Leblond
Keyword(s):  
Surface Tension ◽  
Gas Exchange ◽  
Gas Bubbles ◽  
Gas Diffusion ◽  
Gas Pressure ◽  
Pressure Balance ◽  
Spherical Bubble ◽  
Gas Leakage ◽  
Quantitative Results ◽  
Ascent Velocity

General qualitative rules are derived for the behaviour of the volume of an ascending spherical bubble and of the gas pressure within it. Three modes of behaviour are discerned, corresponding to as many possible orderings of the relative influences of ascent velocity, gas leakage and surface tension on the volume and the pressure balance. These general results are nearly independent of the particular forms of the ascent velocity and gas exchange functions. Quantitative results are presented for the Stokes law régime.

scholarly journals Application of Depletion Attraction in Mineral Flotation: II. Effects of Depletant Concentration

Minerals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 450 ◽  
Author(s):  
Gahee Kim ◽  
Junhyun Choi ◽  
Sowon Choi ◽  
KyuHan Kim ◽  
Yosep Han ◽  
...  
Keyword(s):  
Surface Tension ◽  
Polymer Brush ◽  
Bubble Surface ◽  
Mass Ratio ◽  
Attraction Force ◽  
Surface Acting ◽  
Pure Silica ◽  
Mineral Flotation ◽  
Air Water Interface ◽  
High Concentrations

Along with the accompanying theory article, we experimentally investigate the effect of the depletion attraction force on the flotation of malachite. While varying the concentration of the depletion agent (polyethylene glycol), three different systems are studied: pure malachite, pure silica and a 1:1 mass ratio of malachite and silica binary system. We find that the recovery increases significantly as the concentration of the depletion reagents increases for all three systems. However, the recovery suddenly decreases in a certain concentration range, which corresponds to the onset of the decreased surface tension when high concentrations of the depletion agent are used. The decreased surface tension of the air/water interface suggests that the recovery rate is lowered due to the adsorption of the depletion agent to the bubble surface, acting as a polymer brush. We also perform experiments in the presence of a small amount of a collector, sodium oleate. An extremely small amount of the collector (10−10–10−5 M) leads to the increase in the overall recovery, which eventually reaches nearly 100 percent. Nevertheless, the grade worsens as the depletant provides the force to silica particles as well as target malachite particles.

Modeling of collapsing cavitation bubble near solid wall by 3D pseudopotential multi-relaxation-time lattice Boltzmann method

2017 ◽  
Vol 232 (3) ◽  
pp. 445-456 ◽  
Author(s):  
Minglei Shan ◽  
Yu Yang ◽  
Hao Peng ◽  
Qingbang Han ◽  
Changping Zhu
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Cavitation Bubble ◽  
Solid Wall ◽  
Three Dimensional ◽  
Lattice Boltzmann Model ◽  
Bubble Collapse ◽  
Lattice Boltzmann Simulation ◽  
Boltzmann Method ◽  
Boltzmann Model

Understanding the dynamic characteristic of the cavitation bubble near a solid wall is a fundamental issue for the bubble collapse application and prevention. In the present work, an improved three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model is adopted to investigate the cavitation bubble collapse near the solid wall. With respect to thermodynamic consistency, Laplace law verification, the three-dimensional pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. By the theoretical analysis, it is proved that the model can be regarded as a solver of the Rayleigh–Plesset equation, and confirmed by comparing the results of the lattice Boltzmann simulation and the Rayleigh–Plesset equation calculation for the case of cavitation bubble collapse in the infinite medium field. The bubble collapse near the solid wall is modeled using the improved pseudopotential multi-relaxation-time lattice Boltzmann model. We find the lattice Boltzmann simulation and the experimental results have the same dynamic process by comparing the bubble profiles evolution. Form the pressure field and the velocity field evolution it is found that the tapered higher pressure region formed near the top of the bubble is a crucial driving force inducing the bubble collapse. This exploratory research demonstrates that the lattice Boltzmann method is an alternative tool for the study of the interaction between collapsing cavitation bubble and matter.

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