Spherical gas bubble

Similarly, some solid foams (e.g. foam rubber) consist of spherical gas bubbles trapped within a solid network, whereas others (e.g. expanded polystyrene) consist of as little as 1 per cent solid volume and are composed of polyhedral gas cells separated by very thin solid walls. 

Another study carried out by these authors [93] modeled the collapsing motion of a single bubble near an electrode surface, and equations for the motion of a spherical gas bubble were obtained. The jet speed and water hammer pressure during jet flow (liquid jet) were calculated, and when the jet speed was 120 m/s, the water hammer pressure was approximately 200 MPa upon the electrode surface. This pressure played an important part in the fineness of the crystal deposits. Mass transfer during the electrode reaction was by turbulent diffusion. The diffusion layer thickness was reduced to approximately 1/10th its size in the presence of the ultrasonic field. The baths contained the ions Cl-, SO -, and Zn2+. The ultrasonic frequency employed in the experiments was 40 kHz and it was seen that ultrasound considerably increased the deposition rate and current efficiency, as well as the smoothness and hardness of the deposit. Microscopy studies showed that the... 

Figure 9.6. Idealized view of (a) spherical gas bubbles in a liquid, (h) liquid droplets in a gas, and (c) cylindrical gas jets in a liquid. Diffusion in bubbles, drops, and jets may be modeled by solving the diffusion equations for cylindrical and spherical coordinates.

Assuming spherical gas bubbles with an average bubble diameter dt = 32 according to ... 

Biesheuvel, a. Spoelstra, S. 1989 The added mass coefficient of a dispersion of spherical gas bubbles in liquid. International Journal of Multiphase Flow 15, 911-924. 

Problem 4-10. An Alternative Derivation of the Rayleigh-Plesset Equation. Find the total kinetic energy Ek of the liquid outside a spherical gas bubble that is undergoing time-dependent changes in volume in an unbounded, incompressible, Newtonian fluid. Show that the net rate of working by the pressure inside the bubble p at the inner side of the bubble boundary is... 

Problem 7-10. Translation of a Bubble Through a Quiescent Fluid. A spherical gas bubble rises through a stationary liquid that is sufficiently viscous that the creeping-flow approximation is valid. Assume that the boundary conditions for the liquid motion at the bubble surface are... 

Problem 9-10. Mass Transfer From a Spherical Gas Bubble for Re -C 1, Pc -C 1. Consider a spherical gas bubble and suppose that it contains a gaseous species A that is soluble in the liquid that surrounds the bubble and a second dominant species B that is insoluble in... 

Problem 9-20. Mass Transfer From a Spherical Bubble in an Extensional Flow. Consider a spherical gas bubble that is suspended in a liquid that undergoes an axisymmetric extensional flow. The bubble contains a component A that is soluble in the exterior liquid... 

Consider a spherical gas bubble of initial radius R, placed in a quiescent liquid [16]. Assume that the bubble center does not move relative to the liquid, but the bubble volume changes with time due to the difference of pressures inside the bubble and in the ambient liquid, and also as a result of dynamic and heat-... 

Consider the initial stage of growth of a spherical gas bubble with initial radius Ro in a multicomponent supersaturated solution due to the diffusion of components with low concentration that dissolved in the liquid. Assume that the process is isothermal, and the factors Du, B, and Z are constants. The bubble is small enough to ignore its lifting inside the liquid. The dynamics of bubble growth is described by Eqs. (22.1)-(22.5), in which we must set uy = 0. 

To examine the influence of surfactants on bubble growth, consider the following problem. A spherical gas bubble is placed in a binary solution, supersaturated at the given pressure and temperature. As a result, there emerges a diffusion flux toward the bubble surface. The process is accompanied by adsorption of a surfactant, which is present in the liquid, on the bubble surface. Assume that the process is diffusion-controlled, i.e. adsorption-desorption of surfactant molecules at the interface occurs sufficiently quickly. In such a case, the surface concentration of surfactant T may be taken equal to the equilibrium value [4] ... 

Figure 5.5 Drag on spherical gas bubbles in power-law fluids in creeping...

Brahston, D.C. and Keller, H.B., Viscous flows past spherical gas bubbles, J. Fluid Mech., 69, 179-189, 1975. 

We consider an isolated gas bubble in an unbounded incompressible liquid initially at rest. We neglecting diffusions effects and changes in temperature. The following differential equation describes the nonlinear oscillations of the spherical gas bubble boundary[3],[4]... 

Let us dwell upon this point by discussing a few examples. First, we shall consider a small spherical gas bubble submerged in water (Component 1) that is supersaturated with the gaseous component (Component 2). Choosing the surface of tension as the dividing surface, the Laplace condition in its standard form, that is. 

FIG. 4 A spherical gas bubble submerged in water saturated with gas at the pressure of the gas in the bubble. The equilibrium is stable for a thermodynamically closed bubble but unstable for an open bubble. 

Astarita, G., Spherical gas bubble motion through Maxwell liquids, Ind. Eng. Chem. Fundam. 5 548 (1966). 

Dynamics of spherical gas bubbles in viscoelastic liquids, following different rheological equations, was also the subject of later studies. " " The basic findings are similar to those discussed above. Bubble dynamics in inelastic... 

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