Bubble interface

Analytical analyses for the growth of a single bubble have been performed for simple geometrical shapes, using a simplified heat transfer model. Plesset and Zwick (1954) solved the problem by considering the heat transfer through the bubble interface in a uniformly superheated fluid. The bubble growth equation was obtained... 

The vapor pressure in the bubble is related to the liquid pressure at the bubble interface and the surface tension force by Eq. (2-3). Introducing this result into Eq. (2-28), the Rayleigh equation (Rayleigh, 1917) for isothermal bubble dynamics is obtained as... 

The circulation of liquid in the vicinity of a growing bubble due to thermocapi-larity effects on vapor-liquid bubble interface is negligible... 

The absolute rates of vaporization and condensation are evaluated by using the rate expressions discussed in Section III,B. The net rate of phase change at the bubble interface or equivalently the rate of bubble growth, has been widely studied for single bubbles in stationary systems. Bankoff (B2) has reviewed the results of these studies. Ruckenstein (R2) has analyzed bubble growth in flowing systems. 

Figure 2. Flow of a single gas bubble through a liquid-filled cylindrical capillary. The liquid contains a soluble surfactant whose distribution along the bubble interface is sketched.

It is based on equilibrium properties and is directly related to the Gibbs elasticity (17.). In the present context a gauges how strongly the surface tension depends on the surfactant distribution along the bubble interface. Second, captures the kinetics of the adsorption process and is defined by... 

For gas-liquid bubble flow, F and F+ are the gas and liquid velocities, respectively, and the zero-level set of 4> marks the bubble interface, which moves with time. For gas-droplets flows, on the other hand, F and V+ represent the... 

For a pseudo first-order reaction, the rate with respect to oxygen = kC (per unit volume of liquid). If Q is the concentration at the bubble interface and Ch the concentration in the bulk, then assuming that ... 

Aromatic compounds undergo carbonisation during sonication [44]. The reaction can occur either at the bubble interface or inside the cavity, according to the hydrophUicity of the substrate. Generally it would appear that apolar, hydrophobic compounds, e. g. benzene and halocarbons are pyrolysed inside the bubble [45,46]. 

The occurrence of an optimum frequency at 200 kHz was explained through a two step reaction pathway. In the first step water sonolysis produces radicals within the bubble. In step two the radicals must migrate to the bubble interface or into the bulk aqueous medium to form peroxide or react with the phenolic substrate. The authors suggest that the lower frequencies are the most efficient for the decomposition of molecules inside the bubble but a proportion of the radicals recombine inside the bubble at high temperature to form water thereby reducing the overall yield of H2O2 (Eqs.4.1 and 4.2). 

We also need to develop the theories for hquid film coefficient to use in the aforementioned equations. For drops that are close to spherical, without separation, Levich (1962) assumed that the concentration boundary layer developed as the bubble interface moved from the top to the bottom of a spherical bubble. Then, it is possible to use the concepts applied in Section 8.C and some relations for the streamlines around a bubble to determine Kl. ... 

The particle velocity at the bubble interface r = R(t) is, which is he bubble growth rate. Using this boundary condition, from Eq. (13.27), we have... 

Hua et al. (1995) proposed a supercritical water region in addition to two reaction regions such as the gas phase in the center of a collapsing cavitation bubble and a thin shell of superheated liquid surrounding the vapor phase. Chemical transformations are initiated predominantly by pyrolysis at the bubble interface or in the gas phase and attack by hydroxyl radicals generated from the decomposition of water. Depending on its physical properties, a molecule can simultaneously or sequentially react in both the gas and interfacial liquid regions. 

Ultrasonically irradiated solution of p-NPA exhibits an observed rate constant that is enhanced by about two orders of magnitude in comparison to the same hydrolysis under ambient conditions at 25°C. Observations in unsonified solutions suggest that the reaction rate enhancement occurs at the cavitation-bubble interface. Both the enhanced hydrolysis rate and its pH independence may be explained by the existence of SCW around the... 

V.P. Lehto, I. Kantola, T. Tervo and L.A. Laitinen, Ruthenium red staining of blood-bubble interface in acute decompression sickness in rats, Undersea Biomed. Res. 8(1981) 101-111. 

V.P. Lehto and L.A. Laitinen, Scanning and transmission electron microscopy of the blood-bubble interface in decompressed rats, Aviat. Space Environ. Med. 50 (1979) 803-807. 

Figure 13.4 Illustration of the adsorption of partially-coalesced fat globules and their associated protein membranes to an air bubble interface. From Goff [815]. Copyright 1997, Elsevier.

A few simple differences in the properties of immiscible phases make possible their relative displacement. Most simply, if the phases have different densities they will automatically acquire a relative motion in a gravitational field. Thus in adsorptive bubble separation methods, bubbles injected into a column of liquid rise toward the upper surface. Separation occurs by combining the relative enrichment of components at the bubble interface with the continuous displacement of bubbles through the liquid [33-35]. 

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