Bubble diffusion

Mass transfer in the continuous phase is less of a problem for liquid-liquid systems unless the drops are very small or the velocity difference between the phases is small. In gas-liquid systems, the resistance is always on the liquid side, unless the reaction is very fast and occurs at the interface. The Sherwood number for mass transfer in a system with dispersed bubbles tends to be almost constant and mass transfer is mainly a function of diffusivity, bubble size, and local gas holdup. 

Lux G. (1987). The behavior of noble gases in silicate liquids Solution, diffusion, bubbles and surface effects, with application to natural samples. Geochim. Cosmochim. Acta, 51 1549-1560. 

Proussevitch A.A., Sahagian D.F., and Anderson A.T. (1993) Dynamics of diffusive bubble growth in magmas isothermal case. /. Geophys. Res. 98, 22283-22307. 

The shape of polyhedra and the number of faces in them change continuously in the process of foam evolution (as a result of diffusion gas transfer and coalescence). Because of gas diffusion bubbles pass through transformation stages in which a body with five faces (pentahedron), then another body with four face (tetrahedron) [71] are formed and then they disappear. 

The decrease in foam dispersity results from both bubble coalescence and diffusion bubble expansion. So, depending on the surfactant kind and the time elapsed after foam formation, one of these processes can have a prevailing effect on the rate of foam collapse. 

The comparison of the experimentally determined rate of decrease in the number of foam cells in a foam from an aqueous NaDoS solution, with that calculated from the equation for the diffusion bubble expansion, supports the conclusion that coalescence contributes significantly to the internal foam collapse. This has been evidenced by New [28], Film rupture in the foam was registered directly by a camera. 

A more important fact is the change in the mechanism of foam column destruction with the increase in the applied pressure drop. For example, at small pressure drops a slow diffusion bubble expansion along with the corresponding slow rate of structural rearrangement (either zero or very slow rates of coalescence) occurs in a NaDoS foam with CBF or NBF. This is expressed in the layer-by-layer reduction of foam column height ending with the disappearance of the last bubble layer. In such a foam the critical pressure of the foam column destruction is not reached at any dispersity, and only the foam column height and the rate of internal foam collapse determine the foam lifetime. 

For stable foams with a not very high expansion ratio (at Ap - 1 kPa) a quantitative relation between the rates of internal foam collapse and foam column decay during its entire lifetime is also established (see Eq. (6.50)). Thus, the foam lifetime can be calculated on the basis of the regularities of its internal collapse mainly from the data about the diffusion bubble... 

The study of the foam lifetime versus concentration for the widely used foaming agents Volgonate (at Ap = 10 kPa) indicates that foam stability decreases visibly at concentrations less than 0.1%. The rate of diffusion bubble expansion gradually decreases, starting from concentrations -1%. Additional rise in foam stability is obtained with addition of various additives (electrolytes, water soluble polymers, fatty alcohols, etc.). 

Archimedes number Area of bed cross section Membrane surface area per cell, n Particle diameter Heat capacity Dispersion coefficient Gas diffusivity Bubble phase fraction Emulsion phase fraction Activation energy for hydrogen permeation Gravitational acceleration ( = 9.81) Enthalpy of species j Enthalpy of component i at temperature T at position x... 

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