Bubble displacement, discussion

The above discussion is concerned with single bubble displacement. To obtain results analogous to Equations 6, 8, and 9 for bubble trains, it is necessary to account for changes in curvature at the bubble ends (in the Plateau border regions) due to the compression between adjacent bubbles. Referring to Figure 5(b), the contact radius Rc can be related to the capillary pressure Pc = Pi - Pi = P - P by... 

Measurement of the velocity of a large particle. The investigation of the turbulence characteristics in the liquid phase of a bubbly flow has generated detailed studies on the use of thermal anemometry and optical anemometry in gas-liquid two-phase flows. These techniques have been proved to be accurate and reliable for the measurement of the instantaneous liquid velocity in bubble flow. However, the velocity of the gas bubbles—or, more precisely, the speed of displacement of the gas-liquid interfaces—is still an active research area. Three techniques that have been proposed to achieve such measurement were reviewed by Delhaye (1986), as discussed in the following paragraphs. 

In this chapter, we discuss much of the work accomplished since Fried, but without attempting a complete review. Useful synopses are available in the articles and reports of Hirasaki (2, 3), Marsden (4), Heller and Kuntamukkula (5), Baghidikian and Handy (6), and Rossen (7). Our goals are to present a unified perspective of foam flow in porous media to delineate important pore-level foam generation, coalescence, and transport mechanisms and to propose a readily applicable one-dimensional mechanistic model for transient foam displacement based upon gas-bubble size evolution [i.e., bubble or lamella population-balance (8, 9)]. Because foam microstructure or texture (i.e., the size of individual foam bubbles) has important effects on flow phenomena in porous media, it is mandatory that foam texture be accounted for in understanding foam transport. 

In order to evaluate the usefulness of C02 foam as a displacing fluid, more quantitative reference must be made to some of the topics that were introduced more qualitatively and more briefly in the introductory discussions of this chapter. The flow of foam in pipes has been discussed. For foam flowing in pipes, the pipe diameter is much larger than the cell size, and no shear flow occurs throughout most of the cross-section of the mass of foam in the pipe. The shearing strain is concentrated instead in a thin water-film around the inside perimeter of the pipe, and the foam plug rides on this film of water. This circumstance is quite different from that in which foam flows in porous media, in which immobile containing boundaries are close to every part of the flow. The flow of a hypothetical foam in porous media, which consisted of a mass of bubbles in every pore, would be almost impossible. This follows from some of the theoretical work about the motion of two-dimensional arrays of foam cells. 

There has been a discussion in the literature whether the nonionic surfactants in solution do bear some charge because of the adsorption of ions (say OH") on the eth-yleneoxide chains. Recent precise electrophoretic measurements with air bubbles and oil droplets in pine water or nonionic surfactant solutions reveal that the observed negative surface charge is an inherent property of the interface water-hydrophobic phase (air, oil), which can be attributed to the adsorption of hydroxyl ions at the interface [22]. The nonionic surfactant molecules themselves are not charged, but they can reduce the surface charge by displacing the adsorbed OH" from the interface for details see Ref. 22 and the literature cited therein. 

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