Bubble distortion

Slug flow is the dominant flow regime in multiphase systems. Flow visualization has shown that bubbles distort and elongate in the vicinity of a pipe wall in a manner similar to collapsing bubbles. The corrosion rate increases because of a thinning of the mass transfer and corrosion product layers, as well as because of localized damage of the corrosion product film. 

As a result, this equation is usually the only one needed for liquid or solid aerosols. Figure 6.18 shows several sets of experimental data compared with the Einstein equation. In practice once cp reaches between 0.1 and 0.5, dispersion viscosity increases significantly and can also become non-Newtonian (due to particle/droplet/bubble crowding or structural viscosity). The maximum volume fraction possible for an internal phase made up of uniform, incompressible spheres is 0.74, although emulsions and foams with an internal volume fraction of over 0.99 can exist as a consequence of droplet/bubble distortion. Figure 6.18 and Equation 6.33 illustrate why volume fraction is such a theoretically and experimentally favoured concentration unit in rheology. In the simplest case, a colloidal system can be considered Einsteinian, but in most cases the viscosity dependence is more complicated. 

Figure 6-11. Bubble distortions near the pipe wall in the mixing zone of the slug.

Small drops or bubbles will tend to be spherical because surface forces depend on the area, which decreases as the square of the linear dimension, whereas distortions due to gravitational effects depend on the volume, which decreases as the cube of the linear dimension. Likewise, too, a drop of liquid in a second liquid of equal density will be spherical. However, when gravitational and surface tensional effects are comparable, then one can determine in principle the surface tension from measurements of the shape of the drop or bubble. The variations situations to which Eq. 11-16 applies are shown in Fig. 11-16. 

The preceding upper limit to particle size can be exceeded if more than one bubble is attached to the particle, t A matter relating to this and to the barrier that exists for a bubble to attach itself to a particle is discussed by Leja and Poling [63] see also Refs. 64 and 65. The attachment of a bubble to a surface may be divided into steps, as illustrated in Figs. XIII-8a-c, in which the bubble is first distorted, then allowed to adhere to the surface. Step 1, the distortion step, is not actually unrealistic, as a bubble impacting a surface does distort, and only after the liquid film between it and the surface has sufficiently thinned does... 

Ca is replaced by a rare-earth element, resulting in a distorted perovskite stmcture, which is essentially orthorhombic. Orthoferrites, studied extensively in the early 1970s as potential data storage materials based on magnetic bubble domains (10), have been largely replaced by the garnet materials (see... 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

These coatings bubble and foam to form a thermal insulation when subjected to a fire. They have been used for many decades. Such coatings cannot be differentiated from conventional coatings prior to the occurrence of a fire situation. Thereupon, however, they decompose to form a thick, nonflammable, multicellular, insulative barrier over the surface on which they are applied. This insulative foam is a very effective insulation that maintains the temperature of a flammable or heat distortable substrate below its ignition or distortion point. It also restricts the flow of air (oxygen) to fuel the substrate. 

Equation (17) indicates that the entire distribution may be determined if one parameter, av, is known as a function of the physical properties of the system and the operating variables. It is constant for a particular system under constant operating conditions. This equation has been checked in a batch system of hydrosols coagulating in Brownian motion, where a changes with time due to coalescence and breakup of particles, and in a liquid-liquid dispersion, in which av is not a function of time (B4, G5). The agreement in both cases is good. The deviation in Fig. 2 probably results from the distortion of the bubbles from spherical shape and a departure from random collisions, coalescence, and breakup of bubbles. 

In region III near the tube center, viscous stresses scale by the tube radius and for small capillary numbers do not significantly distort the bubble shape from a spherical segment. Thus, even though surfactant collects near the front stagnation point (and depletes near the rear stagnation point), the bubble ends are treated as spherical caps at the equilibrium tension, aQ. Region... 

Tuziuti T, Yasui K, Lee J, Kozuka T, Towata A, Iida Y (2009) Influence of surface active solute on ultrasonic waveform distortion in liquid containing air bubbles. J Phys Chem A... 

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