Davies and Taylor equation

The rise velocity of a single spherical cap bubble in an infinite liquid medium can be described by the Davies and Taylor equation [Davies and Taylor, 1950] (Problem 9.6). Experimental results indicate that the Davies and Taylor equation is valid for large bubbles (4oo > 0.02 m, in general) with bubble Reynolds numbers greater than 40, while for bubbles in fluidized beds, the bubble Reynolds numbers are typically on the order of 10 or less [Clift, 1986]. By analogy, the rise velocity of an isolated single spherical cap bubble in an infinite gas-solid medium can be expressed in terms of the volume bubble diameter by [Davidson and Harrison, 1963]... 

Davidson and Harrison [48] have studied bubbling phenomena in fluidized beds extensively and have shown that the rising velocity of gas bubbles in fluidized beds may be estimated with the aid of the Davies and Taylor equation, which was originally developed for the rise of large (spherical cap) gas bubbles in liquids ... 

The formation of bubbles at orifices in a fluidised bed, including measurement of their size, the conditions under which they will coalesce with one another, and their rate of rise in the bed has been investigated. Davidson el alP4) injected air from an orifice into a fluidised bed composed of particles of sand (0.3-0.5 mm) and glass ballotini (0.15 mm) fluidised by air at a velocity just above the minimum required for fluidisation. By varying the depth of the injection point from the free surface, it was shown that the injected bubble rises through the bed with a constant velocity, which is dependent only on the volume of the bubble. In addition, this velocity of rise corresponds with that of a spherical cap bubble in an inviscid liquid of zero surface tension, as determined from the equation of Davies and Taylor ... 

Equation (85) was verified experimentally by Nicklin et al. (1962) for application to a finite bubble or to a slug rising in a tube. Davies and Taylor (1950) also provided a solution with a slightly different empirical constant. 

When the centrifugal force is larger than the surface tension force, the bubble would be stretched in the x-direction. During the stretching, the aspect ratio, a, becomes smaller while d, and M), can be assumed to remain constant. As a result, the centrifugal force increases, the surface tension force decreases, and the bubble stretching becomes an irreversible process. Using the Davies-Taylor equation (Davies and Taylor, 1950) for the bubble rise velocity, the maximum stable bubble size is expressed by... 

When the surface of an emulsion droplet is mobile, it can transmit the motion of the outer fluid to the fluid within the droplet. This leads to a special pattern of the fluid flow and affects the dissipation of energy in the system. The problem concerning the approach of two nondeformed (spherical) drops or bubbles of pure phases has been investigated by many authors [657,685,686,692,693,777-782]. A number of solutions, generalizing the Taylor equation (Equation 4.271), have been obtained. For example, the velocity of central approach, ]/, of two spherical drops in pure liquid is related to the hydrodynamic resistance force, F, by means of a Pade-type expression derived by Davis et al. [692] ... 

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