Bubble volume

In any study on bubble formation, the measurement of bubble volume is of primary importance. The bubbles formed at a nozzle ascend through the liquid column and rupture at the surface of the liquid. During their ascent, 

Methods which yield the bubble size directly make use of photography in one form or another. 

If the reduction ratio is independently known in terms of the distance between the object and the camera, then the bubble size can be known by measuring the size of image by means of an ocular micrometer. 

Alternatively, the camera is kept at a fixed distance, and a scale is first photographed. The ratio of the image size to the actual size gives the reduction ratio. If the camera is then positioned at the same distance and the bubble photographed, the actual dimension of the bubble can be obtained from the image size by dividing it by the reduction ratio. 

The photographic method for evaluating the bubble volume suffers from the disadvantage that it does not yield the volume directly but only gives the contour of the bubble in a single plane. The lighting used is purely a matter of trial and error. Assumptions have to be made regarding the symmetry of 

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Complete wetting caimot occur until either the clump is broken up to let the gas escape or the trapped gas dissolves in the Hquid. A sudden decrease in hydrostatic pressure can help remove gas trapped in a submerged clump by expanding the bubble volume to break up the clump or extend the bubble past the clump s exterior so that it may escape. 

Forveiy thin hquids, Eqs. (14-206) and (14-207) are expected to be vahd up to a gas-flow Reynolds number of 200 (Valentin, op. cit., p. 8). For liquid viscosities up to 100 cP, Datta, Napier, and Newitt [Trans. In.st. Chem. Eng., 28, 14 (1950)] and Siems and Kauffman [Chem. Eng. Sci, 5, 127 (1956)] have shown that liquid viscosity has veiy little effec t on the bubble volume, but Davidson and Schuler [Trans. Instn. Chem. Eng., 38, 144 (I960)] and Krishnamiirthi et al. [Ind. Eng. Chem. Fundam., 7, 549 (1968)] have shown that bubble size increases considerably over that predic ted by Eq. (14-206) for hquid viscosities above 1000 cP. In fac t, Davidson et al. (op. cit.) found that their data agreed veiy well with a theoretical equation obtained by equating the buoyant force to drag based on Stokes law and the velocity of the bubble equator at break-off ... 

When a gas is blown steadily through an orifice into an essentially inviscid liquid, a regular stream of bubbles is formed. A theoretical expression that relates the bubble volume V to volumetric gas flow rate G and gravitational acceleration g is the following ... 

It should be pointed out that Eq. (10) can correctly represent experimental results (cited papers recorded reasonable agreement between theory and experiment) only when diffusion of gas from bubble to bubble can be ignored. When the bubble is small, surface Laplace pressure PL P, and coalescence of bubbles occurs in such a way as to make the volume of the resul tant bubble greater than the sum of the original bubble volumes [27]. 

Gas hold-up is defined as Ha = Bubble volume/Reactor volume, which is the volume of gas per unit volume of reactor. Assume the system is an agitated vessel. Let us use Richard s data to define gas hold-up 3... 

Fig. 2.56 Dependence of bubble volume on time, q = lOkW/m. Reprinted from Hetsroni et al. (2006c) with permission...

In bubbling, the control of the bubble diameter is a little easier. In these methods bubbles are made at an orifice or a multitude of orifices. If there is only one orifice, of radius r, and if bubble formation is slow and undisturbed, the greatest possible bubble volume is 27rry/gp] y is the surface tension of the liquid, p the difference between the densities of liquid and gas (practically equal to the density of the liquid), and g is acceleration due to gravity. Every type of agitation lowers the real bubble size. On the other hand, if there are many orifices near enough to each other, the actual bubble may be much larger than predicted by the above expression. 

Another question that arises is the limiting size of the gas bubbles. As the bubble volume Vj, increases, the buoyancy force V gAp of the bubble increases (g is the acceleration of gravity and Ap is the density difference between the liquid and the gas). The bubble will tear away from the electrode surface as soon as this buoyancy force becomes larger than the forceretaining the bubbles. 

The latent heat transport accounts for only 2% of the total heat flux in this case. However, it was observed by several investigators that the total heat transfer rate is proportional to this value, <7, lenl, because it is proportional to the bubble volume and the number of bubbles that cause intense agitation of the liquid layer close to the surface. This agitation, termed microconvection, together with the liquid-vapor exchange, were considered to be the key to excellent characteristics of boiling heat transfer (Forster and Greif, 1959). 

The Davidson and Harrison (1963) model assumed there was no net exchange of gas between the bubble and the emulsion phase. The validity of this assumption was later questioned by Botterill et al. (1966), Rowe and Matsuno (1971), Nguyen and Leung (1972), and Barreto et al. (1983). The predicted bubble volume, if assumed no net gas exchange, was considerably larger than the actual bubble volume experimentally observed. 

A model was developed to describe this phenomenon by assuming that the gas leaks out through the bubble boundary at a superficial velocity equivalent to the superficial minimum fluidization velocity. For a hemispherical bubble in a semicircular bed, the rate of change of bubble volume can be expressed as ... 

The ratio of cloud volume to bubble volume is given by Kunii and Levenspiel(1991, p. 157), and from this we obtain the volume fraction in the cloud region1 ... 

The notation used here for bed traction is used for ratio with respect to bubble volume by Kunii and Levenspiel. 

In these methods the volumetric flow corrected to the nozzle tip, Q, and the frequency of bubble formation, /, are directly measured. The bubble volume is then calculated. These methods have a number of limitations. 

First, they cannot be used for the evaluation of volumes of individual bubbles. Only an average bubble volume is obtained. Bubble formation is generally a cyclic phenomenon, and for a definite flow rate in a particular system, the frequency and the bubble volume are time-independent. However, there are situations where each bubble is followed by smaller secondary bubbles. In such cases, the above methods cannot yield reliable values and photographic methods have to be resorted to. 

Even with the above-mentioned limitations, the indirect methods constitute the simplest way of evaluating bubble volumes from single nozzles, and hence are most extensively used. As these methods involve a knowledge of the two quantities Q and f the ways of measuring each of them are separately discussed below. 

This device has been successfully employed for measuring bubble volumes when the chemical reaction between a gas and a liquid is being studied (V2). The conditions under which the gas is measured are converted to the conditions of pressure, temperature, etc. existing at the nozzle tip. 

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