Bubble volume direct methods

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... 

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. 

The principle of the experiment is shown in Fig. 6.5. A small air bubble is formed at the tip of a capillary which is immersed in the solution. Via an electrodynamic excitation system and a membrane, a gas volume directly connected with the capillary is excited to harmonic oscillations. From the excitation voltage of the system in dependence on frequency, while keeping the bubble oscillation amplitude constant, the dilational elasticity and the exchange of matter can be calculated. The comparatively complex theory for data interpretation was described recently by Wantke et al. (1980, 1993). The method can be applied in a frequency interval from 5 Hz up to about 150 Hz. 

Flow meters on field sampling instruments are calibrated using one of several methods. Primary standards are tliose which measure volume directly and are, therefore, preferred. Primary air flow standards include bubble meters, spirometers and Mariotti botdes. The time required to draw a measured volume of air through these systems is measured and the resulting flow rate is calculated. These methods are typically accurate to within one percent. 

The method of Theofanous et al. (1969) should be the most accurate for predicting bubble growth rates in large volumes of liquid metals at uniform superheats, although there has been no experimental data against which to test it directly. 

While the main driving force in [43, 44] was to avoid direct particle transfers, Escobedo and de Pablo [38] designed a pseudo-NPT method to avoid direct volume fluctuations which may be inefficient for polymeric systems, especially on lattices. Escobedo [45] extended the concept for bubble-point and dew-point calculations in a pseudo-Gibbs method and proposed extensions of the Gibbs-Duhem integration techniques for tracing coexistence lines in multicomponent systems [46]. 

The normal procedure for estimating formation volume factor at pressures above the bubble point is first to estimate the factor at bubble-point pressure and reservoir temperature using one of the methods just described. Then, adjust the factor to higher pressure through the use of the coefficient of isothermal compressibility. The equation used for this adjustment follows directly from the definition of the compressibility coefficient at pressures above the bubble point. 

The population balance simulator has been developed for three-dimensional porous media. It is based on the integrated experimental and theoretical studies of the Shell group (38,39,41,74,75). As described above, experiments have shown that dispersion mobility is dominated by droplet size and that droplet sizes in turn are sensitive to flow through porous media. Hence, the Shell model seeks to incorporate all mechanisms of formation, division, destruction, and transport of lamellae to obtain the steady-state distribution of droplet sizes for the dispersed phase when the various "forward and backward mechanisms become balanced. For incorporation in a reservoir simulator, the resulting equations are coupled to the flow equations found in a conventional simulator by means of the mobility in Darcy s Law. A simplified one-dimensional transient solution to the bubble population balance equations for capillary snap-off was presented and experimentally verified earlier. Patzek s chapter (Chapter 16) generalizes and extends this method to obtain the population balance averaged over the volume of mobile and stationary dispersions. The resulting equations are reduced by a series expansion to a simplified form for direct incorporation into reservoir simulators. 

The density of melts is usually measured by weighing a platinum body in air and in the melt. Gas bubbles adhering to the body are the main source of errors involved in the method. It is also possible to measure directly a volume of the melt (Volarovich and Leonteva, 1936) or with high-density glasses to weigh the melt in a platinum vessel in molten salts, e.g. NaCl (Hanlein, 1932). 

The specific surface area of contact for mass transfer in a gas-liquid dispersion (or in any type of gas-liquid reactor) is defined as the interfacial area of all the bubbles or drops (or phase elements such as films or rivulets) within a volume element divided by the volume of the element. It is necessary to distinguish between the overall specific contact area S for the whole reactor with volume Vr and the local specific contact area 51 for a small volume element AVi- In practice AVi is directly determined by physical methods. The main difficulty in determining overall specific area from local specific areas is that Si varies strongly with the location of AVi in the reactor—a consequence of variations in local gas holdup and in the local Sauter mean diameter [Eq. (64)]. So there is a need for a direct determination of overall interfacial area, over the entire reactor, which is possible with use of the chemical technique. 

Multi-stage extraction is used to achieve a higher efficiency of separation, in which the product is almost completely removed from the raffinate. The solvent is split up into several portions and fed to a series of mixers and settlers. The disadvantage of this method is the need to use large volumes of solvent. A more complicated system, called countercurrent, multi-stage extraction, uses a series of mixers and settlers arranged as before, but the feed liquid and pure solvent are passed through the system in opposite directions, that is counter-currently. Continuous countercurrent operation may be carried out by means of spray columns, packed columns (similar to those used in distillation), plate columns, or, sometimes, bubble cap columns. 

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