Bubble volume fraction

The surface-emulsion phase contact time tc can be estimated by assuming that the time fraction for the surface to be covered by bubbles equals the bubble volume fraction in the bed... 

J = 1 1 1 1 1 1 1 - 4> 0.97 0.95 L A r no rigure viscosity as a lunc-tion of shear stress for an aqueous polymer-surfactant foam at the bubble volume fractions 0 shown. (From Khan et al. 1988, with permission... 

Figure 8.1.12 Bubble volume fractions for stable and transient bubbles as a function of normalized sound pressure.

Significant differences between beds operated with and without tubes. Initial increase with pressure in mean pierced bubble length, rise velocity, bubble volume fraction and visible bubble flow rate. 

Bubble volume fraction. Otice the bubble diameter has been predicted, a representative bubble velocity can be estimated from the equation... 

In the DBM, the centers of mass and volumes of individual bubbles are tracked. The outcome of a binary coUision between two such bubbles is bounce or coalescence, depending on many factors including the surface tension and relative velocity. Under sufficiently strong deformations, bubbles can even break up into a number of smaUer bubbles. At larger bubble volume fractions, the bubble motion leads to a strong mixing of the continuous fluid and therefore a large dispersion of dissolved chemicals. 

Several papers on Euler—Euler simulations (both RANS based and of the above EELES type) report about the need to include a separate turbulent dispersion term (or force) for reproducing a correct spatial distribution of suspended particle clouds or bubble swarms. Various models for this turbulent dispersion have been suggested, all of them modeling this effect in terms of the gradient of the particle or bubble volume fraction. Sometimes, this additional term is in the continuity equations (Bakker and Van den Akker, 1994 Sardeshpande and Ranade, 2012 Tamburini et al, 2014) with the justification that is due to fluctuations in the volume fractions however, as the volume fraction which anyhow is an averaged variable does not vary... 

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