Bubble volume-surface mean diamete

Bubble diameter dbub is also referred to as volume-surface mean diameter of bubbles or Sauter mean bubble diameter. SI units are used with this correlation. 

Here, aL is the gas-liquid interfacial area and dsv is the volume-surface mean diameter or Sauter mean diameter. All bubbles are assumed to be spherical dB is the bubble diameter and the number of bubbles of size dUi. The value of dsv can be directly evaluated through a statistical analysis of high speed photomicrographs performed in the dispersion (Calderbank and Rennie, 1962 Vermeulen et al, 1955 Porter et al, 1966 Akita and Yoshida, 1973 Ashley and Haselden, 1972). Photographs have been taken through the walls of a transparent vessel or in the interior of a reactor with the aid of an intrascope (Koetsier and Thoenes, 1972). 

Experimental Mj values determined as the difference between the local mean velocities of bubbles and liquid are also shown in Fig, 34 as open keys. For these bubbles, the volume-surface mean diameters J32 have been measured experimentally. The free-rise velocity of the bubbles (Tl, V6) is... 

Volume-surface mean diameter of drops or bubbles, m or ft mean diameter calculated from Eq. (9.46), mm Height of impeller above vessel floor, m or ft Kinetic energy of fluid, J/m or ft-Iby/ft ... 

The volume - surface mean bubble diameter is defined by Equation 7.25 ... 

The gas-liquid interfacial area per unit volume of gas-liquid mixture a (L 1. or L ), calculated by Equation 7.26 from the measured values of the fractional gas holdup and the volume-surface mean bubble diameter d, were correlated... 

Steady bubble diameter in turbulent bubble flow Diameter of particle Number-averaged mean bubble diameter Volume-surface mean bubble diameter... 

The bubble size can be measured by photographic or probe techniques. In multibubble systems, a mean bubble size is usually used to describe the system. The mean bubble size is commonly expressed through the Sauter, or volume-surface, mean. For a group of bubbles with measured diameters, the Sauter mean is... 

For both bubbles and particles, there will be a distribution of sizes in the dispersion. The above quantities can be related to the volume/surface or Sauter mean bubble and particle diameters <4 and dp (see Volume 2, Chapter 1). 

The physical technique just described directly measures the local surface area. The determination of the overall interfacial area in a gas-liquid or a liquid-liquid mechanically agitated vessel requires the application of this technique at various positions in the vessel because of variations in the local gas (or the dispersed-phase) holdup and/or the local Sauter mean diameter of bubbles or the dispersed phase. The accuracy of the average interfacial area for the entire volume of the vessel thus depends upon the homogeneity of the dispersion and the number of carefully chosen measurement locations within the vessel. 

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. 

It is common to report the average bubble diameter as the Sauter mean diameter which is defined as the diameter of a bubble equivalent to the volume-to-surface area ratio of the entire dispersion (Saxena et al 1988). Assuming all bubbles are spheres,... 

Together with the fractional gas holdup the bubble diameter (volume-to-surface mean value) decisively determines the gas-liquid interfacial area which is given by... 

An additional factor affecting the stability of the bubble is the size of the bubble. We foxmd that PFC gases enabled us to prepare smaller, stable bubbles than using air or nitrogen. This is predominantly due to the very low surface tension at the gas water interface. LaPlace pressures, which describe the pressure at both the inside and outside of the shell surface, increase inversely as the decrease of the bubble diameter. As the diameter of the bubble decreases, the pressure increases xmtil the microbubble either collapses, or the surface area to volume increases so much that proportionately more surface area allows diffusion of the gas across the bubble into the circulation. Perfluoropentane (C5F12) is a liquid at room temperature and boils at 28.5 degrees C. We have found that perfluoropentane emulsion can be stabilized as an emulsion with mean diameter of about 200 nm at room temperature. The material can be activated by heat or other energy to form microbubbles. 

In many cases, irregular-shaped particles or a size distribution of particles can be treated as spheres with an equivalent diameter that gives the same sinface/volmne ratio as the irregular-shaped particle. The Saunter mean diameter, usually denoted t/j2, defined as the total volume divided by the total surface area, is a very common method used to characterize a size distribution of bubbles or drops. With this definition, the total volume can be calculated from the munber of particles multiphed by the volume of a sphere with diameter and the total sinface area can be calculated by multiplying the number of particles by the surface of the sphere. 

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

Note that re-arranging the above relationship to give d/, = 6ea/a shows how a mean bubble size might be calculated from measurements of and a. A mean bubble diameter defined in this way (Volume 2, Chapter 1) is called a Sauter mean (i.e. a surface volume mean see also Section 4.3.4). 

Under the real operating conditions of a fluidized-bed reactor, a number of interacting bubbles occur in the interior of the fluidized bed. As a rule, the interaction leads to coalescence. As detailed studies have shown, this process is quite different from that between gas bubbles in liquids because of the absence of surface-tension effects in the fluidized bed [31, 32], Werther has derived a simple empirical correlation (based on the mechanism of bubble coalescence) for the growth of the mean bubble size dy (diameter of the sphere of equal volume) with increasing height h above the grid [33, 34] ... 

Note Mean and standard deviations are given. Sauter mean bubble diameter is the volume to surface averaged bubble diameter in a bubble swarm. 

Using 6-blade disc turbines in baffled tanks with pure liquids, i.e. coalescing systems, Calderbank measured interfacial area and hold-up and obtained an equation for the surface/volume mean bubble diameter (in SI units) ... 

Clb liquid reactant concentration (moles/m ) ds bubble diameter (surface-volume mean) (m)... 

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