Average interfacial area

Figure 8-10 2H NMR spectra of dimyristoyl phosphatidyl-cholme-d27/water in lamellar phases at 40°C. One chain of the phosphatidylcholine is fully deuterated, containing 27 atoms of 2H. The mole ratios of water to lipid were 5.0 in (A) and 25.0 in (B). The average interfacial areas per alkyl chain as measured hy X-ray diffraction were 0.252 nm2 for (A) and 0.313 nm2 for (B). 2H NMR spectra are presented as "powder patterns" because the lipid molecules are randomly oriented in the magnetic field of the spectrometer as if in a powder. This gives rise to pairs of peaks symmetrically located on both sides of the origin. The separation distances are a measure of the quadrupole splitting of the NMR absorption line caused by the 2H nucleus. The various splittings of the resonances of the 13 -CH2- and one -CH3 groups reflect differences in mobility.109 The peaks have been assigned tentatively as indicated. From Boden, Jones, and Sixl.115 Courtesy of N. Boden.

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 overall interfacial area for the whole reactor can be determined by chemical techniques. These techniques, however, must be used with restrictions. For example, chemical methods are difficult to use for fast-coalescing systems, since the presence of a chemical compound may reduce coalescence rates. Furthermore, in fast-coalescing systems, the specific area may depend strongly on the position in the reactor, which complicates the interpretation of an average value obtained with chemical methods. Indeed, both physical and chemical techniques should be used together to describe the phenomena that occur within gas-liquid reactors. While chemical methods allow the determination of the much-needed average interfacial area, information on the variations of the interfacial parameters, such as aL and dsv, within the reactor, which is important for scale-up, cannot be obtained by this method. 

The first moment of the interfacial area is then used to obtain the average interfacial area for a given axial position. 

Averaging the product of the absolute value of the gradient and the fluxes gives as the result the average contributory effect of mass and molecular fluxes at the interfaces over the whole domain of integration [67]. Drew [54] defined the averaged interfacial area per unit volume by ... 

The situation can, however, be optimized by noting that the aggregates are formed under the constraint of a constant ratio of average interfacial area to enclosed volume, set by the concentration ratio of surfactant to internal component. With this constraint, the minimum aggregate size corresponds to a spherical shape. Due to... 

An estimate of the average interfacial area may be obtained from i e. 

Also included in Table 1 are the average areas and Ay obtained from the entire chains (i.e. order parameters accounts for the fact that half thickness <(> [19,20,8]. The problems encountered when correlating chain order parameters and the average interfacial areas per chain in liquid crystalline aggregates have been recently discussed by Nagle [21]. 

Partial molar area occupied by species i at the interface (m /mol or /molecule) The average interfacial area occupied by an amino acid residue (A /molecule) Partial molar area occupied by protein at the interface as defined by either Eq. (17) or (18) (m /mol or A /molecule)... 

Increased agitation of a given acid—hydrocarbon dispersion results in an increase in interfacial areas owing to a decrease in the average diameter of the dispersed droplets. In addition, the diameters of the droplets also decrease to relatively low and nearly constant values as the volume % acid in the dispersions approaches either 0 or 100%. As the droplets decrease in si2e, the ease of separation of the two phases, following completion of nitration, also decreases. 

Equations (13-111) to (13-114), (13-118) and (13-119), contain terms, Njj, for rates of mass transfer of components from the vapor phase to the liquid phase (rates are negative if transfer is from the liquid phase to the vapor phase). These rates are estimated from diffusive and bulk-flow contributions, where the former are based on interfacial area, average mole-fraction driving forces, and mass-... 

Drop Size and Interfacial Area The drops produced have a size range [SuUivan and Lindsey, Ind. Eng. Chem. Fundam., 1, 87 (1962) Sprow, Chem. Eng. Sci., 22, 435 (1967) and Chen and Middleman, Am. Inst. Chem. Eng. J., 13, 989 (1967)]. The average drop size may be expressed as... 

In general, p (r) is a function of the vector position of the point of observation r. However, if one is concerned mainly with the inhomogeneity of the confined fluid in the normal (z) direction, the average over the interfacial area is adequate. Averaging yields... 

Pave = average total pressure in tower, atmospheres Hl = height of liquid film transfer unit, ft Hg = height of gas film transfer unit, ft a = effective interfacial area for contacting gas and liquid phases, ft /ft. Because this is very difficult to evaluate, it is usually retained as a part of the coefficient such as Kca, Ki a, kca, and k.La. 

These results are, however, only valid for the particle sizes referred to. Lee (L3) has reported measurements of average bubble diameter and gas-liquid interfacial area for gas-liquid fluidized beds of glass beads of 6-mm... 

Yoshida and Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

Calderbank et al. (C1-C4), who worked with systems quite similar geometrically to that of Yoshida and Miura, found that the average bubble diameter for air in water at 15°C ranged from 3 to 5 mm. Westerterp et al. (W2-W4) found the range to be 1-5 mm for air in sodium sulfite solution at 30°C. In addition, they noted that any increase in interfacial area between the bubbles and the liquid was due primarily to the increase in gas holdup, and the average bubble diameter was essentially unaffected by the impeller speed and was approximately 4.5 mm (W3). 

Most studies on heat- and mass-transfer to or from bubbles in continuous media have primarily been limited to the transfer mechanism for a single moving bubble. Transfer to or from swarms of bubbles moving in an arbitrary fluid field is complex and has only been analyzed theoretically for certain simple cases. To achieve a useful analysis, the assumption is commonly made that the bubbles are of uniform size. This permits calculation of the total interfacial area of the dispersion, the contact time of the bubble, and the transfer coefficient based on the average size. However, it is well known that the bubble-size distribution is not uniform, and the assumption of uniformity may lead to error. Of particular importance is the effect of the coalescence and breakup of bubbles and the effect of these phenomena on the bubble-size distribution. In addition, the interaction between adjacent bubbles in the dispersion should be taken into account in the estimation of the transfer rates... 

Interfacial area measurement. Knowledge of the interfacial area is indispensable in modeling two-phase flow (Dejesus and Kawaji, 1990), which determines the interphase transfer of mass, momentum, and energy in steady and transient flow. Ultrasonic techniques are used for such measurements. Since there is no direct relationship between the measurement of ultrasonic transmission and the volumetric interfacial area in bubbly flow, some estimate of the average bubble size is necessary to permit access to the volumetric interfacial area (Delhaye, 1986). In bubbly flows with bubbles several millimeters in diameter and with high void fractions, Stravs and von Stocker (1985) were apparently the first, in 1981, to propose the use of pulsed, 1- to 10-MHz ultrasound for measuring interfacial area. Independently, Amblard et al. (1983) used the same technique but at frequencies lower than 1 MHz. The volumetric interfacial area, T, is defined by (Delhaye, 1986)... 

Collins and Knudsen (C6) recently reported drop-size distribution produced by two immiscible liquids in turbulent flow, and the average drop size can be calculated from these distributions. From a knowledge of the average drop size, the interfacial area per drop a and the drop volume can be calculated. The number of drops per unit volume is given by... 

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