Enhancement factor with physical

Fig. 17 Enhancement factor with physical absorption of CO in aqueous solutions as a function of the activated carbon concentration in a stirred cell with O) = 1.33 s and d < 5 ym.

Thus, in Fig. 12, for 10% SO in the gas phase, the advent of fast reaction results in an asymptote somewhat higher than that for physical absorption. In the case of 3% SO, the enhancement factor initially increases relatively substantially, but nevertheless still reaches an asymptote which is much very less than expected if heat release were to be ignored. For instance at /m = 10, the enhancement factor with heat release due to reaction is about 2.3, whereas it would be 10 for isothermal pseudo first order reaction. 

The numerical solution of these equations is shown in Fig. 23-28. This is a plot of the enhancement fac tor E against the Hatta number, with several other parameters. The factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption with zero concentration of A in the liquid. The uppermost line on the upper right represents the pseudo-first-order reaction, for which E = P coth p. 

Figure 1.2 Modulus of the field enhancement factor versus the aspect ratio a = b and wavelengths X for SPM tips of different materials (a) gold, (b) platinum, (c) silver, (d) p-doped silicon, (e) tungsten. Reprinted with permission from J. Jersch, Applied Physics A, 66, 29 (1998). Copyright 1998, Springer-Verlag.

Sulfite Oxidation Method The sulfite oxidation method is a classical, but still useful, technique for measuring /cgfl (or [4]. The method is based on the air oxidation of an aqueous solution of sodium sulfite (Na SOg) to sodium sulfate (Na.,SO ) with a cupric ion (Cu " ") or cobaltous ion (Co ) catalyst. With appropriate concentrations of sodium sulfite (about 1 N) or cupric ions (>10 inolH ), the value of k for the rate of oxygen absorption into sulfite solution, which can be determined by chemical analysis, is practically equal to Zr, for the physical oxygen absorption into sulfate solution in other words, the enhancement factor E, as defined by Equation 6.20, is essentially equal to unity. 

Fermentation broths are suspensions of microbial cells in a culture media. Although we need not consider the enhancement factor E for respiration reactions (as noted above), the physical presence per se of microbial cells in the broth will affect the k a values in bubbling-type fermentors. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in (i) an unaerated stirred tank with a known free gas-liquid interfacial area (ii) a bubble column and (iii) an aerated stirred tank [6]. Data acquired with scheme (i) showed that the A l values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and k a values were decreased somewhat with increasing cell concentrations, because of smaller a due to increased bubble sizes. 

A convention used in most literature on ozone mass transfer and in the rest of this book is to define the mass transfer coefficient as the one that describes the mass transfer rate without reaction, and to use the enhancement factor E to describe the increase due to the chemical reaction. Furthermore, the simplification that the major resistance lies in the liquid phase is used throughout the rest of the book. This is also based on the assumption that the mass transfer rate describes physical absorption of ozone or oxygen, since the presence of a chemical reaction can change this. This means that KLa - kLa and the concentration gradient can be described by the difference between the concentration in equilibrium with the bulk gas phase cL and the bulk liquid concentration cL. So the mass transfer rate is defined as ... 

The mass-transfer coefficient with a reactive solvent can be represented by multiplying the purely physical mass-transfer coefficient by an enhancement factor E that depends on a parameter called the Hatta number (analogous to the Thiele modulus in porous catalyst particles). 

Recently, many methods in the synthesis of c-BN films were studied, which include physical vapor deposition [1,5-7] (PVD) and chemical vapor deposition [1,8,9] (CVD, such as PECVD, HFCVD, MW-ECR-CVD). Most experiments have indicated that the commercial application of c-BN films depends on enhancement and improvement in the stability and repeatability of preparation process. Generally, ion energy flow density or ion bombardment was attributed to the essential factor with the influence in the c-BN formation [1,10-13]. However, it is noted that the discrepancy between PVD and CVD maybe result from the difference in the substrate temperature (Ts , ). Unfortunately, the role which Tjub plays on the growth of cubic phase in PVD was seldom investigated systemically. 

Figure 15.2 Chemiluminescence emission intensity from both the glass and the silvered surface (Ag) (Top). Insert - photographs of the silvered and glass surfaces, with (insert - Bottom) and without (insert -Top) chemiluminescence material in the experimental sandwich.The enhancement factor was >20, i.e. intensity on Ag / intensity on glass. Experimental sample sandwich (Bottom). Reproduced from Applied Physics Letters 88 173104. (2006).

The mass exchange rate between two phases during the course of the chemical reaction is compared with that for purely physical absorption. The ratio of these two rates (eq. (4)), is known as the enhancement factor E for mass transfer on the liquid side during the occurrence of a chemical reaction ... 

In [556] an attempt was made to describe the increase of k a values with increasing disperse phase fraction (here octene the droplets being stabilized by adding the anionic tenside sodium-dodecyl-sulfate) by a film variable hold-up model , that takes into consideration the change in oil/water fraction in the G/L film and diffusion in the droplets. It succeeded in approximating the test data much better than the two-film model or Higby s penetration model. The measurements by authors and other publications consulted, showed, however, that the linear relationship between the enhancement factor m for physical absorption and the fraction ... 

Zlokarnik [623] made use of this possibility in his investigations. They consisted of measuring kia values by means of manometric method, see Section 4.3.1.2 and Fig. 4.2, at constant stirrer speed for a large number of aqueous solutions of inorganic salts and acids with different concentrations in the absorption of pure nitrogen. They were represented in the form of the enhancement factor m (qt physical absorption ... 

Fig. 4.16 Enhancement factor m for physical absorption for several water structure builders with different molar concentrations from [630],...

The effective interfacial areas for absorption with a chemical reaction [6] in packed columns are the same as those for physical absorption except that absorption is accompanied by rapid, second-order reactions. For absorption with a moderately fast first-order or pseudo first-order reaction, almost the entire interfacial area is effective, because the absorption rates are independent of kL as can be seen from Equation 6.24 for the enhancement factor for such cases. For a new system with an unknown reaction rate constant, an experimental determination of the enhancement factor by using an experimental absorber with a known interfacial area would serve as a guide. 

The enhancement factor involves an atomic physics calculation along the lines as described above for PNC transitions. Because only a nonvanishing effect is sought, the demands on the accuracy of the calculation axe not as stringent, with really only the correct order of magnitude needed. This would of course change were a nonvanishing result to be found, but at present only bounds have been set. The bound from cesium is [65]... 

The enhancement factor, .,y is obtained by dividing eq. (9.79) with the expression for physical absorption... 

The heterogeneous process can be seen as a combination of physical absorption with chemical reaction. The reaction zone can penetrate in the liquid phase, if the reaction is relatively slow, or takes place only at the interface, if the reaction rate is infinite. The chemical reaction can accelerate considerably the pure physical process. The ratio of actual process rate by the physical process rate is known as enhancement factor E. In the case of a bimolecular reaction the enhancement factor can be expressed as function... 

For intermediate reaction rates the use of the enhancement factor is not consistent with the standard approach of diffusional limitations in reactor design and may be somewhat confusing. Furthermore, there are cases where there simply is no purely physical mass transfer process to refer to. For example, the chlorination of decane, which is dealt with in the coming Sec. 6.3.f on complex reactions or the oxidation of o-xylene in the liquid phase. Since those processes do not involve a diluent there is no corresponding mass transfer process to be referred to. This contrasts with gas-absorption processes like COj-absorption in aqueous alkaline solutions for which a comparison with C02-absorption in water is possible. The utilization factor approach for pseudo-first-order reactions leads to = tfikC i and, for these cases, refers to known concentrations C., and C . For very fast reactions, however, the utilization factor approach is less convenient, since the reaction rate coefficient frequently is not accurately known. The enhancement factor is based on the readily determined and in this case there is no problem with the driving force, since Cm = 0- Note also that both factors and Fji are closely related. Indeed, from Eqs. 6.3.C-5 and 6.3.C-10 for instantaneous reactions ... 

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