Mass transfer relationship experimental data

The first quantitative representation of the mass transfer relationship came from Cooper, Fernstrom and Miller in 1944 [84]. They worked with a vaned disk with 16 radial vanes in three different sizes (scale 1 3) in 1 N sodium sulfite solution and formulated the kia value with the oxygen partial pressure as Ky [kmol 02/m h at], since the oxygen solubility in the sulfite solution was then unknown. The result for this stirrer in a completely coalescence-inhibited material system was  

For the German reader it is interesting to know, that the authors made the decision in favor of a volume-related stirrer power P/V with reference to the paper of Buche [61]  

Van t Riet [560] already in 1979 could evaluate and compare 76 publications in which the turbine stirrer had been utilized as gas disperser. He derived the following dimensionally formulated mass transfer relationships  

The work of Robinson and Wilke [469] was probably the first one which quantitatively investigated the effect of salts on gassing of liquids. The ionic strength was established as an influence quantity, which was calculated as follows I = 0.5 52 2 Wi [g-ion/1] all ions have therefore to be taken into consideration, (zj is the charge number of an ion i and m is its molality.) 

Examples of the calculation of the factor k, with which the salt concentration in g/mol must be multiplied to determine the ionic strength in g-ion/L, are  

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For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Using the model equations described above and from the experimental data yielding Fig. 7.13, the calculated data are given in Fig. 7.18 as the plot of kG versus nn. By regression, the experimental data are fitted to represent the relationship between gas-film mass transfer coefficient and impinging velocity by... 

Packed height is determined from the relationships in Section III. Application of these relationships requires knowledge of the liquid and gas mass transfer coefficients. It is best to obtain these from experimental data on the system if available, but caution is required when extending such data to column design, because mass transfer coefficients depend on packing geometry, liquid and gas distribution, physical properties, and gas and liquid loads, and these may vary from one contactor to another. 

Effective Area. - The catalyst consists of active metal dispersed on a substrate material. Therefore, there is a difference between the effective area used in mass transfer calculations of chemical reaction and the effective area used in heat transfer culculations which corresponds to the monolith surface area including surface roughness. The ratio of both effective areas must be defined based on experimental results, as they depend on catalyst type and manufacturing processes. The Thiele number is sometimes used for this same purpose. The relationship between effective area ratio and conversion efficiency is shown in Figure 3. This effective area ratio may be one of the characteristic values of the catalyst, which affects catalyst performance and catalyst temperature. The effective area ratio in the present study is estimated to be 0.3 for mass transfer and 1 for heat transfer based on the experimental data. 

Equations (1,2) constitute a powerful tool for the analysis of the mass transfer process. Indeed, if a reliable equilibrium relationship is available for the ion exchange reaction and the mass transfer coefficients are known, then it is possible to evaluate the mass transfer rate for given compositions of the liquid and solid phases. On the other hand, experimental data relative to the mass transfer rate can be used to evaluate unknown mass transfer coefficients. 

Numerous workers (B16, F2, F4, H17, J4, K4, K7, L8, M2, S5, and others) estimated the external heat-transfer coefficient in the continuous phase by assuming a velocity profile in the boundary layer and ambient fluid. Except for very low Reynolds numbers, the exact boundary layer solutions only apply to the front part of the drop, up to the separation point. Fortunately, simple assumptions sometimes suffice for extending the derivation to the entire drop, and the relationships obtained are in agreement with experimental data. The limitations of the analytical solutions, as well as their application to nonspherical drops, is concisely demonstrated in Lochiel and Calderbank s (LI8) recent study on mass transfer around axisymmetric bodies of revolutions. 

Calculation of the density of deposited layers of sublimate, and of associated variables, as an aid towards the optimization of sublimate condenser design, is discussed by Wintermantel, Holzknecht and Thoma (1987). The starting point of the analysis is the assumption that the growth of sublimate layers is governed mainly by heat and mass transfer the model is based on conditions in the diffusion boundary layer. The main process-determining factors (growth rate, mass transfer, and gas concentration) are accounted for. The derived theoretical relationship is shown to fit experimental data. 

Gas- and liquid-side mass transfer coefficients in packed absotptkm columns exhibit comfdex dependencies on the gas and liquid rates and the column packing, transfer area will bis a function of the hydrodynamics and packing. Correlations on experimental data, are usually devdoped in terms of the height of a transfisr and lk uid heights of transfer units are tinned 1 die relationships. with countercurrent flows In addition, the interfigial for such situations, based unit (HTU) concqit Gas... 

One approach to deriving correlations for mass transfer coefficients in process systems is to generate experimental data in momentum transport studies. In this approach, it is assumed that both molecular and eddy diffusions play a role in the intermediate region. Then at any distance y from the wall, the rate of mass transfer can be expressed as a function of both the molecular and eddy diffusivities. However, applications of these models rely on a knowledge of the eddy diffusivity, Ed, as a function of y, a relationship that is usually inferred from the experimental data [7-10]. There the eddy diffusivity can be inferred from the eddy viscosity by similarity arguments. A substantial amount of published works is along this line [11-13]. 

Average transport coefficients for transfer between the bulk-fluid and particle surface can be correlated in terms of dimensionless groups that characterize the flow conditions. It is common practice to correlate experimental data in terms of y -factors. Usually, the mass transfer coefficient is obtained from the j factor for mass the heat transfer coefficient is obtained from j factor analogy. There have been many experimental studies of mass transfer in fixed-beds and summaries and analyses of the results are available (Whitaker 1972 Dwivedi and Upadhay 1977). For Reynolds numbers greater than 10, the following relationship (Dwivedi and Upadhay 1977) between jo and the Reynolds number represents available data ... 

To find the exact value of the exponent n in Eq. (9), three different effects have to be considered the influence of the parameter B related to the unsteady nature of the process the already discussed relationship between n and the circulation intensity and the possible response to B regarding the wide range of gas-liquid mass transfer resistance ratio values (0 < J < qo) which are employed in practice. The first of these effects could be analyzed by the vast experimental data obtained [3] as well as by the detailed studies on methanol-water system. As mentioned above it has been shown [16] that the Marangoni number varies only due to variations of B, at constant concmitration, mean saturation and achievement of the second critical level of mass transfer... 

Nevertheless, there remain considerable deviations between the composite pressure dec indicated by experimental data and that predicted according to their models. Moreover, neither of these contributions proposes a direct relationship between pressure gradient and a mass transfer coefficient of the volatile gas mixture out of the laminate and towards the heat / (ignition) source (s), i.e. there is no model for the physical mechanism of gas transport of a sort proposed by Staggs, [8]. Equation 14.18 is rather primarily focused on directly relating solid resin mass loss, and hence material failure, to overpressure, based on the assumption of an accumulating volatile phase, which neglects volatile escape from the structure. 

We do not intend in this chapter to present an extensive analysis of mass transfer concepts but, rather, to summarize the basics of mass transfer as required in the design and analysis of polymer processing operations. In this regard, we give only an extensive overview of the estimation techniques for the diffusivity, solubility, and permeability of solvents in polymers. The laws of diffusional mass transfer, as well as the relationships for convective mass transfer, remain the same as applied to any material. The books by Perry and Chilton (1973), Reid et al. (1977), and Brandmp and Immergut (1989) provide an extensive overview of experimental data and formulas for the calculation of diffusivity, solubility, and permeability of various polymer systems. 

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