Mass transfer mutual

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

When the soHd substrate is placed in the bath, the air is displaced by the bath, fl, and the 37T interface is replaced by an SB interface. Similarly, an interface replaces the interface. The equiHbrium free energy values of these new interfaces are not estabHshed immediately but gradually through mass transfer (if there is any mutual solubiHty between F and fl it is assumed that B does not dissolve 3) and through adsorption of dissolved components. When these processes have gone to completion the new relationship is... 

The description of mass transfer requires a separation of the contributions of convection and mutual diffusion. While convection means macroscopic motion of complete volume elements, mutual diffusion denotes the macroscopically perceptible relative motion of the individual particles due to concentration gradients. Hence, when measuring mutual diffusion coefficients, one has to avoid convection in the system or, at least has to take it into consideration. 

In general, mass transfer processes involving polymer-penetrant mixtures are generally analyzed by using a mutual diffusion coefficient. Therefore, a relationship between the mutual diffusion coefficient, D, and self-diffusion coefficients, ZVs is needed. Vrentas et al. [30] proposed an equation relating D to D, for polymer-penetrant systems in which Dx is much larger than Dr. 

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. 

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. 

The previous chapters have demonstrated that liquid-liquid extraction is a mass transfer unit operation involving two liquid phases, the raffinate and the extract phase, which have very small mutual solubihty. Let us assume that the raffinate phase is wastewater from a coke plant polluted with phenol. To separate the phenol from the water, there must be close contact with the extract phase, toluene in this case. Water and toluene are not mutually soluble, but toluene is a better solvent for phenol and can extract it from water. Thus, toluene and phenol together are the extract phase. If the solvent reacts with the extracted substance during the extraction, the whole process is called reactive extraction. The reaction is usually used to alter the properties of inorganic cations and anions so they can be extracted from an aqueous solution into the nonpolar organic phase. The mechanisms for these reactions involve ion pah-formation, solvation of an ionic compound, or formation of covalent metal-extractant complexes (see Chapters 3 and 4). Often formation of these new species is a slow process and, in many cases, it is not possible to use columns for this type of extraction mixer-settlers are used instead (Chapter 8). 

It is generally agreed that mass transfer coefficients are only correlated for negligibly small convectional motion of the transitional component, which is vertical to the interface. However, when the mass transfer is mutual and equimolar, no such convections normal to the interface result otherwise the transfer coefficient and the driving force must be corrected with the aid of theories of mass transfer [18]. The transitional rates and, accordingly, convectional flow rates normal to the interface are only low for the extraction process, so that the uncorrected Eq. (9.31) may be used. 

What is the mechanism which results in rapid coalescence if mass transfer occurs from the drops but slow or no coalescence if both phases are mutually saturated Interfacial turbulence caused by local gradients in interfacial tension looks promising. 

Such reactions can take place predominantly in either the continuous or disperse phase or in both phases or mainly at the interface. Mutual solubilities, distribution coefficients, and the amount of interfadal surface are factors that determine the overall rate of conversion. Stirred tanks with power inputs of 5-10 HP/1000 gal or extraction-type equipment of various kinds are used to enhance mass transfer. Horizontal TFRs usually are impractical unless sufficiently stable emulsions can be formed, but mixing baffles at intervals are helpful if there are strong reasons for using such equipment. Multistage stirred chambers in a single shell are used for example in butene-isobutane alkylation with sulfuric acid catalyst. Other liquid-liquid processes listed in Table 17.1 are numbers 8, 27, 45, 78, and 90. 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

While the multiple steady-state phenomena may be, at least qualitatively, explained in terms of a simple one-step kinetic mechanism and interactions of the intraphase and interparticle heat and mass transfer (thermokinetic model), there is no acceptable explanation for the periodic activity (12). Since the values of the Lewis number are at least by a factor of 10 lower than those necessary to produce undamped oscillations, there is no doubt that the instability cannot be viewed in terms of mutual... 

Fundamentals of a method for developing models of mass transfer of low-molecular substances in non-reconstructing microheterogeneous membranes were formulated. The local properties of membranes differ in sorbability with respect to species and in the probability for a species to jump from one sorption site to another. Because of this, the permeability of a membrane depends on the amounts of different-type sites, their mutual arrangement, mutual influence of adjacent molecules, and the probabilities of jumps between different sites. The probabilities of occupation of different sorption sites are described by kinetic equations, which take into account the interactions between species. The atomic-molecular discrete and continuous models of mass transfer for thin and thick films are constructed. 

The aim of extraction is to promote mass transfer or extraction reaction between two phases (a mutually insoluble liquid-liquid system) by dispersing one liquid phase in another. In principle, creating a larger interface area in this operation is advantageous. However, it is necessary to consider that interface phenomena depend on the type of system. Extractors are classified into three types ... 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Helfferich [2,3,30] states that in addition to the mutual interference of substances i and j, characterized by the phenomenological cross coefficients of the type L,j, one should take into account the presence of a coion in the ion exchanger as well. As a result, the simplified solution is inappropriate, even to the problem of ordinary IE. By use of only one diffusion mass-transfer equation, as in this case, account for the presence of co-ion has been neglected. It is, as a consequence, necessary to consider the Nemst-Planck relation for the co-ion also. 

A final note concerns what effect the precipitous decline of mutual diffusion coefficients might have as the critical point is approached. We saw no effect in our experimental results which might be attributable to this decline. Its effect must be either, masked by other mechanisms, or, as Cussler has suggested (University of Minnesota, personal communication, 1988), it may simply result in a steep concentration gradient over a very small distance in most engineering experiments where, as is here the case, a relatively large temperature spread is used and the resulting increase in mass transfer resistance is small. 

As Saville and Churchill [3.51] showed, the results obtained with this method are only sufficiently accurate if the Schmidt and Prandtl numbers of the mixtures are the same. In any other case the mutual influence of the mass transfer and the flow field will not be sufficiently taken into account. 

Forced and free flow can, depending on the direction of the inertia and buoyancy forces, either mutually stimulate or dampen each other. In a forced flow overlapping a free flow, the heat and mass transfer can either be improved or inhibited. As an example of this we will look at a heated plate, Fig. 3.51. A free flow in the upwards direction develops, which can be strengthened Fig. 3.51a, or weakened, Fig. 3.51b, by a forced flow generated by a blower. Experiments have shown that the heat transfer coefficient can be calculated well by using equations of the form... 

Mass transfer in a porous structure strongly depends on macro-geometric parameters, but the electrochemical properties of the surface of the solid phase depend on the mutual relation of the active particles on it, being independent of the macrogeometry of the system. 

Yoshida, H. Kataoka, T. Intraparticle mass transfer in bidispersed porous ion exchanger, part II. Mutual ion exchange. Can. J. Chem. Eng. 1985, 62, 430. 

Several criteria must be considered in the selection of the diluent solvent. The first one is biocompatibility, that is, the solvent must not be toxic to the biodegrading microorganism [10]. The second criterion is the resistance to biodegradation and/or utilization by the active microorganism used, that is, so-caUed (non)bioavailability [8]. Third criterion is the favorable mass-transfer characteristics for the biodegraded pollutant [1], and the fourth criterion is the mutual immiscibility of the diluent with the treated waste-water [1]. The fifth criterion is the hmited volatility of the diluent [11]. 

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