Types of mass transfer

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

In this chapter we consider how to construct reactions paths that account for the effects of simple reactants, a name given to reactants that are added to or removed from a system at constant rates. We take on other types of mass transfer in later chapters. Chapter 14 treats the mass transfer implicit in setting a species activity or gas fugacity over a reaction path. In Chapter 16 we develop reaction models in which the rates of mineral precipitation and dissolution are governed by kinetic rate laws. 

Liss and Slater (1974) have, based on the value of HA, evaluated which type of mass transfer resistance exists. They propose the following criteria, valid for most systems (cf. Table 4.1) ... 

Most publications dealing with chromatographic reactors focus on theoretical issues of this very complex system. Models of different complexity were derived and used to predict the behavior of chromatographic reactors. Such models typically take into consideration different types of mass transfer, adsorption isotherms, flow profiles, and reactions. A general scheme of these models, not including the reaction, is presented in Fig. 4. There are also several review papers... 

Figure 1 shows several types of mass transfer or diffusion cells, which are of the simplest design for performing bulk liquid membrane (BLM) processes. Each of the devices is divided into two parts a common part containing the membrane liquid, M and a second part in which the donor solution F and acceptor solution R are separated by a solid impermeable barrier. The liquid, M contacts with the two other liquids and affects the transfer between them. All three liquids are stirred with an appropriate intensity avoiding mixing of the donor and acceptor solutions. For a liquid-ion exchange in a BLM system. Fig. 2 shows the transfer mechanism of cephalosporin anions, P , from donor (F) to acceptor (R) solution... 

Numerous types of equipment are available for gas-liquid, liquid-liquid, and solid-liquid mass transfer operations. However, at this point only few representative types are described, on a conceptual basis. Some schematic illustrations of three types of mass transfer equipment are shown in Figure 6.2. 

Figure 6.2 Types of mass transfer equipment (a) packed column, (b) packings, (c) bubble column, and (d) packed bed.

Another type of mass transfer equipment, shown in Figure 6.2d, is normally referred to as the packed- (fixed-) bed. Unlike the packed column for gas-liquid mass transfer, the packed-bed column is used for mass transfer between the surface of packed solid particles (e.g., catalyst particles or immobilized enzyme particles) and a single-phase liquid or gas. This type of equipment, which is widely used as reactors, adsorption columns, chromatography columns, and so on, is discussed in greater detail in Chapters 7 and 11. 

In most types of mass-transfer equipment, the interfacial area, a, that is effective for mass transfer cannot be determined accurately. For this reason, it is customary to report experimentally observed rates of transfer in terms of mass-transfer coefficients based on a unit volume of the apparatus, rather than on a unit of interfacial area. Calculation of the overall coefficients from the individual volumetric coefficients is made practically, for example, by means of the equations ... 

As mentioned previously, axial flow impellers are typically used for solids suspension. It is also typical to use radial flow impellers for gas-liquid mass transfer. In combination gas-liquid-solid systems, it is more common to use radial flow impellers because the desired power level for mass transfer normally accomplishes solids suspension as well. The less effective flow pattern of the axial flow impeller is not often used in high-uptake-rate systems for industrial mass transfer problems. There is one exception, and that is in the aeration of waste. The uptake rate in biological oxidation systems is on the order of 30 ppm/hr, which is about to the rate that may be required in industrial processes. In waste treatment, surface aerators typically use axial flow impellers, and there are many types of draft tube aerators that use axial flow impellers in a draft tube. The gas rates are such that the axial flow characteristic of the impeller can drive the gas to whatever depth is required and provide a very effective type of mass transfer unit. 

Mass transfer can result from several different phenomena. There is a mass transfer associated with convection in that mass is transported from one place to another in the flow system. This type of mass transfer occurs on a macroscopic level and is usually treated in the subject of fluid mechanics. When a mixture of gases or liquids is contained such that there exists a concentration gradient of one or more of the constituents across the system, there will be a mass transfer on a microscopic level as the result of diffusion from regions of high concentration to regions of low concentration. In this chapter we are primarily concerned with some of the simple relations which may be used to calculate mass diffusion and their relation to heat transfer. Nevertheless, one must remember that the general subject of mass transfer encompasses both mass diffusion on a molecular scale and the bulk mass transport, which may result from a convection process. 

Knudsen coefficient — The term relates to a particular type of mass transfer of gases through the pores of a specific porous medium. The gas transport characteristics depends on the ratio of the mean free path for the gas molecule, A, to the pore diameter, dpore, which is called the Knudsen number, Kn (Kn = -7 —). 

The design of most mass-transfer equipment requires evaluation of the number of theoretical stages or transfer units. Methods for carrying out these calculations for various types of mass-transfer operations are presented in many general chemical engineering books, such as those indicated in the Chemical Engineering Series list of books given at the front of this text. 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

The effects of mass transfer are different in the stationary and mobile phases. The resistance to mass transfer in the mobile phase varies with the reciprocals of mobile phase velocity and the diffusivity of the species. The resistance to mass transfer inside the stationary phase varies with the reciprocal of diffusivity and is proportional to the radius of the adsorbent granules attached to the chromatography plate, or the structural complexity of the internal pores in chromatographic paper. For both types of mass-transfer resistance, band stretching is proportional in each direction, as measured from the geometrical spot center, and increases in magnitude the greater the resistance. 

The different values ofkifl depending on the type of mass-transfer process (vaporization, chemical, or physical absorption) are due not only to variations of the liquid areas involved in mass transfer operation (JIO, P16), but also to variations in the local mass-transfer coefficients within these zones (B2, B3, P13), for example, those due to the effect of interfacial turbulence which may accompany chemical absorption (L15). 

Of course, other types of mass transfer coefficient are commonly encountered and can also be used to compute the height of packing required ... 

In Table 4.1 L and G refer to liquid and gas phases AP, Ap, AC and A Vare the differences in pressures, partial pressures, concentrations and voltages, respectively porous and dense refer to the type of the material and sieving, solubility-diffusion and Donnan are types of mass-transfer mechanism. 

The difference between the thermal behavior in predominantly distillative and predominantly absorptive processes is a consequence of the different types of mass transfer in each case. In the former, mass is transferred from the liquid phase to the vapor phase and vice versa at approximately the same molar rate. The net material transfer between the phases is therefore small and the ratio of liquid flow to vapor flow (L/V) in a column section is nearly constant. In absorption or stripping columns, there is a net mass transfer in one direction and the L/V ratio is not constant. 

Table 1 divides the field of agitation into five basic classifications, liquid-solid, liquid-gas, liquid-liquid, miscible liquids and fluid motion. This can be further divided into two parts—on the left are shown those applications which depend upon some type of uniformity as a criterion, while the processes on the right are typical of those that require some type of mass transfer or chemical reaction as a criterion. 

Three main types of mass transfer resistances are recognized film diffusion (which occnrs at the external surface of the adsorbent), intraparticle diffusion (which occnrs within the pores or amorphous structure of the adsorbent), and adsorption/desorption kinetics (which occnrs at the internal surface of the adsorbent). 

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