The different types of mass transfer

Mass transfer is the transport of one or more components of a mixture, of fluid or solid material, within a phase12 or over the phase boundary. Mass transport within a phase up to the phase boundary is called mass transfer. When this occurs over the phase boundary into another phase, it is then known as overall mass transfer. These terms correspond to those in heat transfer. 

The driving forces for mass transfer are concentration, temperature or pressure gradients. We will explore the most common of these three, namely mass transfer due to a concentration gradient. As experience tells us, the components of a mixture move from regions of higher concentration to those with lower concentration. Equilibrium with respect to mass transfer is realised when the driving force, in this case the concentration difference, has disappeared. 

As a simple example of mass transfer we will consider a glass filled with water in a room of dry air. Immediately above the liquid surface there is a large amount of water vapour, whilst further away there is far less. As a result of this concentration drop the air enriches itself with water vapour. This flows in the direction of the concentration or partial pressure drop. In a volume element above the surface of the water, the velocity of the water molecules perpendicular to the liquid surface 

12The phase is understood here to be the area of the system, in which each volume element has values for the thermodynamic variables of pressure, temperature and concentration, among others. Only steady, rather than irregular changes in these quantities are permitted within a phase. In thermodynamics a phase is a homogeneous region in a system. In a phase in the sense of thermodynamics all the defined intensive variables of state are spatially constant. 

In order to understand mass transfer due to molecular diffusion we will study the process in a vessel filled with a coloured solution, for example iodine solution. Water is carefully poured over the iodine solution, to avoid as far as possible convection currents. The coloured solution and the water are noticeably separate at the beginning of the experiment. After some time the upper layer becomes coloured, while the layer beneath it is clear enough to see through. Eventually, after long enough time has passed, the solution is the same colour throughout. So quite obviously despite there being no convection currents iodine molecules were transported from the lower to the upper part of the vessel. This can be explained by the diffusion of iodine molecules in water. 

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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. 

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... 

In general a mass spectrometer consists of an ion source, a mass-selective analyzer, and an ion detector. Since mass spectrometers create and manipulate gas-phase ions, they operate in a high vacuum system. The magnetic-sector, quadrupole, and time-of-flight designs also require extraction and acceleration ion optics to transfer ions from the source region into the mass analyzer. Tables 2 and 3 provide brief descriptions of the most commonly used ionization techniques and the different types of mass spectrometers available, respectively [163,232-235,241,242,244-246]. 

Various mathematical concepts and techniques have been used to derive the functions that describe the different types of dispersion and to simplify further development of the rate theory two of these procedures will be discussed in some detail. The two processes are, firstly, the Random Walk Concept [1] which was introduced to the rate theory by Giddings [2] and, secondly, the mathematics of diffusion which is both critical in the study of dispersion due to longitudinal diffusion and that due to solute mass transfer between the two phases. The random walk model allows the relatively simple derivation of the variance contributions from two of the dispersion processes that occur in the column and, so, this model will be the first to be discussed. 

For future studies on MOF-based slurry systems, there is basic selection of criteria that needs to be satisfied by both MOF and the liquid solution. The selection of the MOF possessing the appropriate pore size for the preparation of the slurry system is very important to guarantee that the size of the liquid is large enough and does not occupy the pores which leaves no space for C02 to adsorb. Moreover, the structural stability of the MOF in the aqueous solution is essential so that it does not lose its porous framework nor its surface area. The selection of the liquid candidate is crucial, as it should not provide any extra mass transfer resistance for C02 molecules. Further, experimental and computational investigations are still required to understand the separation mechanism in slurry mixtures and to have insight into the different types of interactions between the gas, liquid, and solid materials. 

This chapter describes the different types of batch and continuous bioreactors. The basic reactor concepts are described as well as the respective basic bioreactors design equations. The comparison of enzyme reactors is performed taking into account the enzyme kinetics. The modelhng and design of real reactors is discussed based on the several factors which influence their performance the immobilized biocatalyst kinetics, the external and internal mass transfer effects, the axial dispersion effects, and the operational stabihty of the immobilized biocatalyst. 

Mass spectrometers are used not only to detect the masses of proteins and peptides, but also to identify the proteins, to compare patterns of proteins and peptides, and to scan tissue sections for specific masses. MS is able to do this by giving the mass-to-charge ratio of an ionized species as well as its relative abundance. For biological sample analysis, mass spectrometers are connected to an ionizing source, which is usually matrix-assisted laser desorption ionization (MALDI) [14], surface-enhanced laser desorption/ioni-zation (SELDI, a modified form of MALDI) [15], or electrospray ionization [16]. These interfaces enable the transfer of the peptides or proteins from the solid or liquid phase, respectively, to the gas (vacuum) phase inside the mass spectrometer. Both MALDI and electrospray ionization can be connected to different types of mass analyzers, such as quadrupole, quadruple-ion-traps, time of flight (TOF), or hybrid instruments such as quadrupole-TOF or Fourier transform-ion cyclotron resonance. Each of these instruments can... 

In order to denote singular points, a clear terminology is needed. The well-known term a-zeo-trope should only be used for phase equilibrium-controlled singular points, whilst the newer term, a-rheo-trope, is proposed for mass transfer-controlled processes. Translated, the latter term means that the composition is not changing with flux . The different types of azeotropes and arheotropes, together with the names of those investigators who were the first to deal with these singular points, are summarized in Tab. 4.4. 

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. 

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). 

From a macroscopic standpoint molecular diffusion is mass transfer due to a concentration difference. Other types of diffusion, namely diffusion due to pressure differences (pressure diffusion) or temperature differences (thermal diffusion) will not be discussed here. The mechanism of molecular diffusion corresponds to that of heat conduction, whilst mass transfer in a flowing fluid, known for short as convective mass transfer corresponds to convective mass transfer. Mass transfer by diffusion and convection are the only sorts of mass transfer. Radiative heat transfer has no corresponding mass transfer process. 

The mass transfer coefficient (3C with SI units of m/s or m3/(sm2) is defined using these equations. It is a measure of the volumetric flow transferred per area. The concentration difference Aca defines the mass transfer coefficient. A useful choice of the decisive concentration difference for mass transfer has to be made. A good example of this is for mass transfer in a liquid film, see Fig. 1.41 where the concentration difference cA0 — cM between the wall and the surface of the film would be a a suitable choice. The mass transfer coefficient is generally dependent on the type of flow, whether it is laminar or turbulent, the physical properties of the material, the geometry of the system and also fairly often the concentration difference Aca. When a fluid flows over a quiescent surface, with which a substance will be exchanged, a thin layer develops close to the surface. In this layer the flow velocity is small and drops to zero at the surface. Therefore close to the surface the convective part of mass transfer is very low and the diffusive part, which is often decisive in mass transfer, dominates. 

Our main concern here is to present the mass transfer enhancement in several rate-controlled separation processes and how they are affected by the flow instabilities. These processes include membrane processes of reverse osmosis, ultra/microfiltration, gas permeation, and chromatography. In the following section, the different types of flow instabilities are classified and discussed. The axial dispersion in curved tubes is also discussed to understand the dispersion in the biological systems and radial mass transport in the chromatographic columns. Several experimental and theoretical studies have been reported on dispersion of solute in curved and coiled tubes under various laminar Newtonian and non-Newtonian flow conditions. The prior literature on dispersion in the laminar flow of Newtonian and non-Newtonian fluids through... 

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. 

Figure 3. Diagram of the transfer of air masses for the different types of pollution sources.

The water adsorbed on the carbon will also influence adsorption kinetics. Various authors [137,138] have demonstrated this. In contradiction to the capacity which can be influenced positively or negatively (see section 6.5.1), mass transfer will always slow down. The overall mass transfer coefficient, of the Wheeler-Jonas equation does not differentiate between the different types of diffusion. Consequently, every impact of water on the adsorption kinetics win be translated into a drop of k, values. 

Figure 2 indicates the different types of emulsions. Simple emulsions are labeled as oil-in-water (0/W) when they exhibit oil drops dispersed in an aqueous phase, or water-in-oil (W/O) if the opposite occurs, while multiple or double emulsions are symbolized either by W,/0/Wi or Oi/W/O . Wi (respectively 0 ) and W2 (respectively O2) indicate the most internal phase and the most external one. Note that phases with subscript I and 2 may be identical or different. If they are not the same a likely difference in chemical potential may drive a mass transfer process, a phenomenon that is advantageously harnessed for controlled-release applications. Bieniulsions are emulsions containing two different internal phase droplets, either of the same nature (but different size) or of different nature (whatever the size). The first kind of biemulsion is used to control some property, as, for example, emulsion viscosity, whereas the second may be used to produce controlled chemical reaction or mass transfer between the two internal phases. 

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