Principles of Mass Transfer

Individual adsorbent particles within a packed bed are surrounded by a boundary layer, which is looked upon as a stagnant liquid film of the fiuid phase. The thickness of the film depends on the fluid distribution in the bulk phase of the packed bed. Molecular transport toward the boundary layer of the particle by convection or diffusion is the first step (1) of the separation process. 

The second relevant step is diffusive transport of the solute molecule through the film layer, which is called film diffusion (2). Transport of the solute molecules toward the adsorption centers inside the pore system of the adsorbent particles is the third step of the adsorption process. This step can follow two different transport mechanisms, which can occur separately or parallel to each other pore diffusion (3a) and surface diffusion (3b). 

If mass transport occurs by surface diffusion (3b), a solute molecule is adsorbed and transported deeper into the pore system by movement along the pore surface. During the whole transport process, molecules are within the attraction forces of the adsorbent surface. Notably, the attractive forces between the surface and adsorbed molecules are often so strong (Ruthven, 1984) that, for many common adsorpt-adsorbent systems encountered in preparative chromatography, surface diffusion is not very relevant. 

Pore diffusion (3a) is driven by restricted Fickian diffusion of the solute molecules within the free pore volume. During the transport process, the solute molecules are outside the attraction forces of the adsorbent surface. 

Once a solute molecule reaches a free adsorption site on the surface, actual adsorption takes place (4). If the adsorption processes (1-4) are slow compared with the convective fluid flow through the packed bed, the eluted peaks show a non-symmetrical band broadening. Severe tailing can be observed, due to the slower movement of those solute molecules, which penetrate deeper into the pore system. 

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This section also includes a treatment of distillation-type separations from a rate-based point of view that utilizes principles of mass transfer and heat transfer. Section 14 also presents details of that subject as applied to absorption and stripping. 

In order to establish the conditions for thermodynamic feasibility of reactive mass exchange, it is necessary to invoke the basic principles of mass transfer with chemical reactions. Consider a lean phase j that contains a set Bj = z —... 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

This chapter will focus on three types of membrane extracorporeal devices, hemodialyzers, plasma filters for fractionating blood components, and artificial liver systems. These applications share the same physical principles of mass transfer by diffusion and convection across a microfiltration or ultrafiltration membrane (Figure 18.1). A considerable amount of research and development has been undertaken by membrane and modules manufacturers for producing more biocompatible and permeable membranes, while improving modules performance by optimizing their internal fluid mechanics and their geometry. 

The principles of mass transfer determine the rate at which the equilibrium is established, that is, the rate at which the solute is transferred into the solvent. 

In the following, the principles of mass-transfer separation processes will be outlined first. Details of mass-transfer calculations will be introduced next and examples will be given of both equilibrium-stage processes and diffusional rate processes. The chapter will then conclude with a detailed discussion of the two single most applied mass-transfer processes in the chemical industries, namely distillation and absorption. 

Figure 5.15 Principle of mass transfer model integration with a neural net (hybrid neural-regression model).

My objective in writing this book is to provide a means to teach undergraduate chemical engineering students the basic principles of mass transfer and to apply these principles, aided by modem computational tools, to the design of equipment used in separation processes. The idea for it was bom out of my experiences during the last 25 years teaching mass-transfer operations courses at the University of Puerto Rico. 

In Chapter 5 some of the principles of mass transfer were discussed and these are now applied to microbial fouling. When a clean surface comes into contact... 

The basic principles of mass transfer are discussed in detail in [1.95-1.97]. Thermal separation processes are actually mass transfer processes matter is transported between phases and across phase interfaces. Mass transfer is caused by differences in concentration within a phase and by disturbances of the phase equilibrium. The time taken to return to the phase equilibrium depends mainly on mass transfer, but also on heat transfer (heat is transported not only by convection and radiation at higher temperature, but also by mass). For the design of thermal separation processes, along with a knowledge of phase equilibria, it is also important to have a detailed understanding of how equilibrium is reached and the time required, taking into account restrictions in the mass transfer rate. 

Principles of Mass Transfer and 7. Principles of Unsteady-State and Convective Mass Transfer. 

Rummaging ihroogh the attic, I happened upon my old college textbooks. Much to my dismay, these treasured volumes, elucidating the principles of mass transfer, fluid flow, and differential calculus, seemed slightly incomprehensible and rather irrelevant. After 15 years of applying the fundamentals of chemical engineering in a dozen refineries, I still did not feel ready for that final exam in advanced thermodynamics. 

In order to establish the conations for thermodynmnic feasibility of reactive mass exchange, it is necessary to invoke the basic principles of mass transfer with chemical reactions. Consider a lean phase j that contains a set Bj = [B j z — I,..., NZy of reactive species (i.e., the set Bj contains NZj reactive species, each denoted by B j, where the index z assumes values from 1 to NZy). These species react with the transferable key solute. A, or ammig themselves via Qj independent chemical reactions which may be represented by... 

In section 4.3 the concept of the reactor configuration for multi-phase reactions is introduced. This concept has to do with the way the phases that have to be contacted in the reactor are arranged with respect to each other. The principles of mass transfer are treated in section 4.4. The remaining sections in Oiapter 4 deal with mass transfer rates in various reactor configurations. 

The principle of mass transfer followed by a chemical reaction in a larjge bulk would also apply for liquid/liquid and solid/liquid systems, for those situations where the resistance to mass transfer lies predominantly in the continuous reaction phase, e.g., in the case where a solid reactant dissolves into a solution where it is chemically converted. This is also conceivable in systems where the reaction phase is a gas. 

In order to illustrate the use of packed columns in absorption operations, it is necessary to refer to mass transfer theory. The initial part of this chapter has been devoted to a review of the fundamental principles of mass transfer that need to be understood to design absorption and stripping columns. 

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