Diffusional rate processes

The second main class of mass-transfer operations take place in packed towers or similar equipment and are usually handled using the concept of a diffusional process. When considering this class of processes, the assumption of staging can no longer be made and the material and 

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The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

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. 

Mass-transfer calculations, such as the analysis or design of separation units, can be solved by two distinctly different methods, based on either the concept of (1) Equilibrium stage processes or (2) Diffusional rate processes. 

As mentioned earlier, calculations of diffusional rate processes are difficult as they involve the solution of partial differential equations. Even for processes which are clearly diffusional controlled, such as absorption, chemical engineers normally simplify the calculations by assuming equilibrium stages and may instead correct for possible deviations by using efficiency factors afterwards. Most commercial process design software, such as HYSYS, AspenPlus and ChemCAD, make the assumption of staged equilibrium processes. 

For unsteady-state diffusion into a quiescent medium with no chemical reaction, the mass transfer Peclet number does not appear in the dimensionless mass transfer equation for species i because it is not appropriate to make variable time t dimensionless via division by L/ v) if there is no bulk fluid flow (i.e., (d) = 0). In this case, the first term on each side of equation (10-11) survives, which corresponds to the unsteady-state diffusion equation. However, the characteristic time for diffusion of species i over a length scale L, given by L /50i,mix. replaces L/ v) to make variable time t dimensionless. Now, the accumulation and diffusional rate processes scale as CAo i.mix/A, with dimensions of moles per volume per time. Since both surviving mass transfer rate processes exhibit the same dimensional scaling factor, there are no dimensionless numbers in the mass transfer equation which describes unsteady-state diffusion for species i in nonreactive systems. 

Catalytic reactions take place on the exposed surface of a catalyst. Consequently, a higher surface area available for the reaction yields a higher rate of reaction. It is therefore necessary to disperse an expensive catalyst on a support of small volume and high surface area. Use of such a supported catalyst in the form of a pellet is not without its adverse effects. Reactants have to diffuse through the pores of the support for the reaction to take place, and therefore, the actual rate can be limited by the rate at which the diffusing reactants reach the catalyst. This actual rate can be determined in terms of intrinsic kinetics and pertinent physical parameters of the diffusional rate process. 

If the bimolecular process is not diffusion-limited kq = pfci, where p is the efficiency of the reaction and ki is the diffusional rate constant. 

If the bimolecular process is diffusion-limited kq is identical to the diffusional rate constant ki, which can be written in the following simplified form (proposed for the first time by Smoluchowski) ... 

Because formation ofexcimer E is a diffusion-controlled process, Eqs (4.11)-(4.13) apply to the diffusional rate constant ki for excimer formation. Under the approximation that ki is time-independent, the d-pulse responses, under the initial conditions (at t = 0), [M ] = [M ]o and [E ]o = 0, are... 

The burning rate of propellants is one of the important parameters for rocket mo-tordesign. As described in Section 7.1.2, the burning rate of AP composite propellants is altered by changing the particle size of the AP used. The diffusional mixing process between the gaseous decomposition products of the AP particles and of the polymeric binder used as a fuel component determines the heat flux feedback from the gas phase to the condensed phase at the burning surface. - This process is a... 

Excitons in solids can move with velocities far beyond the diffusional rates in liquids at comparable temperatures. It should therefore never be assumed that photochemical processes can be neglected in the solid phase. 

The applicability of Maxwell s equation is limited in describing particle growth or depletion by mass transfer. Strictly speaking, mass transfer to a small droplet cannot be a steady process because the radius changes, causing a change in the transfer rate. However, when the difference between vapor concentration far from the droplet and at the droplet surface is small, the transport rate given by Maxwell s equation holds at any instant. That is, the diffusional transport process proceeds as a quasi-stationary process. 

Higuchi, W.I. Diffusional models useful in biopharmaceutics. Drug release rate processes. J. Pharm. Sci. 1967, 56, 315-324. 

Ionic transport through these perfluorinated ionomers is considered now to be essentially a diffusional process whenever no flow of current is imposed. This diffusion can be defined as a rate process with an average energy barrier for diffusion that must be exceeded before transport can occur. This approach is useful because this activation energy provides a convenient inde-cator of the minimum energy requirements for ion transport... 

The temperature at which the binding experiment is carried out is critical. A change in the temperature can affect the diffusional rates and equilibria of the chromatographic process itself or the rates and equilibria of the reaction between the ccm-plexing agents. However, in many reports a careful control of temperature has been... 

The rate at which such processes occur depends on a variety of factors. These include the diffusional rates of the relevant species in the respective phases, the rates of bulk reactions, and the rates of interfacial reactions, if any. Consider the following reaction, where we assume that the reaction takes place on the aqueous side ... 

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