Mass transport processes stationary phase

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

If the rate constants for the sorption-desorption processes are small equilibrium between phases need not be achieved instantaneously. This effect is often called resistance-to-mass transfer, and thus transport of solute from one phase to another can be assumed diffusional in nature. As the solute migrates through the column it is sorbed from the mobile phase into the stationary phase. Flow is through the void volume of the solid particles with the result that the solute molecules diffuse through the interstices to reach surface of stationary phase. Likewise, the solute has to diffuse from the interior of the stationary phase to get back into the mobile phase. 

We have already dealt with stationary phase processes and have noted that they can be treated with some success by either macroscopic (bulk transport) or microscopic (molecular-statistical) models. For the mobile phase, the molecular-statistical model has little competition from bulk transport theory. This is because of the difficulty in formulating mass transport in complex pore space with erratic flow. (One treatment based on bulk transport has been developed but not yet worked out in detail for realistic models of packed beds [11,12].) Recent progress in this area has been summarized by Weber and Carr [13]. 

In a chromatographic separation, a mixture of substances is transported by a carrier, the mobile phase, over a surface, the stationary phase. Between the two phases mass transfer processes take place, which lead to different transport velocities along the surface of the stationary phase for different components of the mixture. The components reach the end of the stationary phase at different times and can be detected and collected separately. 

Process models for RD have to take into account both the chemical and the physical side of the process. Two basic types of model are used stage models, which are based on the idea of the equilibrium stage with phase equilibrium between the outlet streams, and rate-based models, which explicitly take into account heat and mass transfer. Similarly to the physical side of RD, the chemical reaction is either modeled using the assumption of chemical equilibrium or reaction kinetics are taken into account. Note that a kinetic model, either for physical transport processes or for chemical reactions, always includes an equilibrium model. The equilibrium model is the stationary solution of the kinetic model, for which all derivatives with respect to time become zero. Hence, whatever model type is used, it has to be based on a sound knowledge of the chemical and phase equilibrium, which is supplied by thermodynamic methods. Starting from there, kinetic effects can be included. 

In Eq. (1), Ja is the diffusive flux of species A (mass or moles per unit area per unit time), a vector quantity Dab is the binary or mutual diffusion tensor describing the diffusion of A in a mixture of A and B and Vc a is the spatial concentration gradient of A. If diffusion is isotropic, then it may be characterized by a scalar value Z ah- Pick s law is a phenomenological description of diffusion on a macroscopic scale. It is useful in the design and analysis of processes like chromatography that involve nonequilibrium mass transport, as mathematical models of chromatography concern themselves with how fast a solute penetrates into the stationary phase, i.e., the flux. 

The effect of mass transfer is most readily understood if one considers the process occurring in a chromatographic column for a single component. Following injection, part of the sample passes into the stationary phase and the other part remains in the gas phase. If the flow rate of the carrier gas becomes zero, an equilibrium partition between the two phases is-reached. As the flow rate is constant throughout the experiment, the stream of carrier gas transports the component from the gas phase to the next section of the column where it is retained by the stationary phase. The component freed from the stationary phase continues to travel downstream. During their flow through the column the molecules in gas phase do not encounter the stationary phase in the identical cross section of the column. Thus, the flow continuously shifts the molecules while the mass transfer tends to reach an equilibrium. As a result, at each point of a component band, a non-equilibrium state is established flow tends, to spread the band while the fast mass transfer tends to make it narrower. 

Vapor pressure osmometry [34—36] constitutes a very helpful nonequilibrium method for obtaining thermodynamic information for solutions of oligomers and polymers of low molar mass, for which osmometry and light scattering experiments do no longer yield reUable data. Such experiments are based on the establishment of stationary states for the transport of solvent via the gas phase from a drop of pure solvent fixed on one thermistor to the drop of oligomer solution positioned on another thermistor. Because of the heats of vaporization and of condensation, respectively, this transport process causes a time-independent temperature difference from which the required information is available after calibrating the equipment. 

A pyrite decomposition process is an instationary process since the solid phase reactant is being consumed under pyrite-oxidizing conditions causing changes in both reactive surface and mineral mass. Only in a fictitious system, in which the velocity of the depyritization front penetration by chance equals the surface erosion stationary conditions may be found. Diffusion under instationary conditions may be described by numerical solutions of the transport reaction equation considering Picks second law. Reactions can be integrated quite simply, if transport and reaction are decoupled in a... 

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