Internal and External Transport Processes

The importance of internal diffusion can also be appreciated from a different point of view the fact that the internal diffusion plays a pivotal role in internal and external transport processes. For negligible concentration gradient in the pellet, Eq. 4.57 still holds. However, the value of r Da will be larger than that for diffusion-limited case for the same intrinsic rate since 17 is larger and therefore the pellet will be more isothermal as Figure 4.7 reveals. Further, a relativdy large Biot number for mass under realistic conditions still ensures negligible external mass transfer resistance. It is seen then that in the absence of diffusional resistance, the pellet tends to be more isothermal and the only major resistance is likely to be external heat transfer. 

Unfortunately, to the best of our knowledge, there is no appropriate published experimental data on a 3D spray drying process for the pilot-scale spray chamber used here. However, the developed model of internal and external transport phenomena can be validated by experimental values available for a closely similar drying process, for example, pneumatic drying. For this purpose, the presented model, with slight modifications, has been utilized to perform steady-state numerical simulations of 3D pneumatic... 

Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

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. 

Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well-known since the days of Thiele (1) and Frank-Kamenetskii (2). Transport phenomena coupled to chemical reactions is not frequently used for complex organic systems. A systematic approach to the problem is presented. 

Organized bi- and multilayers, composed of lipids, proteins, and other components, which constitute the internal and external cell walls. Biological membranes allow selective transport of materials into and out of cells and, thus, mediate numerous biochemical processes. 

The measured surface area consists of both external and internal area where internal surface area includes all cracks or connected pores that are deeper than they are wide, varying from subatomic defects to pores of extreme size (Gregg and Sing, 1982). For example, micropores are dehned as pores with radius <2 nm, mesopores as pores with radius from 2 nm to 50 nm, and macropores as those with pores of diameter >50 nm. The main distinction between internal and external surface is that advection can control transport to and away from external surface while diffusion must control transport for internal pore space (Hochella and Banheld, 1995). Porosity may be related to crystallization or replacement processes (Putnis, 2002). 

As with organic solvents, proteins are not soluble in most of the ionic Uquids when they are used as pure solvent (examples of the solubility of enzymes in ionic hquids can be found in S ection 8.4). As a result the enzyme is either applied as immobihzed enzyme coupled to a support or as a suspension in its native form. For production processes the majority of enzymes are used as immobilized catalysts in order to facilitate handling and to improve their operational stabihty [25-27]. As a support either inorganic materials, such as porous glass, or different organic polymers are used [28]. These heterogeneous catalyst particles are subject to internal and external mass transport limitations which are strongly influenced by the viscosity of the... 

For process modeling proposes the effective chemical reaction rate has to be expressed as a function of the liquid bulk composition x, the local temperature T, and the catalyst properties such as its number of active sites per catalyst volume c, its porosity e, and its tortuosity t. As discussed in Section 5.4.2, the chemical reaction in the catalyst particles can be influenced by internal and external mass transport processes. To separate the influence of these transport resistances from the intrinsic reaction kinetics, a catalyst effectiveness factor p is introduced by... 

Increasing values of Bi correspond to increasing internal diffusion resistance compared to the external mass transfer. For Bi — oo, the external mass transfer is fast and the reactant concentration on the outer catalyst surface is equal to the bulk-phase concentration the reaction is only influenced by internal transport processes. The influence of internal and external mass transfers on the overall efficiency (Eq. (11.2)) is shown in Figure 11.4 as an example. The catalyst efficiency decreases strongly at small mass Biot numbers. This is because of the reduced... 

Basically, there are four kinds of physical or chemical processes in nano continua, discontinua, and spaces of interactions (1) processes in the nanospace over surface, line, or point elements (2) processes in the nanospaces inside surface, hne, and point elements (3) barrier processes — mass and energy transfer processes, with or without physical and chemical transformations, through internal and external nanospaces (4) membrane processes — mass and energy transport processes through membranes (double gas, hquid, and sohd surface, hne and point elements). Membrane processes are presented in Figure 1.13. 

Transport phenomena often accompany processes conducted in reactors with a catalyst bed. Included are internal and external diffusion, and internal and external energy transfer. Chemical reactions taking place on the surface of non-porous catalyst grains usually meet a resistance in a form of an external mass or energy transfer, whereas the internal mass transfer and an external energy transfer most often accompany non-isodiermal processes in porous grains. 

The intrinsic catalytic cycle contains only the chemical steps 3-4-5 of the 7-step sequence listed in the so-called continuous reaction model. It is necessary to make the assumption of zero gradients with respect to heat and mass transport both outside and within the catalyst particle. Therefore, experimental conditions in the laboratory have to be adjusted to ensure that (i) external transport processes (steps 1 and 7 of the sequence) are very rapid compared to chemical steps and (ii) internal transport processes (steps 2 and 6 of the sequence) are negligible, that is, particle sizes are small enough to ignore pore structure. In Figure 2.3, the reactant concentration profile labeled as IV represents the case for intrinsic kinetics. 

The particle shape can generally be established by simple visual observation or by using a microscope. The transport characteristics of particulate solids are quite sensitive to the particle shape. Both the internal and external coefficient of friction can change substantially with variations in particle shape even if the major particle dimensions remain unchanged. Small differences in the pelletizing process can cause major problems in a downstream extrusion process. Variations in the ratio of regrind to virgin polymer can cause variations in the extrusion process. 

The fact that the Biot number of mass (a measure of the ratio of internal diffusion to external mass transfer resistance) is much larger than unity, implies that the major resistance lies in the internal diffusion process. A simple analysis can be made to assess the relative importance of internal and external mass transport processes now that the pellet can be considered isothermal. For an isothermal pellet, Eq. 4.32 can be written as ... 

The experiments were continued by Hoffman and Whittam, who concluded that a protein, an ATPase, in the membrane was necessary for active transport and was vectorially organized, with ATP and Na+ being required internally and K+ externally where ouabain was inhibitory. The ATPase was finally identified as the sodium pump by Skou (1957) it vectorially translocated Na+ and K+ across the membrane, and was phosphorylated transiently in the process. 

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