Internal diffusion phenomena

As an example there can serve the internal diffusion phenomenon which cannot be observed in the direct laboratory experiment but can be observed and assessed quantitatively using the computer simulation methods. In the last few years the revolutionary progress in the field is connected with developing new algorithms and with striking increases in computing speed. 

Recent developments are pushing towards elucidating complex binding phenomenon between clustered carbohydrate epitopes and multivalent lectins. Ligand valency often results in aggregation, and the kinetic of the process may complicate the ITC measurements.86 For polymers presenting multiple carbohydrate epitopes, such as mucins, it has been proposed that the enhanced affinity observed for these interactions are due to internal diffusion of lectin molecules from epitope to epitope in these multivalent ligands before dissociation.87,88... 

Once adequate airflow rate, temperature, and moisture are defined to intensify the external exchange processes, drying operation usually becomes completely dependent on internal mass transfer rate. To calculate the effective diffusivity, Aff. one has to combine experimental results with Fick-type model. However, diffusion phenomenon has to be studied out the starting drying time (1 0). Hence, a starting accessibility is defined as the difference between the initial moistme content Wj and the value Wq calculated by extrapolating the diffusion model till f = 0. 

Additionally, in highly porous solids like zeolites and activated carbons there may be internal diffusion processes of the adsorbed molecules (admolecules). These can occur without external exchange of mass, i. e. at constant mass adsorbed, cp. Sects. 4, 5. An example for such a phenomenon is presented in Chap. 6, Fig. 6.29, [1.4, 1.7-1.9]. 

For FTS process, two main mesoscale phenomena can be summarized (1) the interaction between internal diffusion and external diffusion, which is determined by the texture properties of catalyst and flow type of reactor. Generally, the texture properties, such as the size and morphology of catalyst pellet, always influence the flow type of reactor. Therefore, those should be combined to discuss their effects on FTS reaction (Kim et al., 1989 Lee et al., 2004 Mikkola et al., 2007 Schneider and Mitschka, 1966). (2) The relationship between internal difiusion and the intrinsic properties of active site, which is influenced by texture properties and active phase of catalyst. As well known, texture properties and active phase of catalyst always influence each other, such as the catalyst with low-surface area is always difficult to form highly dispersed active metal particle. The above mesoscale phenomenon significantly affects on the deviation from the ASF distribution of FTS products. 

Peak diffuseness may be a result of the kinetics of the sorption-desorption process (i.e., slow mass transfer or exchange at sorbent surfaces). Peak diffusion in this case is usually nonsymmetric because the rates of sorption and desorption are not the same. Band spreading due to the final rate of mass exchange is closely related to the diffusion phenomenon. Physical adsorption, for all practical purposes, is instantaneous. The overall process of sorption, however, consists of several parts (a) the movement of sorbate molecules toward the sorbent surface, resulting fi om intergrain diffusion (outer diffusion), (b) movement of sorbate molecules to the inside of pores (i.e., internal diffusion of the sorbate molecules in the pores and surface diffusion in the pores), and (c) the sorption process in general. 

In the case of alloys having one constituent considerably more reactive to oxygen than the others, conditions of temperature, pressure and atmosphere may be selected in which the reactive element is preferentially oxidised. Price and Thomas used this technique to develop films of the oxides of beryllium, aluminium, etc. on silver-base alloys, and thereby to confer improved tarnish resistance on these alloys. If conditions are so selected that the inward diffusion of oxygen is faster than outward diffusion of the reactive element, the oxide will be formed as small dispersed particles beneath the surface of the alloy. The phenomenon is known as internal oxidation and is of quite common occurrence, usually in association with a continuous surface layer of oxides of the major constituents of the alloy. 

The internal energy balance equation for the fluid is based on the momentum balance equation. The assumption of local thermodynamic equilibrium will enable us to introduce the thermodynamic relationships linking intensive quantities in the state of equilibrium and to derive the internal energy balance equation on the basis of equilibrium partial quantities. By assuming that the diffusion is a slow phenomenon, 1" J/p pv2, the change of the total energy of all components per unit volume becomes... 

Like other FFF subtechniques, materials are retained in thermal FFF as a result of their field-induced concentration at one wall of the channel. In thermal FFF, that field is a temperature gradient. Several terms are used to express the movement of material in response to a temperature gradient, including thermal diffusion, thermodiffusion, thermophoresis, and the Soret effect. The term thermodiffusion is used here, as it has been adopted by the scientific committee for The International Symposium on Thermodiffusion, which is devoted to the scientific study of this phenomenon. 

Another phenomenon that may affect the critical moisture content is known as case-hardening. In this instance, the surface of the material is dried so rapidly that a layer of dry, non-porous material forms. This over-dried surface acts as a barrier to moisture diffusion, since diffusivity decreases with moisture concentration. This may occur in vacuum drying, which will be discussed later in the chapter. To reduce the risk of case-hardening, the relative humidity of the drying gas may be increased to assist in maintaining a higher surface EMC until the internal moisture has diffused to the surface. 

When an n-type semiconductor which is in contact with a metal ion-containing electrolyte is illuminated, then two equal partial currents occur under open-circuit conditions (Fig. 11.25a). The anodic photocurrent is due to O2 formation in H2O, whereas the cathodic partial current corresponds to the reduction of the metallic ions. Since the holes cannot diffuse very far, most of them collect at the illuminated interface. In the case of an n-type semiconductor, sufficient electrons are availabe everywhere, so that metal deposition should occur at illuminated as well as at dark surface sites (Fig. 11.25b), according to which conclusion, selective deposition would be impossible. Experimentally, however, selective metal deposition has been observed, e.g. at CdS at illuminated surfaces [130] and at Ti02 at the dark sites [131]. In the case of CdS, this phenomenon was interpreted as a downward shift of the energy bands at the illuminated surface which is more favorable to an electron transfer there [130]. The result obtained with Ti02 has been explained by strong internal and external recombination... 

The techniques of Cylindrical Internal Reflectance (CIR) and Diffuse Reflectance spectroscopies are described herein. The CIR phenomenon was employed in three different apparatus. Two different high pressure CIR cells were used to study reactions homogeneously catalyzed by [y-HW2(CO)10]-. Low temperature reactions of Mo and W complexes were studied using an ambient pressure CIR cell. The diffuse reflectance technique was employed to study powdered samples of Ru carbonyl complexes supported on A1203. 

If the phenomenon of internal convection flow is ignored, the effective diffusivity "apparent" effective diffusivity) increases along with external fluid flow, and even more so as the permeability coefficient grows larger. 

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