Diffusion through immobile region

To quantify such transport, the advection-dispersion equation, which requires a narrow pore-size distribution, often is used in a modified framework. Van Genuchten and Wierenga (1976) discuss a conceptualization of preferential solute transport throngh mobile and immobile regions. In this framework, contaminants advance mostly through macropores containing mobile water and diffuse into and out of relatively immobile water resident in micropores. The mobile-immobile model involves two coupled equations (in one-dimensional form) ... 

Physical immobilization methods do not involve covalent bond formation with the enzyme, so that the native composition of the enzyme remains unaltered. Physical immobilization methods are subclassified as adsorption, entrapment, and encapsulation methods. Adsorption of proteins to the surface of a carrier is, in principle, reversible, but careful selection of the carrier material and the immobilization conditions can render desorption negligible. Entrapment of enzymes in a cross-linked polymer is accomplished by carrying out the polymerization reaction in the presence of enzyme the enzyme becomes trapped in interstitial spaces in the polymer matrix. Encapsulation of enzymes results in regions of high enzyme concentration being separated from the bulk solvent system by a semipermeable membrane, through which substrate, but not enzyme, may diffuse. Physical immobilization methods are represented in Figure 4.1 (c-e). 

Diffusion through the immobile region is described as slow mass transfer between mobile and immobile water. The solute concentrations in the two regions are related by ... 

The lower W/Al ratio observed in the region closer to the surface seems to indicate that the outermost surface it less enriched in W. The results suggest that the metal complex diffuses through the AlTUD-1 and their immobilization sites are preferentially in the microporous region of the AlTUD-1 in agreement with N2 adsorption. 

Consider two compartments, occupying the regions — 1 < x < 0 and 0 < x < 1, respectively, filled with solutions of the same univalent electrolyte at concentrations 1 and A, respectively. Let at some moment t — 0 the wall separating the compartments at x = 0 be removed. The solution within the compartments is assumed immobilized, say, with gelatin, so that the entire transport is due to electro-diffusion only. The initial values of the electrolyte concentration are maintained at the external walls x = 1. These walls are electrically insulated so that no electric current can pass through them. 

The charge was introduced through oxidation of the excited polypyridyl complexes by an irreversible oxidant, 4-methoxybenzenediazonium tetrafluoroborate in acetonitrile solvent. Remarkably, the Ru excited states in the mixed-valent polymer were found not to be quenched by Ru or Os. This was attributed to the fact that these electron transfer reactions lie in the inverted region. This behavior differs from that found in homogeneous aqueous solution where excited state quenching is near diffusion controlled. Possibly the relative immobilization of the reactants on the polymer, along with the smaller value for Aout in acetonitrile, prevents their reaction at the separations and orientations at which electron transfer occurs in homogeneous solution. 

Most of the above problems can be overcome by using immobilized enzymes in other words, enzymes which are confined in a well-defined region of space by means of a selective membrane, or immobilized by, for example, absorption or entrapment within the polymeric matrix of a membrane. Enzymes are prohibited, due to their molecular size, from diffusing out or permeating through the membrane, while substrates and products can readily permeate the membrane. The enzymes retain their catalytic properties and can be repeatedly and continuously used. Traditional immobilization techniques are summarized in Rg. 1.1. They include adsorption on a surface, covalent binding to an insoluble support, co-polymerization with a proteic carrier, encapsulation in a membrane shell and confinement in a gel. A comparison between some different techniques is also reported in Table 1.2. Hollow fibre membranes are commonly used for membrane reactors... 

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