Membrane processes series resistances

In fine wool such as that obtained from merino sheep, the cuticle is normally one cell thick (20 x 30 x 0.5 mm, approximate dimensions) and usually constitutes about 10% by weight of the total fiber. Sections of cuticle cells show an internal series of laminations (Figs. 1 and 2) comprising outer sulfur-rich bands known as the exocuticle and inner regions of lower sulfur content called the endocuticle (13). On the exposed surface of cuticle cells, a membrane-like proteinaceous band (epicuticle) and a unique hpid component form a hydrophobic resistant barrier (14). These hpid and protein components are the functional moieties of the fiber surface and are important in fiber protection and textile processing (15). 

The coupled processes described by Eqs. (8), (14), (17), and (22) can be added in (20) as parallel solute transport pathways across the membrane. The phenomenological coefficients (Ly) describe the membrane permeability by these pathways [potential-dependent, Eq. (8) via membrane lipid partition and diffusion, Eq. (14) carrier-mediated, Eq. (17) and convectively coupled, Eq. (22)]. These pathways define parallel resistances through the intestinal barrier in series with precellular resistances to solute transport. 

The first, and currently only, successful solvent-permeable hyperfiltration membrane is the Starmem series of solvent-resistant membranes developed by W.R. Grace [40]. These are asymmetric polyimide phase-inversion membranes prepared from Matrimid (Ciba-Geigy) and related materials. The Matrimid polyimide structure is extremely rigid with a Tg of 305 °C and the polymer remains glassy and unswollen even in aggressive solvents. These membranes found their first large-scale commercial use in Mobil Oil s processes to separate lube oil from methyl ethyl ketone-toluene solvent mixtures [41-43], Scarpello et al. [44] have also achieved rejections of >99 % when using these membranes to separate dissolved phase transfer catalysts (MW 600) from tetrahydrofuran and ethyl acetate solutions. 

Table 3.1 illustrates that the separation between the different processes is not precise, as the processes overlap. Therefore, filtration and separation models are generally applicable to mote than one process. Often several phenomena are operative simultaneously and which one dominates depends on the membrane and the solute or particle in question. Concepts such as the resistance-in-series model, the osmotic pressure model or concentration polarisation are principles which are applicable to any membrane operation. These wiU be described in the MF section. 

To reach the systemic circulation, a drug must move from the intestinal lumen through an unstirred water layer and mucous coat adjacent to the epithelial cell structure. Movement across the epithelial layers takes place by two independent routes, transcellular flux (i.e., movement across the cells) and paracellular flux or movement between adjacent epithelial cells. The solute molecules then encounter a basement membrane, interstitial space, and mesenteric capillary wall to access the mesenteric circulation. Any and all of these microenvironments can be considered a resistance to solute molecule movement, each with an associated permeability coefficient. Therefore, the overall process consists of a number of resistances (i.e., reciprocal of permeability) in series. Furthermore, the influence of drug structure with permeability in these different domains may be different. For example, permeability in an unstirred water layer is inversely related to solute size, whereas paracellular permeability Is a function of both size and charge. Furthermore, cations exhibit greater permeability than neutral species, which in turn manifest greater permeability than anions. 

This concept of resistances in series can be applied to various processes (see also chapter V6.2 and VI.4.4.1) and the approach is to determine the mass transfer coefficients by means of the semi-empirical relationships given in table VII. 1 (see also ref. [ 1 ]). When the resistances in the boundary layers are small compared to that of the membrane resistance the permeation rate is given by eq. VII - 49. 

The phenomenon of fouling is very complex and difficult to describe theoretically. Even for a given solution, fouling will depend on physical and chemical parameters such as concentration, temperature, pH, ionic strength and specific interactions (hydrogen bonding, dipole-dipole interactions). However, reliable values of flux decline are necessary for process design. The flux may also be described by a resistances-in-series model, in which a resistance of a cake layer is in series with the membrane resistance. The flux can be described by... 

As can be observed, two semicircles were obtained for dense membrane/NaCl solution and the equivalent circuit is (ReCe)-(RmCm), that is, a series association of two resistance-capacitor subcircuits, one for the electrolyte solution and other for the membrane while data for the ultrafiltration membrane corresponds to a depressed semicircle (associated with a CPE) and the equivalent circuit for the total membrane system is (ReCe)-(RmQm)- However, for the porous membrane/NaCI solution and charged membrane/KCl solution systems, a unique relaxation process (a semicircle) was obtained, which makes it impossible to evaluate the separate contributions associated with the membrane and the electrolyte solution in both cases the equivalent circuit is given by a parallel association of resistance and capacitor representing the total membrane system (RsmQm)-Nevertheless, these two latter systems (shown in Figure 9.3e, f) represent two completely different situations, as can be seem when the corresponding impedance plots for 0.002 M NaCl and 0.01 M KCl solutions are also considered (measurements carried out without membranes in the test cell) ... 

EIS data can be analyzed by modeling or fitting the impedance spectrum with an equivalent circuit to extract the physically meaningful properties of the studied system. However, the design of the equivalent circuit is very important, and sometimes, the complexity of the PEM fuel cell system makes this process difficult. Depending on the shape of the EIS spectrum, the equivalent circuit model is usually composed of resistors (R), conductors (L), and capacitors (C), which are connected in series or in parallel, as shown in Fig. 3.11 in this equivalent circuit, R, R, and Rmt represent the membrane resistance, charge transfer resistance, and mass transfer resistance, respectively, and CPEi and CPE2 represent the Rt and Rmt associated capacitances, respectively. 

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