Sieving function

The Renkin function is the dimensionless molecular sieving function for cylindrical channels (Renkin, 1954 Curry, 1984) and is defined as... 

The permeability coefficients and molecular radii are known. The effective pore radius, R, is the only unknown and is readily calculated by successive approximation. Consequently, unknown parameters (i.e., porosity, tortuosity, path length, electrical factors) cancel, and the effective pore radius is calculated to be 12.0 1.9 A. Because the Renkin function [see Eq. (35)] is a rapidly decaying polynomial function of molecular radius, the estimation of R is more sensitive to small uncertainties in the calculated molecular radius values than it is to experimental variabilities in the permeability coefficients. The placement of the perme-ants within the molecular sieving function is shown in Figure 9 for the effective... 

Since Pparaceii is proportional to the molecular sieving function F(r/R), the interrelationships of Ppaiacen between mannitol and sucrose, including mannitol-manitol and sucrose-sucrose, can be put into perspective via a normalized plot of F(r/R) versus r/R for control and perturbed monolayers (Fig. 12). As pointed out before, F(r/R) is a rapid, monotonically decreasing function bounded by 1.0 and zero. One observes that mannitol is less restricted by the pores of the control monolayer than the larger sucrose molecule. However, in the larger pores of the perturbed monolayer, the increase in permeability is less for mannitol than it is... 

De Vos, D.E., Dams, M., Sels, B.F. and Jacobs, P.A. (2002) Ordered mesoporous and microporous molecular sieves functionalized with transition metal complexes as catalysts for selective... 

There are no recent improvement in the paracellular pathway permeation models, probably because there is no specific in vitro or in vivo system to measure the paracellular pathway contribution. The paracellular pathway models was constructed using very hydrophilic compounds [107] or subtracting the contribution of transcel-lular pathway from the total passive permeation [78]. Paracellular pathway was modeled as permeation through a charged aqueous pore. A combination of size sieving function and electric field function was found to model the paracellular pathway [78, 87, 88]. 

Molecular sieves function by both absorption and separation mechanisms. Through absorption, polar compounds such as water and H2S are absorbed. Through separation, molecules which are held within the pores of the sieve are retained. 

Other examples of screw feed/process devices are feeders with pre-breaker sections, granulating, and/or sieving functions. An example of a pre-breaker with a screening section and an integral feed screw is shown in Fig. 7.4. 

Membranes were originally developed as agents (filters, sieves) for solid-liqnid separations by mechanical means. In this context any interaction (adsorption) of the components with the membrane material was to be avoided. Recently however, the controlled (selective) adsorption of certain molecules on such membranes has become the object of intensive study. This does not mean that the primary sieving function of the membrane has lost its importance in such cases. Quite the opposite, it is the combination of the two functions of the membranes, sieving and adsorption, which opens up new possibilities for improving the efficiency of separation processes, especially in areas such as biotechnology and medicine (bioseparation). 

Sohd sorbent materials have the abiUty to adsorb water vapor until an equiUbrium condition is attained. The total weight of water that can be adsorbed in a particular material is a function of the temperature of the material and of the relative humidity of the air (see Adsorption). To regenerate the sorbent, its temperature must be raised or the relative humidity lowered. The sohd sorbents most commonly used are siUca (qv), alumina (see Aluminum compounds), and molecular sieves (qv). 

The purity of oxygen from chlorate candles before and after gas filtration is indicated in Table 2. A particulate filter is always used. Filter chemicals are HopcaUte, which oxidizes CO to CO2 molecular sieves (qv), which remove chlorine compounds and basic materials, eg, soda lime, which removes CO2 and chlorine compounds. Other than H2O and N2, impurity levels of <1 ppm can be attained. Moisture can be reduced by using a desiccant (see Desiccants). Gas purity is a function of candle packaging as well as composition. A hotter burning unit, eg, one in which steel wool is the binder, generates more impurities. 

Porin channels are impHcated in the transport of cephalosporins because ceds deficient in porins are much more impermeable than are ceds that are rich in porins. The porins appear to function as a molecular sieve, adowing molecules of relatively low molecular weight to gain access to the periplasmic space by passive diffusion. In enterobacteria, a clear correlation exists between porin quantity and cephalosporin resistance, suggesting that the outer membrane is the sole barrier to permeabdity. However, such a relationship is not clearly defined for Pseudomonas aeruginosa where additional barriers may be involved (139,144,146). 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

FIG. 14-118 Aerodynamic cut diameter for a single-sieve-plate scrubber as a function of bole size, bole-gas velocity, and froth density, F, g/cm. To convert meters per second to feet per second, multiply by 3.281 to convert grams per cubic centimeter to pounds per cubic foot, multiply by 62.43. [Calveti, J. Air Pollut. Control Assoc., 24, 929 (1974).]... 

Modeling the pore size in terms of a probability distribution function enables a mathematical description of the pore characteristics. The narrower the pore size distribution, the more likely the absoluteness of retention. The particle-size distribution represented by the rectangular block is the more securely retained, by sieve capture, the narrower the pore-size distribution. 

Column diameter for a particular service is a function of the physical properties of the vapor and liquid at the tray conditions, efficiency and capacity characteristics of the contacting mechanism (bubble trays, sieve trays, etc.) as represented by velocity effects including entrainment, and the pressure of the operation. Unfortunately the interrelationship of these is not clearly understood. Therefore, diameters are determined by relations correlated by empirical factors. The factors influencing bubble cap and similar devices, sieve tray and perforated plate columns are somewhat different. 

For tray columns, bubble caps, valves or sieve, the feed liquid usually enters the column either in between functioning trays or at the top (reflux). The liquid or liq-uid/vapor mixture for flashing liquids must be dispersed uniformly across the tray. Such an arrangement often requires a special tray designed for the purpose to allow... 

Further investigation revealed that the sieving rate constant was a function of several variables ... 

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