Back-diffusive transport

When the pressure is increased, the flux does increase initially. The increase results in a higher rate of convective transport of solute to surface of the membrane. If the system is not "gel-polarized", the solute concentration at the surface (Cs) increases resulting in an increase in the concentration driven back diffusive transport away from the membrane. In fact, Cs will increase until the back-diffusive transport of solute just equals the forward convective transport. 

In the steady state, the convective transport to the membrane must equal the back-diffusive transport away from the membrane. 

These observations lead to the conclusion that the back-diffusive transport of colloidal particles away from the membrane surface into the bulk stream is substantially augmented over that predicted by the Leveque or Dittus-Boelter relationships. It is known that colloidal particles flowing down a tube tend to migrate across the velocity gradient toward the region of maximum velocity this is called the "tubular pinch effect". 

Green and Belfort39 have combined the equations for particle migration due to the tubular pinch effect with the normal back-diffusive transport to calculate... 

Fig. 14 Diagram showing three transport mechanisms of water vapor within the fuei cell membrane pressure driven flow, electro-osmotic drag, and back diffusion. Transport due to pressure driven flow can occur flnm either electrode, electro-osmotic drag occurs solely from the anode to the cathode, and back-diffusion typically occurs from the cathode to the anode since the water concentration is usually higher at the cathode (from Evans, 2003).

Commercially available membranes are usually reinforced with woven, synthetic fabrics to improve the mechanical properties. Several hundred thousand square meters of IX membranes are now produced aimuaHy, and the mechanical and electrochemical properties are varied by the manufacturers to suit the proposed appHcations. The electrochemical properties of most importance for ED are (/) the electrical resistance per unit area of membrane (2) the ion transport number, related to current efficiency (2) the electrical water transport, related to process efficiency and (4) the back-diffusion, also related to process efficiency. 

Back-diffusion is the transport of co-ions, and an equivalent number of counterions, under the influence of the concentration gradients developed between enriched and depleted compartments during ED. Such back-diffusion counteracts the electrical transport of ions and hence causes a decrease in process efficiency. Back-diffusion depends on the concentration difference across the membrane and the selectivity of the membrane the greater the concentration difference and the lower the selectivity, the greater the back-diffusion. Designers of ED apparatus, therefore, try to minimize concentration differences across membranes and utilize highly selective membranes. Back-diffusion between sodium chloride solutions of zero and one normal is generally [Pg.173]

Various works has pointed out the role of the nanostructure of the catalysts in their design.18-26 There is a general agreement that the nanostructure of the oxide particles is a key to control the reactivity and selectivity. Several papers have discussed the features and properties of nanostructured catalysts and oxides,27-41 but often the concept of nanostructure is not clearly defined. A heterogeneous catalyst should be optimized on a multiscale level, e.g. from the molecular level to the nano, micro- and meso-scale level.42 Therefore, not only the active site itself (molecular level) is relevant, but also the environment around the active site which orients or assist the coordination of the reactants, may induce sterical constrains on the transition state, and affect the short-range transport effects (nano-scale level).42 The catalytic surface process is in series with the transport of the reactants and the back-diffusion of the products which should be concerted with the catalytic transformation. Heat... 

The EOD coefficient, is the ratio of the water flux through the membrane to the proton flux in the absence of a water concentration gradient. As r/d,3g increases with increasing current density during PEMFC operation, the level of dehydration increases at the anode and normally exceeds the ability of the PEM to use back diffusion to the anode to achieve balanced water content in the membrane. In addition, accumulation of water at the cathode leads to flooding and concomitant mass transport losses in the PEMFC due to the reduced diffusion rate of O2 reaching the cathode. 

After testing a number of DLs with and without MPLs, Lin and Nguyen [108] postulated that the MPL seemed to push more liquid water back to the anode through the membrane. Basically, the small hydrophobic pores in the MPL result in low liquid water permeability and reduce the water transport from the CL toward the DL. Therefore, more liquid water accumulated in the CL is forced toward the anode (back diffusion). This reduces the amount of water removed through the cathode DL, decreases the number of blocked pores within the cathode diffusion layer, and improves the overall gas transport from the DL toward the active zones. 

Though drugs appear to cross the blood-brain barrier by passive diffusion, transporter systems in the blood-brain barrier pump drugs back out into the systemic circulation. As in the gut, the Pgp transporter system is the primary active transporter in the blood-brain barrier identified to date. This ATP-dependent transporter system picks up substrates that have crossed the capillary endothelial cells and transports them back to the systemic circulation, limiting their penetration into the CNS. Thus, not only are the physicochemical properties of the drug a determinant for penetration into the CNS but penetration also depends on whether the drug is a substrate for the Pgp transporter system. 

The mechanism by which cations are transported across a membrane is represented in Figure 18a. A cation-carrier complex is initially formed at the interface. This lipophilic species then diffuses across the membrane as an ion pair and dissociates at the other interface to water soluble ion pair and membrane-soluble carrier. The final step is back diffusion of the free carrier to the initial interface. The factors which influence transport rates and selectivity have been the subject of much research (79PAC979, B-81MI52102). 

This transporter is selectively blocked by diuretic agents known as "loop" diuretics (see later in chapter). Although the Na+/K+/2Cr transporter is itself electrically neutral (two cations and two anions are cotransported), the action of the transporter contributes to excess K+ accumulation within the cell. Back diffusion of this K+ into the tubular lumen causes a lumen-positive electrical potential that provides the driving force for reabsorption of cations—including magnesium and calcium—via the paracellular pathway. Thus, inhibition of salt transport in the TAL by loop diuretics, which reduces the lumen-positive potential, causes an increase in urinary excretion of divalent cations in addition to NaCI. 

Ion transport pathways across the luminal and basolateral membranes of the thick ascending limb cell. The lumen positive electrical potential created by K+ back diffusion drives divalent (and monovalent) cation reabsorption via the paracellular pathway. NKCC2 is the primary transporter in the luminal membrane. 

Molecules at or near the interface may diffuse back into the bulk solution, particularly if the free energy of adsorption is not very high. Mass transport equations which account for back diffusion are available 3,31,32). 

Carrier-mediated transport (or facilitated diffusion) consists of the transfer of a substrate across a membrane, facilitated by a carrier molecule located in the membrane. It is a cyclic process comprising four steps (1) formation of the carrier-substrate complex at one interface (2) diffusion of the complex through the membrane phase (3) release of the substrate at the other interface (4) back diffusion of the free carrier. 

The metal-insulator—semiconductor (MIS) structure is employed in the heterophase blocking where the thickness of the insulator used is the key factor in satisfying the blocking requirement. Differently from the solar cell with MIS structure, in which an insulating film tens of angstroms thick is used to avoid the back-diffusion of photoinduced carriers (Wronski et al., 1981), the photoreceptor of electrophotography has necessarily a rather thick insulating film to block carrier transport. 

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