Solute flux, enhancement

Figure 8 Griseofulvin flux enhancement factor = . Closed symbols represent TW 20 solutions, open symbols represent emulsions plotted as a function of the apparent TW 20 concentration in the emulsion aqueous phase.

Both secondary active transport and positive cooperativity effects enhance carrier-mediated solute flux, in contrast to negative cooperativity and inhibition phenomena, which depress this flux. Most secondary active transport in intestinal epithelia is driven by transmembrane ion gradients in which an inorganic cation is cotransported with the solute (usually a nutrient or inorganic anion). Carriers which translocate more than one solute species in the same direction across the membrane are referred to as cotransporters. Carriers which translocate different solutes in opposite directions across the membrane are called countertransporters or exchangers (Figs. 10 and 11). 

In natural waters, unattached microorganisms move with the bulk fluid [55], so that no flux enhancement will occur due to fluid motion for the uptake of typical (small) solutes by small, freely suspended microorganisms [25,27,35,41,56,57], On the other hand, swimming and sedimentation have been postulated to alleviate diffusive transport limitation for larger organisms. Indeed, in the planar case (large r0), the diffusion boundary layer, 8, has been shown to depend on advection and will vary with D according to a power function of Da (the value of a is between 0.3 and 0.7 [43,46,58]). For example, in Chapter 3, it was demonstrated that in the presence of a laminar flow parallel to a planar surface, the thickness of the diffusion boundary layer could be estimated by ... 

The enhancement of solute fluxes, predominantly Ca " ", HCO, and SOl , was —20-30% over a distance of —1 km at Finsterwalderbreen (Wadham et al., 2001). These values are likely to be high in comparison with other lithologies, since carbonate, sulfide, and kerogen are present in relatively high concentrations. 

Wadham J. L., Cooper R. J., Tranter M., and Hodgkins R. (2001) Enhancement of glacial solute fluxes in the proglacial zone of a polythermal glacier. J. Glaciol. 47, 378-386. 

Mallubhotla H, Schmidt M, Lee KH, and Belfort G, Flux enhancement during Dean vortex tubular membrane nanoflltration 13. Effect of concentration and solute type, J. Membr. Sci. 1999 153 259-269. 

Subsequent studies have supported the above results. For instance, ibuprofen terpene eutectic systems vs. a saturated aqueous solution of ibuprofen applied to untreated and to terpene pretreated skin were reported to cause a significant flux enhancement [59]. A system composed of ibuprofen thymol 40 60 (% w/w) produced a flux 5.9 and 12.7 times higher than the flux values from a saturated aqueous solution with thymol pretreated skin and from a saturated aqueous solution across nonpretreated skin, respectively. Analogous data were achieved in permeation experiments through snake skin with lidocaine menthol eutectic mixtures [60]. 

General analytical solution is not possible. A variety of numerical solutions have been developed, as well as analytical approximations, as described in the aforementioned reviews. The analytical solutions are generally applicable to either the thln film" regime - l.e., in which diffusion times are comparable to or less than reaction times, and minimal flux enhancement occurs, or the "thick film" regime in which perturbations from local reaction equilibrium are small (18). Frledlander and Keller (19) showed that there is a characteristic length scale, A, a function of the reaction and diffusion constants, such that L/X is a measure of the approach to local reaction equilibrium. It is thus similar to the Thiele modulus of porous catalysts. 

As stated above, the use of a liquid phase can enhance the solute flux due to the higher diffusion coefficients in liquids than in solids. Further enhancement can be accomplished by adding a nonvolatile complexing agent to the liquid membrane (7,8). This carrier molecule can selectively and reversibly react with the solute. This reversible reaction provides a means of enhancing the solute flux and improving the selectivity at the same time. There are two basic mechanisms for this enhanced transport. 

---