Carrier-facilitated mass transport

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

The mode of transport through a membrane may be passive, active, or facilitated type. In passive transport, the membrane acts as a barrier and permeation of the components is determined by their diffusivity and concentration in the membrane or just by their size. In facilitated transport along with the chemical potential gradient, the mass transport is coupled to specific carrier components in the membrane. In active transport driving force for transport is achieved by a chemical reaction in the membrane phase. 

The etching process in Br2 containing HF solutions, unlike that in the HNO3 solutions, is mainly of a chemical nature [64]. At OCP, Si reacts directly with Br2 without involving charge carriers in the bands. The reduction of Br2 at cathodic potentials is facilitated by the electrons from the conduction band. The etch rate, which is independent of doping type and surface orientation, is limited by the mass transport of the Br2 in the solution. Thus, for p-Si, the etch rate is almost constant at cathodic potentials at which no electron is present on the surface. On the other hand, the etch rate ofra-Si decreases to zero at cathodic potentials because Br2 is efficiently reduced with the conduction band electrons. 

The basic parameters of a facilitated, coupled transport are related to properties of the solute, carrier, and its solvent and membrane supports. These are individual and overall mass-transfer coefficients (in diffusional and chemical reactions kinetics regime), distribution constants, extraction, and couphng coefficients of forward extraction, Kq, and Kf p, respectively, and... 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

In many cases of practical interest, the membrane s mass transfer resistance is significant, i.e., the wall Sherwood number is small, leading to relatively low mass transfer rates of the solute. The diffusive flux of the permeate through the membrane can be increased by introducing a carrier species into the membrane. The augmentation of the flux of a solute by a mobile carrier species, which reacts reversibly with the solute, is known as carrier-facilitated transport (25). The use of carrier-facilitated transport in industrial membrane separation processes is of considerable interest because of the increased mass transfer rates for the solute of interest and the improved selectivity over other solutes (26). 

In this paper, we analyze mass transfer in a parallel-plate mass exchanger with reactive membranes. We consider the case of fully developed, one-dimensional laminar flow between two membranes. Equilibrium carrier-facilitated transport of the solute takes place in the membrane phase. The effect of the diffusion and reaction parameters of the carrier-facilitated system on solute separation is Investigated. 

Concerning the preparation techniques, there are different approaches from vapor or liquid phase. The critical aspects, that have to be taken into account, are the reliability of the preparation process, the quality of the nanostructures prepared and the integration into final devices. Among the most promising techniques there are catalyst assisted vapor phase transport and thermal oxidation. Vapor phase technique consists in the evaporation of the oxide powder in a furnace with controlled atmosphere. In general the pressure is lower than lOOmbar to ease the vaporization of the oxide powder and an inert gas carrier is used to facilitate the mass transport from the source to the substrates, where the vapors condense in form of nanowires. 

Facilitated mass transfer Similarly to LLE, the selectivity and efficiency of the liquid membrane separation process can be considerably improved if a suitable extractant with a high selectivity for the analyte of interest is used. This extractant, often referred to as the carrier, facilitates the mass transfer of the analyte between the feed and receiver solutions. The liquid membrane phase in this case usually consists of a suitable liquid extractant or an extractant dissolved in an organic solvent (diluent). The extractant facilitates the transport of the analyte from the feed phase to the liquid membrane phase by chemically interacting with it. This interaction leads to the selective extraction of the analyte into the... 

Kedari, C.S., Pandit, S.S., Misra, S.K. Ramanujam, A. (2001) Mass transfer mechanism of the carrier-facilitated transport of uranium VI across 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester immobilised liquid membranes. Hydrometallurgy, 62 (1), 47-56. 

The theory for ELMs may be classified into two categories 1) diffusion-type mass transfer models for Type 1 facilitation and 2) carrier facilitated transport models for Type 2 facilitation (2,7). 

Carrier Facilitated Transport Models for Type 2 FacUitation. The models take into account the diffusion of the carrier and carrier-metal complex in emulsion globules and reversible reactions at the external and internal interfaces. Teramoto et al. (77) and Kataoka et al. (18) included the external phase mass transfer resistance and an additional mass transfer resistance in the peripheral thin membrane layer of the emulsion globule in their models. The Teramoto et al. model also considered leakage. These models have complicated equations and many parameters. Teramoto et al. evaluated their model parameters experimentally, which was quite tedious. 

Example 1.3-6 Facilitated transport across membranes Some membranes contain a mobile carrier, a reactive species that reacts with diffusing solutes, facilitating their transport across the membrane. Such membranes can be used to concentrate copper ions from industrial waste and to remove carbon dioxide from coal gas. Diffusion across these membranes does not vary linearly with the concentration difference across them. The diffusion can be highly selective, but it is often easily poisoned. Should this diffusion be described with mass transfer coefficients or with diffusion coefficients ... 

This simple mass transfer model based on simplified film theory has been proposed to describe the process of facilitated transport of penicillin-G across a SLM system [53]. In the authors laboratory, CPC transport using Aliquat-336 as the carrier was studied [56] using microporous hydrophobic polypropylene membrane (Celgard 2400) support and the permeation rate was found to be controlled by diffusion across the membrane. 

Example 9.14 Nonisothermal facilitated transport An approximate analysis of facilitated transport based on the nonequilibrium thermodynamics approach is reported (Selegny et al., 1997) for the nonisothermal facilitated transport of boric acid by borate ions as carriers in anion exchange membranes within a reasonable range of chemical potential and temperature differences. A simple arrangement consists of a two-compartment system separated by a membrane. The compartments are maintained at different temperatures T] and T2, and the solutions in these compartments contain equal substrate concentrations. The resulting temperature gradient may induce the flow of the substrate besides the heat flow across the membrane. The direction of mass flow is controlled by the temperature gradient. 

The carrier protein facilitating Pj and phosphate ester transport is of particular interest in leaves in connection with carbon processing - i.e., the synthesis, transport and degradation of carbohydrate, all of which occur in the cytosol [51]. This metabolite carrier, called the phosphate translocator, is a polypeptide with a molecular mass of 29 kDa and is a major component of the inner envelope membrane [52,53]. The phosphate translocator mediates the counter-transport of 3-PGA, DHAP and Pj. The rate of Pj transport alone is three orders of magnitude lower than with simultaneous DHAP or 3-PGA counter-transport [54]. Consequently operation of the phosphate translocator keeps the total amount of esterified phosphate and Pj constant inside the chloroplast. Significantly, the carrier is specific for the divalent anion of phosphate. 

Sastre, A., Madi, M., Cortina, J.L. and. Mira lies, N. (1998). ModeUing of mass transfer in facilitated supported liquid membrane transport of gold(III) using phospholene derivatives as carriers. J. Membr. Sci., 139, 57-65. 

Transport of molecules across the cell membrane occurs by passive and facilitated diffusion and active transport (Stein, 1986 Finkelstein, 1987). Passive transport is governed by a mass-transfer coefficient, surface area for exchange, transmembrane concentration difference, and a partition coefficient. The partition coefficient can be modified by charge, pH, temperature, and presence of other drugs. Facilitated transport may be most simply described by Michaelis-Menten kinetics. Depending upon the carrier system, symmetric or asymmetric models may be used. 

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