Solution-diffusion mechanism, transport

We may conclude that our findings support independent water and salt permeation processes, and suggest that the salt permeation is governed by a solution-diffusion transport mechanism. 

Salt and water permeate reverse osmosis membranes according to the solution-diffusion transport mechanism are described in Chapter 2. The water flux,. /, is linked to the pressure and concentration gradients across the membrane by the equation... 

Solution-diffusion transport mechanism When the feed contacts the membrane, the solutes (denoted i in Fig. 3.6-10) adsorb on and subsequently absorb in the membrane surface by solute-polymer interactions (Fig. 3.6-lOA). Preferential solute-polymer interactions imply that the solvating power of the polymer is higher for the solutes than for the bulk solvent. 

Then Uemiya et al. [2] reported another Pd membrane reactor for WGS reaction using Fe-Cr oxide catalysts. The model of flow in the palladium membrane reactor is illustrated in Figure 6.3. They proposed that hydrogen is permeated through palladium membrane via a solution diffusion transport mechanism, and the rate of hydrogen permeation, /, per unit area of membrane, is written in terms of Fick s first law as follows ... 

The membranes used in GS can be distinguished in two main categories, polymeric and inorganic. Polymeric membranes, specifically used for GS, are generally asymmetric or composite and based on a solution-diffusion transport mechanism. These membranes, made as flat sheet or hollow fibres, have a thin, dense skin layer on a micro-porous support that provides mechanical strength [7]. Typically, polymeric membranes show high, but finite, selectivities with respect to porous inorganic materials due to their low free-volume... 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

The removal of water from aqueous salt notations by reveres osmosis, as in seawater desaiiontion with cellulose acetate menibmues or aylon hollow fibers, is believed to occur primarily by a diffusive transport mechanism for both water and solutes. On the other hand, in the use of membranes for die removal of water from aqueous solutions containing higher molecular weight solutes, such as die ultrafiltration of protein solutions, die solvent is believed transported by a viscous How mechanism within the pores of the membrane and nolute molecules are corrected with the solvent in die larger pores.66-66... 

Gas transport through nonporous inorganic membranes falls into two categories. It is known that the conventional solution-diffusion permeation mechanism is valid for nonporous membranes of silica, zeolite and inorganic salts. It is no longer so when the membrane is metallic in nature (Hwang and Kammermeyer, 1975). Diatomic gases such as O2, H2 and N2 dissolve atomically in the metallic membrane (see (3.3.67)). While a conventional flux expression is valid for atomic species i dissolved in the membrane, Le. 

Ultrafiltration separations range from ca 1 to 100 nm. Above ca 50 nm, the process is often known as microfiltration. Transport through ultrafiltration and microfiltration membranes is described by pore-flow models. Below ca 2 nm, interactions between the membrane material and the solute and solvent become significant. That process, called reverse osmosis or hyperfiltration, is best described by solution—diffusion mechanisms. 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

In either equation, /c is given by Eq. (16-84) for parallel pore and surface diffusion or by Eq. (16-85) for a bidispersed particle. For nearly linear isotherms (0.7 < R < 1.5), the same linear addition of resistance can be used as a good approximation to predict the adsorption behavior of packed beds, since solutions for all mechanisms are nearly identical. With a highly favorable isotherm (R 0), however, the rate at each point is controlled by the resistance that is locally greater, and the principle of additivity of resistances breaks down. For approximate calculations with intermediate values of R, an overall transport parameter for use with the LDF approximation can be calculated from the following relationship for sohd diffusion and film resistance in series... 

FIGt 22-48 Transport mechanisms for separation membranes a) Viscous flow, used in UF and MF. No separation achieved in RO, NF, ED, GAS, or PY (h) Knudsen flow used in some gas membranes. Pore diameter < mean free path, (c) Ultramicroporoiis membrane—precise pore diameter used in gas separation, (d) Solution-diffusion used in gas, RO, PY Molecule dissolves in the membrane and diffuses through. Not shown Electro-dialysis membranes and metallic membranes for hydrogen. 

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

The analytic theory outlined above provides valuable insight into the factors that determine the efficiency of OI.EDs. However, there is no completely analytical solution that includes diffusive transport of carriers, field-dependent mobilities, and specific injection mechanisms. Therefore, numerical simulations have been undertaken in order to provide quantitative solutions to the general case of the bipolar current problem for typical parameters of OLED materials [144—1481. Emphasis was given to the influence of charge injection and transport on OLED performance. 1. Campbell et at. [I47 found that, for Richardson-Dushman thermionic emission from a barrier height lower than 0.4 eV, the contact is able to supply... 

When a polymer film is exposed to a gas or vapour at one side and to vacuum or low pressure at the other, the mechanism generally accepted for the penetrant transport is an activated solution-diffusion model. The gas dissolved in the film surface diffuses through the film by a series of activated steps and evaporates at the lower pressure side. It is clear that both solubility and diffusivity are involved and that the polymer molecular and morphological features will affect the penetrant transport behaviour. Some of the chemical and morphological modification that have been observed for some epoxy-water systems to induce changes of the solubility and diffusivity will be briefly reviewed. 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

Johnson ME, Blankschtein D, Langer R (1997) Evaluation of solute permeation through the stratum corneum lateral bilayer diffusion as the primary transport mechanism. J Pharm Sci 86 1162-1172. 

Because of the similarity of transport in biotilms and in stagnant sediments, information on the parameters that control the conductivity of the biofilm can be obtained from diagenetic models for contaminant diffusion in pore waters. Assuming that molecular diffusion is the dominant transport mechanism, and that instantaneous sorption equilibrium exists between dissolved and particle-bound solutes, the vertical flux ( ) through a stagnant sediment is given by (Berner, 1980)... 

The most serious causes of error are (i) wave and peak distortion caused by excessively fast scan rates, which are themselves caused by diffusion being an inefficient mass transport mechanism, (ii) current maxima caused by convective effects as the mercury drop forms and then grows, and (iii) IR drop, i.e. the resistance of the solution being non-zero. Other causes of error can be minimized by careful experimental design. 

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