Molecular diffusion, transport mechanism

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... 

The solute transport mechanisms considered in the formulation are advection (due to water phase movement), molecular diffusion and mechanical dispersion. 

This paper has presented a summary of a coupled formulation that combines an existing THM formulation with reactive transport equations in a fully coupled way. The reactive transport formulation takes into account some of the most relevant geochemical processes (acid/base, redox, dissolution/precipitation and complex formations). The transport mechanisms included are advection, molecular diffusion and mechanical dispersion. 

Although many users of this book are familiar with the subject of chemical molecular diffusion transport, it may be new to others or they may have limited knowledge about the broader subject area of chemical transport and its fundamentals. There are numerous rapid transport mechanisms compared to the slow process of molecular diffusion. These rapid processes efficiently move chemicals within and across the various media compartments of the Earth. We have thus sought to present the subject of chemical mobility in a handbook-type format so as to make the material applied rather than theoretical, while being useful and accessible and relevant to a broad range of users. Our aim is to document and reflect the present state of the science. ... 

Macropore Diffusion. Transport in a macropore can occur by several different mechanisms, the most important of which ate bulk molecular... 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

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 devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

In passing, it is good to emphasise that the above analysis illustrates the limitations of the widely used Nernst diffusion layer concept. This concept assumes that there is a certain thin layer of static liquid adjacent to the solid plane under consideration at x = 0. Inside this layer, diffusion is supposed to be the sole mechanism of transport, and, outside the layer, the concentration of the diffusing component is constant, as a result of the convection in the liquid. We have seen that, in contradiction with this oversimplified picture, molecular diffusion and liquid motion are not spatially separated, and that the thickness... 

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)... 

Redox processes also tend to be separated in time and space due to the relative sluggishness of solute transport. For example, molecular diffusion is the major mechanism by which solutes can be transported through the pore waters of sediments. In many cases this process is slower than the chemical reaction rates and, thus, prevents... 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

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