Driving diffusion

In each form of attack, solute concentration differences arise primarily by diffusion-related processes. As a consequence, stagnant conditions may promote attack, since concentration gradients near affected areas are reduced by flow and these concentration gradients supply the energy that drives diffusion. Similarly, high concentrations of dissolved species increase attack. Elevated temperature usually stimulates attack by increasing both diffusion and reaction rates. 

Similarly, drugs injected into the SC or IM space are separated from the blood compartment by the endothelial cells of the capillaries. From the interstitial space, such drug molecules must first diffuse toward and then partition into the endothelial cell membrane. After traversing these cells, the drugs must then partition on the luminal, or blood facing, side of these cells into the blood, which carries them away. By this dilution effect, the blood presents sink conditions, thus maintaining a maximal concentration gradient, dCm/dx, to drive diffusion toward the blood. 

As a byproduct, we can learn from Eq. 18-50 that, in fact, it is not the gradient of concentration, C but the chemical activity, a that drives diffusion. Since at constant C activity changes with temperature, ionic strength, and other parameters, a diffusive flux may actually occur even if the concentration gradient is zero. 

Self-Diffusivity Self-diffusivity is denoted by DA A and is the measure of mobility of a species in itself for instance, using a small concentration of molecules tagged with a radioactive isotope so they can be detected. Tagged and untagged molecules presumably do not have significantly different properties. Hence, the solution is ideal, and there are practically no gradients to force or "drive diffusion. This kind of diffusion is presumed to be purely statistical in nature. 

A fully microscopic theory of chemical diffusion can be constructed, however, it requires a careful distinction between the motions of the observed species and the underlying host, and is made complicated by the fact that, as defined, the diffusion coefficient relates flux to the concentration gradient while the actual force that drives diffusion is gradient of the chemical potential. An alternative useful observable is the so-called conductivity diffusion coefficient, which is defined for the motion of charged particles by the Nemst-Einstein equation (11.69)... 

At the interface, we do not know either or a 2 bnt it is reasonable to assume that they are equal. We already assumed that bonding across the interface was as strong and continuous as on either side, i.e., that the interface has no special weakness, and correspondingly we now assume that it is no kind of barrier either. If the interface were a barrier, then, for material to cross, one might ask about a stress difference or potential difference needed to drive diffusing material through the barrier, at the needed rate but if we assume a perfectly well-bonded interface, no stress difference or stress jump is needed and = [Pg.116]

It seems reasonable to consider two extremes. First, we ask can a material be so gaslike, so isotropic in all its behaviors, that the difference drives diffusion of atoms from B to C to exactly the same extent as would an equivalent difference — a, At this extreme, we admit that there is a geometrical difference between the two parts of Figure 11.9 but postulate that no difference in behavior follows in this case, / = 1. 

In the negative feedback mode, the concentration of redox species is the same on both sides of the membrane no concentration gradient exists between the donor and receptor compartments to drive diffusive transport across the pore (11-13). This mode of imaging can be used to obtain topographical maps of the surface where the variation in the SECM tip current arises from differences in the tip-to-sample separation (28). When the tip is far from the sample surface, a steady-state current is measured at the tip,... 

A final point to consider is that because a ejection and diffusion occur at the same boundary—at least in specular hematite (Bahr et al. 1994), apatite (Farley 2000) and titanite (Reiners and Farley 1999), the He gradient that drives diffusion will be more rounded than diffusion alone would produce. For example, in a quickly cooled sample that has experienced a ejection, the He concentration profile would look similar to Figure... 

There is experimental evidence reported in the literature that carbon steel cracks in nitrates that form low melting compounds with iron however, it also cracks when in contact with the high melting point magnetite [64]. Other experimental evidence provided by Oriani [65] shows that the flow of the surface atoms and ions is toward the crack tip instead of the crack walls. It has also been discussed in the Hterature whether there is enough force to drive diffusion of metals and the surface vacancy formation [45]. 

The two preceding effects are due to true polymer-phase sorption and transport phenomena. At veiy high pressures, an additional complexity related to nonideal gas-phase effects may arise and cause potentially incorrect conclusions about the transport phenomena involved. This confusion can be avoided by defining an alternative permeability P" in terms of the fiigacity difference rather than the partial pressure difference driving diffusion across the membrane. The benefit of using this thermodynamic permeability is illustrated for the CO2-CH4 system at elevated pressures. 

Extended Stefan-Maxwell constitutive laws for diffusion Eq. 4 resolve a number of fundamental problems presented by the Nemst-Planck transport formulation Eq. 1. A thermodynamically proper pair of fluxes and driving forces is used, guaranteeing that all the entropy generated by transport is taken into account. The symmetric formulation of Eq. 4 makes it unnecessary to identify a particular species as a solvent - every species in a solution is a solute on equal footing. Use of velocity differences reflects the physical criterion that the forces driving diffusion of species i relative to species j be invariant with respect to the convective velocity. Finally, all possible binary solute/solute interactions are quantified by distinct transport coefficients each species i in the solution has a diffusivity or mobility relative to every other species j, Djj or up, respectively. 

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