Diffusion paths

Most recent studies (69) on elevated temperature performance of carbon fiber-based composites show that the oxidation resistance and elevated temperature mechanical properties of carbon fiber reinforced composites are complex and not always direcdy related to the oxidation resistance of the fiber. To some extent, the matrix acts as a protective barrier limiting the diffusion of oxygen to the encased fibers. It is therefore critical to maintain interfacial bonding between the fiber and the matrix, and limit any microcracking that may serve as a diffusion path for oxygen intmsion. Since interfacial performance typically deteriorates with higher modulus carbon fibers it is important to balance fiber oxidative stabiHty with interfacial performance. 

Dpi is smaller than the diffusivity in a straight cylindrical pore as a result of the random orientation of the pores, which gives a longer diffusion path, and the variation in the pore diameter. Both effects are commonly accounted for by a tortuosity factor Tp such that Dp = DjlXp. In principle, predictions of the tortuosity factor can be made if the... 

A formal derivation of diffusion in a restricted, high diffusivity path which uses no atomic model of the grain boundary is that due to Fisher, who made a flux balance in unit width of a grain boundary having a drickness of <5. There is flux accumulation in the element according to Pick s second law given by... 

In this derivation, the diffusion coefficient which is used is really a parameter, since it is not certain which gas diffusion rate is controlling, that of hydrogen into a pore, or that of water vapour out of die pore. The latter seems to be the most probable, but the path of diffusion will be vety tormous drrough each pore and drerefore the length of the diffusion path is ill-defined. 

Fast diffusion paths grain boundary and dislocation core diffusion... 

Referring to Fig. 9, the effect of the shear is to catalyze the reaction, presumably through suppression of the interfacial barrier by stretching the flow. The latter is believed to reduce the diffusion path, promoting the reaction rate, and hence the rate of increase in the viscosity. A similar effect is produced with temperature as a parameter, which also augments the reaction rate. The modified reaction rate constant in case of any external stimulus or perturbation acting on the system may be computed from the scalar K, where ... 

Calculate (1 - y)M. arithmetic average of non-diffusing gas concentration at ends of diffusing path ... 

In contrast, LiMn204 has a spinel structure. This material has the space group Fd3m in which the transition-metal and lithium ions are located at octahedral 8(a) and tetrahedral 16(d) sites, respectively, and the oxygen ions are at 32(e) sites. There are octahedral 16(c) sites around the 8(a) sites and lithium ions can diffuse through the 16(c) and 8(a) sites. As this structure contains a diffusion path for the lithium ions, these ions can be deinter-calated and intercalated in these compositions. 

Figure 4. Rotation of the structure of LiAlCl4 compared with Fig. 3, as indicated by the b and c axes for clearer representation of the diffusion paths of the lithium ions.

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

The internal structure of the catalyst particle is often of a complex labyrinth-like nature, with interconnected pores of a multiplicity of shapes and sizes, In some cases, the pore size may be less than the mean free path of the molecules, and both molecular and Knudsen diffusion may occur simultaneously. Furthermore, the average length of the diffusion path will be extended as a result of the tortuousity of the channels. In view of the difficulty of precisely defining the pore structure, the particle is assumed to be pseudo-homogeneous in composition, and the diffusion process is characterised by an effective diffusivity D, (equation 10.8). 

A possible layered precursor to the layered nanoproduct conversion mechanism is thus proposed. The silver clusters formed at the initial heating stage by the partial decomposition of AgSR serve as nuclei at further reaction stages, and their distribution naturally inherits the layered pattern of the precursor. The following growth is mainly controlled by the atom concentration and atom diffusion path, which are both constrained by the crystal structure of the precursor [9]. 

The diffusion paths for heat and mass transfer are very small, making micro reactors ideal candidates for heat or mass transfer-limited reactions. 

Diffnsion finxes develop as a result of these concentration gradients. The layer of electrolyte where the concentration changes occur and within which the substances are transported by diffnsion is called the diffusion layer. Its thickness, 5 (the diffusion path length), depends on cell design features and on the intensity of convechve... 

The parameter E, which is called the diffusional field strength, arises only when the Dj values of the cation and anion differ appreciably when they are identical, E is zero. As a result of this field strength in the electrolyte, a diffusional potential difference 9 arises along the diffusion path from x = 0 to = 8 ... 

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