Diffusion direction

Figure 3. Mitochondrial fatty acid oxidation. Long-chain fatty acids are converted to their CoA-esters as described in the text, and their fatty-acyl-groups transferred to CoA in the matrix by the concerted action of CPT 1, the acylcarnitine/carnitine exchange carrier and CPT (A) as described in the text. Medium-chain and short-chain fatty acids (Cg or less) diffuse directly into the matrix where they are converted to their acyl-CoA esters by a acyl-CoA synthase. The mechanism of p-oxidation is shown below (B). Each cycle of P-oxidation removes -CH2-CH2- as an acetyl unit until the fatty acids are completely converted to acetyl-CoA. The enzymes catalyzing each stage of P-oxidation have different but overlapping specificities. In muscle mitochondria, most acetyl-CoA is oxidized to CO2 and H2O by the citrate cycle (Figure 4) some is converted to acylcamitine by carnitine acetyltransferase (associated with the inner face of the inner membrane) and exported from the matrix. Some acetyl-CoA (if in excess) is hydrolyzed to acetate and CoASH by acetyl-CoA hydrolase in the matrix. Enzymes ...

Desorption of an analyte from the SPME fibre depends on the boiling point of the analyte, the thickness of the coating on the fibre, and the temperature of the injection port. The fibre can immediately be used for a successive analysis. Some modifications of the GC injector or addition of a desorption module are required. It is possible to automate SPME for routine analysis of many compounds by either GC-MS or HPLC. A significant advantage of SPME over LLE is the absence of the solvent peak in SPME chromatograms. SPME eliminates the separate concentration step from the SPE and LLE methods because the analytes diffuse directly into the coating of the SPME device and are concentrated there. 

The creep stress was assumed to be shared between the polymer structure yield stress and the cell gas pressure. A finite difference model was used to model the gas loss rate, and thereby predict the creep curves. In this model the gas diffusion direction was assumed to be perpendicular to the line of action of the compressive stress, as the strain is uniform through the thickness, but the gas pressure varies from the side to the centre of the foam block. In a later variant of the model, the diffusion direction was taken to be parallel to the compressive stress axis. Figure 10 compares experimental creep curves with those predicted for an EVA foam of density 270 kg m used in nmning shoes (90), using the parameters ... 

In an isotropic medium, D is a scalar, which may be constant or dependent on time, space coordinates, and/or concentration. In anisotropic media (such as crystals other than cubic symmetry, i.e., most minerals), however, diffusivity also depends on the diffusion direction. The diffusivity in an anisotropic medium is a second-rank symmetric tensor D that can be represented by a 3 x 3 matrix (Equation 3-25a). The tensor is called the diffusivity tensor. Diffusivity along any given direction can be calculated from the diffusivity tensor (Equation 3-25b). Each element in the tensor may be constant, or dependent on time, space coordinates and/or concentration. 

For three-dimensional diffusion in an anisotropic medium, theoretically it is possible to transform the diffusion equation to a form similar to that in an isotropic system. However, in practice, the transformed equation is rarely used, and diffusion is often simplified to be along the fastest diffusion direction. 

If the compositional difference along the diffusion direction is primarily in one component, and the difference in other components is due to the dilution effect, then diffusion of this component (not necessarily the other components) may be treated as effective binary, and the EBDC can be applied reliably to similar situations. Some examples are a diffusion couple made of dry rhyolite on one half and hydrous rhyolite on the other half, the hydration or dehydration of a silicate melt, and adsorption of a gas component by a glass. 

Fe-Mg interdiffusion in olivine along the c-axis (fastest diffusion direction) is... 

More rigorons treatments include hydrodynamic interaction effects and relate the diffusivity directly to the molecular weight of the polymer chain. The general result is that the diffusivity of polymer chains in solntion is related to the molecular weight of the polymer, M ... 

Glucose cannot diffuse directly into cells, but enters by one of two transport mechanisms a Na+-independent, facilitated diffusion transport system or a Na+-monosaccharide co-transporter system. 

In the third variation a mixture of moisturized green coffee beans and activated carbon is filled into the extractor, and the activated carbon pellets used are just big enough to fit between the beans. For 3 kg of coffee beans, 1 kg of activated carbon is needed. At 220 bar and 90°C the caffeine in the supercritical CO2 diffuses directly out of the beans into the activated carbon. A CO2 circulation is not necessary. The required degree of decaffeination is reached after 6 to 8 hours. After extraction, the beans and activated carbon are separated by a vibrating sieve. 

The data of Table 17.8 exhibit a fairly narrow range of xp, an average of about 4, but there seems to be no pattern to xrn, which is not surprising since the diffusions actually are intermediate between bulk and Knudsen in these cases. In order to be able to calculate the effective diffusivity, it is necessary to know the pore size distribution, the specific surface, the porosity, and bulk diffasivity in the reaction mixture under reaction conditions. Such a calculation is primarily of theoretical interest. Practically it is more useful to simply measure the diffusivity directly, or even better to measure the really pertinent property of catalyst effectiveness as defined next. 

In this process, the net flux of substitutional atoms across the interface plane results in local volume changes (i.e., as a crystal plane is removed by climb, the crystal contracts in a direction normal to the plane). However, free expansion in directions parallel to the interface plane is constrained by the specimen ends, where significant diffusion has not occurred, and by the coherence of the interface between the expanding and contracting regions. Therefore, dimensional changes parallel to the interface (i.e., normal to the diffusion direction) are restricted, and in-plane compatibility stresses are generated. No out-of-plane compatibility stresses develop because the diffusion couple can expand freely in the diffusion direction. 

In diffusion specimens that have a relatively narrow diffusion zone compared to the extent of the specimen in the diffusion direction, compatibility stresses are pure shear stresses, and if the stresses exceed the crystal s yield stress, the onset of plastic flow enables the cross section of the diffusion specimen to remain constant.4... 

When the faster-diffusing component is diffused from the vapor phase into a thin sheet, and the diffusion zone is relatively wide compared to the sheet thickness, the constraints on the expansion parallel to the diffusion interface are greatly reduced. Large specimen expansions normal to the diffusion direction have then been observed [5]. 

In many cases, vacancies are bound to the dislocation core by an attractive binding energy and diffuse along the dislocation more rapidly than in the crystal. Many more vacancies may therefore reach jogs by fast diffusion along the dislocation core than by diffusion directly to them through the crystal. 

Comparisons of estimated diffusivity values on zeolites from sorption uptake measurements and those obtained from direct measurements by nuclear magnetic resonance field gradient techniques have indicated large discrepancies between the two for many systems [10]. In addition, the former method has often resulted in an adsorbate diffusivity directly proportional to the adsorbent crystal size [11]. This led some researchers to believe that the resistance to mass transfer may be confined in a skin at the surface of the adsorbent crystal or pellet (surface barrier) [10,11]. The isothermal surface barrier model, however, failed to describe experimental uptake data quantitatively [10,12]. 

Fig. 17 General scheme of an IWAO design, where the input and output ARROW waveguides and the active membrane and the optical fibers are indicated. Notice that the analyte diffusion direction is transverse to the light transmission direction. L membrane length and optical path length, d membrane thickness...

Regarding the analytical features of IWAOs, the main one is that sensitivity can be improved without simultaneously increasing the response times to achieve the steady-state signal. This configuration allows an analyte diffusion direction transverse to the fight transmission, so the response time is independent of the optical path length. 

SIMS has become one of the most important tools for the characterization of experimental products because of its minimal sample requirements, high spatial resolution, excellent sensitivity, and unsurpassed ability for depth-profile measurements. Most of the experimental work can be split into two different areas. The first consists of studies examining diffusion rates of different elements in minerals or melts under a variety of pressure, temperature, and fluid conditions, typically by using an isotopically enriched tracer. These analyses are done either by cutting a surface parallel to the diffusion direction and taking a traverse of spot analyses (for conditions in which profiles in the tens to hundreds of micrometers are expected) or by depth-profiling in from the mineral surface to depths of as much as 5-10 micrometers. In the latter mode, depth resolution on the tens of nanometer scale is possible (see Chapter 4). The second area is focused on determining partition coefficients for trace elements between different minerals and fluids/melts at specific temperatures, pressures, and fluid conditions, to provide the data needed to interpret trace element contents measured in natural minerals. This type of analysis typically involves spot analysis of mineral run products. 

Equation (8-77) expresses the diffuse radiation leaving 1 which arrives at 2 and which may contribute to a diffuse radiosity of surface 2. The factor 1 - ps represents the fraction absorbed plus the fraction reflected diffusely. The inclusion of this factor is most important because we are considering only diffuse direct exchange, and thus must leave out the specular-reflection contribution... 

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