Penetrant flux

The overall penetration flux, q (Watts/meter2), i.e., heat flux absorbed by the compartment boundaries, averaged spatially over the boundary surfaces, and temporarily over the period of full development ... 

The registration system is sensitive enough to register the penetrating flux about... 

Salicylic acid (SA) Human SC Abdomen, leg Propylene glycol containing drug solution applied to skin mounted on in vitro diffusion cell Penetration flux Differences in flux between sites were observed Correlation found between penetration flux and lipid content no correlation with skin thickness and cell layers. 

D and D, respectively. Then, the local penetrant flux, J, normal D H... 

The movement of the rubbery-solvent interface, S, was governed by the difference between the solvent penetration flux and the dissolution rate, derived earlier. An implicit Crank-Nicholson technique with a fixed grid was used to solve the model equations. A typical concentration profile of the polymer is shown in Fig, 24. Typical Case II behavior was observed. The respective positions of the interfaces R and S are shown in Fig. 25. Typical disentanglement-controlled dissolution was observed. Limited comparisons of the model predictions were made with experimental data for a PMMA-MIBK system. 

The most important characteristic of membranes is their ability to separate different chemical species in view of the different permeation rate they can reach across the selective layer. The different penetrant rates are obtained on the basis of their kinetics, their thermodynamic properties, and the interactions established with the membrane matrix. The driving force of the process is the concentration gradient and, as shown in Fig. 7.1, when this is established across the membrane, the penetrant molecules start to move from the high to the low concentration side according to their ability to diffuse within the matrix. In this view, the thickness of the selective layer also plays a relevant role for the determination of the penetrant flux, because the thinner the layer the lower the distance that must be covered by the molecules within the membrane matrix and the larger the permeation rate. 

Independent of the separation application, membranes are typically required to have a simultaneously high transmembrane flux and large selectivity for the target compounds. To maximize the penetrant flux across the membrane, the following strategies can be pursued ... 

The penneation through inorganic manbranes can be described in terms of transport across porous materials, where a penetrant diffuses through small pores according to the pores characteristics and its affinity with the pore walls. Thus the penetrant flux can be described with different mechanisms, as presented in Fig. 7.12 bulk diffusion, Knndsen diffusion, Knudsen diffusion conpled with surface diffusion, surface diffusion conpled with capillary condensation, and molecular sieving. 

As previously noted, the penetration flux will depend on the concentration gradient between the outer and inner compartments and on the ability of the herbicide molecule to partition between compartments. 

A special coil configuration is used to heat thin strips of metal that caimot be heated efficiently with a coil that encircles the load, as the strip thickness is small compared to the depth of penetration. The transverse flux induction coil is positioned on either side of a strip to produce a uniformly heated strip with good efficiency in a much smaller space than conventional radiant or convective strip heating furnaces (6). 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

Another major difference between the use of X rays and neutrons used as solid state probes is the difference in their penetration depths. This is illustrated by the thickness of materials required to reduce the intensity of a beam by 50%. For an aluminum absorber and wavelengths of about 1.5 A (a common laboratory X-ray wavelength), the figures are 0.02 mm for X rays and 55 mm for neutrons. An obvious consequence of the difference in absorbance is the depth of analysis of bulk materials. X-ray diffraction analysis of materials thicker than 20—50 pm will yield results that are severely surface weighted unless special conditions are employed, whereas internal characteristics of physically large pieces are routinely probed with neutrons. The greater penetration of neutrons also allows one to use thick ancillary devices, such as furnaces or pressure cells, without seriously affecting the quality of diffraction data. Thick-walled devices will absorb most of the X-ray flux, while neutron fluxes hardly will be affected. For this reason, neutron diffraction is better suited than X-ray diffraction for in-situ studies. 

NAA is a quantitative method. Quantification can be performed by comparison to standards or by computation from basic principles (parametric analysis). A certified reference material specifically for trace impurities in silicon is not currently available. Since neutron and y rays are penetrating radiations (free from absorption problems, such as those found in X-ray fluorescence), matrix matching between the sample and the comparator standard is not critical. Biological trace impurities standards (e.g., the National Institute of Standards and Technology Standard Rference Material, SRM 1572 Citrus Leaves) can be used as reference materials. For the parametric analysis many instrumental fiictors, such as the neutron flux density and the efficiency of the detector, must be well known. The activation equation can be used to determine concentrations ... 

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