Transportiveness, discretization

In addition to screening molecules for intestinal absorption, Caco-2 cells have also been used to study mechanisms of drug transport. For many compounds, intestinal permeation involves a transporter to either aid or limit transepithelial transport. The value of Caco-2 cells in this type of studies is due to the fact that these cells express various membrane transporters relevant to drug absorption.1719-23,28,30 However, when interpreting results of studies that involve carrier-mediated transport, discretion, and scaling factors may be required because of the difference in expression level of transporters between in vitro and in vivo systems.12 Another important consideration in carrier-mediated transport studies is that some transport systems in Caco-2 cells may achieve maximal expression level at different days in culture.17,21,38,74 Thus, validation of Caco-2 cells for mechanistic studies should include the identification of the time for optimal expression of transporters as well as the qualitative evaluation of the transporters to establish that they are representative of the native intestinal transporters. 

Extension of the streamline Petrov -Galerkin method to transient heat transport problems by a space-time least-squares procedure is reported by Nguen and Reynen (1984). The close relationship between SUPG and the least-squares finite element discretizations is discussed in Chapter 4. An analogous transient upwinding scheme, based on the previously described 0 time-stepping technique, can also be developed (Zienkiewicz and Taylor, 1994). 

Fig. 25. Reverse osmosis, ultrafiltration, microfiltration, and conventional filtration are related processes differing principally in the average pore diameter of the membrane filter. Reverse osmosis membranes are so dense that discrete pores do not exist transport occurs via statistically distributed free volume areas. The relative size of different solutes removed by each class of membrane is illustrated in this schematic.

The discrete distance option of SCREEN allows the user to input specific distances. Any number of distances (s 1 meter) can be input by the user and the maximum concentration for each distance will be calculated. The user will always be given this option whether or not the automated distance array option is used. The option is terminated by entering a distance of zero. SCREEN will accept distances out to 100 km for long-range transport estimates with the discrete distance option. However, for distances greater than 50 km, SCREEN sets the minimum 10 meter wind speed at 2 m/s to avoid unrealistic transport times. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

Davenport [1] has listed more than 60 major leaks of flammable materials, most of which resulted in serious fires or unconfined vapor cloud explosions. Table 9-1, derived from his data, classifies the leak by point of origin and shows that pipe failures accounted for half the failures— more than half if we exclude transport containers. It is therefore important to know why pipe failures occur. Following, a number of typical failures (or near failures) are discussed. These and other failures, summarized in References 2 and 3, show that by far the biggest single cause of pipe failures has been the failure of construction teams to follow instructions or to do well what was left to their discretion. The most effective way of reducing pipe failures is to ... 

In the very early stages of oxidation the oxide layer is discontinuous both kinetic and electron microscope" studies have shown that oxidation commences by the lateral extension of discrete oxide nuclei. It is only once these interlace that the direction of mass transport becomes of importance. In the majority of cases the metal then diffuses across the oxide layer in the form of cations and electrons (cationic diffusion), or as with the heavy metal oxides, oxygen may diffuse as ions with a flow of electrons in the reverse direction (anionic diffusion). The number of metals oxidising by both cationic and anionic diffusion is believed to be small, since a favourable energy of activation for one ion generally means an unfavourable value for the other... 

The term numerical diffusion describes the effect of artificial diffusive fluxes which are induced by discretization errors. This effect becomes visible when the transport of quantities with small diffusivities [with the exact meaning of small yet to be specified in Eq. (42)] is considered. In macroscopic systems such small diffusivities are rarely found, at least when being looked at from a phenomenological point of view. The reason for the reduced importance of numerical diffusion in many macroscopic systems lies in the turbulent nature of most macro flows. The turbulent velocity fluctuations induce an effective diffusivity of comparatively large magnitude which includes transport effects due to turbulent eddies [1]. The effective diffusivity often dominates the numerical diffusivity. In contrast, micro flows are often laminar, and especially for liquid flows numerical diffusion can become the major effect limiting the accuracy of the model predictions. 

Via Eq. (136) the kinematic condition Eq. (131) is fulfilled automatically. Furthermore, a conservative discretization of the transport equation such as achieved with the FVM method guarantees local mass conservation for the two phases separately. With a description based on the volume fraction fimction, the two fluids can be regarded as a single fluid with spatially varying density and viscosity, according to... 

When the transport equation for c is solved with a discretization scheme such as upwind, artificial diffusive fluxes are induced, effecting a smearing of the interface. When these diffusive fluxes are significant on the time-scale of the simulation, the information on the location of different fluid volumes is lost. The use of higher order discretization schemes is usually not sufficient to reduce the artificial smearing of the interface to a tolerable level. Hence special methods are used to guarantee that a physically reasonable distribution of the volume fraction field is maintained. 

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