Artificial diffusive flux

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. 

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. 

Figure 10 shows that for the uptake of Pb(II) by C. kesslerii in an artificial freshwater, the observed permeability is four orders of magnitude lower than the value of the calculated minimum limiting diffusive flux, indicating that... 

The parallel artificial membrane permeability assay (PAMPA) is a recent development in the area of artificial membranes that appears to offer considerable potential. Measuring the flux values (membrane permeation levels) of a range of test compounds by PAMPA and relating these values to the flux curves obtained in Caco-2 studies have shown good correlations, indicating that the PAMPA assay could be a good alternative to Caco-2 cells for the measurement of passively diffusing compounds. 

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