Errors with diffusive systems

Adam et al. carried out systematic measurements of the diffusion coefficient of semi-dilute solutions of polystyrene in benzene using QELS and CGD methods. They found (cf. Fig. 12) that the diffusion coefficients obtained by both methods are equal within experimental error. The diffusion coefficient scales with the concentration as. 67 o.o2 depends only on concentration. These results are identical with those obtained by Munch et al. from QELS experiments performed on the same system PS-benzene (cf. Section D-II) and the results of J. Roots et al. who found for PS-toluene by means of CGD experiments that D c ... 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

Erythrocyte Entrapment of Enzymes. Erythrocytes have been used as carriers for therapeutic enzymes in the treatment of inborn errors (249). Exogenous enzymes encapsulated in erythrocytes may be useful both for dehvery of a given enzyme to the site of its intended function and for the degradation of pathologically elevated, diffusible substances in the plasma. In the use of this approach, it is important to determine that the enzyme is completely internalized without adsorption to the erythrocyte membrane. Since exposed protein on the erythrocyte surface may ehcit an immune response following repeated sensitization with enzyme loaded erythrocytes, an immunologic assessment of each potential system in animal models is required prior to human trials (250). 

In this example, an initial steady-state solution with a = 0 is propagated downstream. At the fourth axial position, the concentration in one cell is increased to 16. This can represent round-off error, a numerical blunder, or the injection of a tracer. Whatever the cause, the magnitude of the upset decreases at downstream points and gradually spreads out due to diffusion in the y-direction. The total quantity of injected material (16 in this case) remains constant. This is how a real system is expected to behave. The solution technique conserves mass and is stable. 

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. 

It should be noted that in a vapour phase the liquid layer on the surface of a sensitive element of the sensor (zinc oxide) must be sufficiently thin, so that it would not produce any influence on the diffusion flux of oxygen through this layer. Possible lack of the film continuity (the presence of voids) does not prevent determination of concentration of oxygen in the bulk of the cell by the vapour - gas method. In this case, one deals with a semi-dry method. On the contrary, the presence of a thick liquid layer causes considerable errors in measuring t, because of different distribution of oxygen in a system gas - liquid layer -semiconductor film (this distribution is close to that in the system semiconductor film - liquid), in addition to substantial slowing down of oxygen diffusion in such systems. 

The sensitivity of diffusion-model output to variations in input has been assessed by workers at Systems Applications, Inc., and at the California Department of Transportation. In each case, reports are in preparation and are therefore not yet available. It is important to distinguish between sensitivity and model performance. True physical or chemical sensitivity that is reflected by the simulation-model equations is a valid reflection of reality. But spurious error propagation through improper numerical integration techniques may be r arded as an artificial sensitivity. Such a distinction must be drawn carefully, lest great sensitivity come to be considered synonymous with unacceptable performance. 

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