Scale of inhomogeneity

The membranes to be considered here may be divided into three classes according to the scale of inhomogeneity which is reflected in their sorption and transport properties ... 

The Gaussian random coil model is appropriate when the scale of inhomogeneity (e.g., the interfacial thickness) is large compared with the length of a bond, b, and the range of interactions, j/. To handle the case where this is not tme, a lattice model has been proposed by Helfand [202-205], in the spirit of the Hory-Huggins approach [206]. For infinite molecular weights, he obtained ... 

We note that there is still much larger difference between the different flasks readings that can be accounted for by the within-flask repeatability. Therefore we press onward to consider another possible cause of the variation in this case we consider the possibility of inhomogeneity of the sample, at a scale not affected by grinding. For example, the sample might contain small specks of material that are too small to be ground further,... 

By definition, LES is inhomogeneous at the scale of the filter. Thus, to simplify the notation, hereinafter we will omit the explicit dependence on x and t. 

As discussed in Chapter 7, when modeling inhomogeneous flows the value of At must be chosen also to be smaller than the minimum convective and diffusive time scales of the flow. 

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