Rheological effects in the presence of depleted layers

How the C(r) profiles are used in the general case to calculate effective viscosity and velocity enhancement factors as functions of flow rate in a capillary will not be considered, but this is fully presented elsewhere (Sorbie, 1989, 1990). 

Simply note that the general hydrodynamic problem of depleted layer flow including shear effects is a highly non-linear problem which must be solved using an iterative numerical scheme. Using a Carreau A curve based on experimental data for xanthan and an Auvray-type model of the tube concentration profile, calculations have been performed of rj ff as a function of 7n by Sorbie (1989, 1990), where is the Newtonian shear rate in a capillary and is given by 

This calculation of the single-tube hydrodynamic problem has been incorporated into network calculations (Sorbie, 1989, 1990) of the same type as discussed in the previous section. The apparent viscosity for the 

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