Apparent flow curve

Fig. 11-30. Apparent flow curves of differeni polymers with the same MFI (at the intersection point).

As a point of departure for finding the law of flow with which to approximate ceramic extrusion compounds in the subject range of shear rates, the apparent flow curve can be plotted to obtain a purely qualitative assertion. 

Fig. 6 Apparent flow curves for typical clay-base ceramic compounds...

Figure 6 shows the apparent flow curves of some typical clay-base ceramic bodies, all of them are linear. By extrapolating the apparent flow curves to F 0 [1/s] - and in this case extrapolation is certainly reliable, because the measured values for Fg extend down to 0.01 1/s. The curves have an axis intercept, meaning that the compounds have a yield value, Xo- That, in turn, means that plug flow or block flow can be expected, if the yield point is fallen below see Fig. 8. This type of flow begins at the center of flow, because that is where the shear stresses are smaller than Xo, as can be seen by transforming equation 2 [7], for r

Fig. 7 Apparent flow curves for different tube diameters...

As indicated in Fig. 7, the apparent flow curve allows no geometry independent representation of the coefficients of the flow law. The yield limit, as well as the viscosity, which is determined from the slope of the curve, show different values for all three different barrel diameters. Only a geometry-independent manner of material-law representation can serve as a material-descriptive basis for calculating complicated geometries such as... 

Thus, within the shear rate range in question, the following material behavior can be derived from the apparent flow curve, as confirmed for aU clay-ceramic extrusion compounds investigated to date Bingham body with shear flow (Qs) and core flow (Qk), plus an additional slippage fraction (Qg) in the flow proflle. 

Several phenomena which make the extrusion of ceramic compounds easy or difficult result in characteristic pressure-time curves p(t) and the resultant apparent flow curves c(t). Some examples of these phenomena are shown in Fig. 5. 

Case 1 in Fig. 5 shows effects caused by material inhomogeneities resulting from fluctuations in concentration, local differences in particle size distribution and the presence of entrapped air. The fluctuations of the measured pressure-time curves do not produce an unequivocal apparent flow curve. Only a more or less broad flow range can be determined. 

A complete determination with the capillary rheometer includes the plotting of apparent flow curves with several dies having different lengths and diameters. This enables several corrections to be carried out, e.g. the Bag-ley correction, to separate the input pressure loss from the flow resistance inside the die the Weihenberg-Rabinowitsch correction to determine the true shear rate, and the Mooney correction to determine wall slippage speed [19, 20], and therefore the differentiated determination of the material s flow properties and the formulation of the material law. 

Fig. 7 Apparent flow curves and Bagley-corrected flow curves for ceramic compound C (aluminium oxide with ammonium alginate)...

The particular ESM extruder was modified in such a manner that it can be used with a measuring barrel serving as a large capillary rheometer, whereby an auger in lieu of a pressure piston forces the material into the nozzle. This means that the pressure drop is measured analogously to the capillary rheometer. The results of this test produce the yield point and the apparent flow curve of the body, amongst other readings. 

Determine the apparent flow curve for the sample using at least two different die lengths (three or more improves accuracy). The same apparent shear rate points must be used for all... 

Brunn, P. O., Wunderlich, T. The role of the mathematical mean value theorem in rheometry an easy way to convert apparent flow curves into exact ones. RheoL Acta (2000) 39, pp. 384-391... 

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