Rabinowitsch-Weissenberg correction

Figure 3.18 Apparent shear rate as a function of the wall stress (tJ. The first derivative of the function is used to perform the Weissenberg-Rabinowitsch correction. The data are for the HDPE resin at 190°C as shown in Fig. 3.17...

Ah is the negative 7-axis intersection. This is independent of the viscosity q, i.e., all straight lines for all different viscosities intersect at the point T=0 and h=-Ah, This is only true for Newtonian fluids or in the case of a Non-Newtonian fluid if the region of the zero shear viscosity is not left in any measurement. Since the shear rate is not constant over the gap, another correction for non-Newtonian fluids, similar to the Weissenberg-Rabinowitsch correction (Eq. 3.5), is necessary ... 

Here aj = M/IttR L is the stress at the inner cylinder and N is the slope of a log-log graph of O vs. M. The corresponding correction for the parallel-disk rheometer is known as the Burgers correction, and is similar to the Weissenberg-Rabinowitsch correction described above for the capillary viscometer ... 

As discussed above, the flow curves of polymer fluids can be obtained by Equations 8.18 and 8.38 (or 8.39), and the viscosities of the fluids can be calculated by Equation 8.41. While deriving these equations, one of the assumptions is that the flow pattern is constant along the pipe. However, in a real capillary flow, the polymer fluid exhibits different flow patterns in the entrance and exit regions of the pipe. For example, the pressure drops at the die entrance and exit regions are different from AP/Z. Therefore, corrections, e.g., Bagley correction, are needed to address the entrance and exit effects. Another assumption is that there is no slip at the wall. However, in a real flow, polymer fluid may slip at the wall and this reduces the shear rate near the wall. The Mooney analysis can be used to address the effect of the wall slip. In addition, the velocity profile shown in Figure 8.13 is a parabolic flow. However, the tme flow in the die orifice is not necessarily a simple parabolic flow, and hence Weissenberg-Rabinowitsch correction often is used to correct the shear rate at the wall for the non-parabohc velocity profile. 

The calculation of the shear rate at the capillary wall, 7 , is computed from the function slope of Fig 3.18 and the apparent shear rate using Eq. 3.36. The derivative of the function appears relatively constant over the shear stress range for Fig. 3.18. Many resin systems will have derivatives that vary from point to point. The corrected viscosity can then be obtained by dividing the shear stress at the wall by the shear rate i ,. Equation 3.36 is known as the Weissenberg-Rabinowitsch equation [9]. 

This rheometer is also similar to the one described in section 3.2.1 except for two differences. Firstly, the capillary used is of very short length and secondly, the polymer is extruded by the use of dead weights (i.e. constant pressure) rather than constant plunger speed. This instrument, popularly known as the Melt Flow Indexer, is very popular in the thermoplastics industry due to its ease of operation and low cost, which more than compensates for ite lack of sophistication. The parameter measured through the melt flow indexer contains mixed information of the elastic and viscous effects of ttie pol)nner. Further, no end loss corrections have been developed for this capillary equipment nor can the melt flow index be easily related to the Weissenberg-Rabinowitsch shear rate expression. 

Plotting T over F produces the true flow curve, which, within the shear rate range in question, is adequately described by the two coefficients Xo and qpi. Correction according to Rabinowitsch/Weissenberg [6] is not necessary, because the material law remains linear within the range ot interest. 

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