The Rabinowitsch Correction

The Rabinowitsch correction accounts for the fact that the true shear rate is often larger (because of shear thinning) than the apparent shear rate for non-Newtonian materials. Hence, for any non-Newtonian fluid the expression for the wall shear rate is given not by Eq. (17.11), but as 

Note that the shear rate is always maximum at the wall, and the fluid velocity is always zero at the wall. On the contrary, the shear rate is zero and the velocity is maximum at the ceuter of the capillary (Eig. 17.4). 

Just to give an idea how different are the apparent and true shear rates, we will notice that the higher the shear thinning effect, the larger the difference. For example, at the power-law index n = 0.8, the difference in shear rates and, hence, apparent and true viscosities is 6.25%. For n = 0.2, the difference is 100%. 

The following figure (Fig. 17.5) shows apparent and corrected shear rates. 

The upper limit on the shear rate in capillary viscometers is about 10 -10 s and the lower limit is about 1-10 s . 

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Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

The ratio (3 + l)/4n is called the Rabinowitsch Correction Factor and it is used to convert Newtonian shear rates to true shear rates. 

The Rabinowitsch equation has been used in the long capillary viscometry data found in Appendix A. Figure E3.1 shows long capillary tw vs. TH. and rw vs. yw results with and without the Rabinowitsch correction. 

The rheological properties of the polymers reported in Table A.l were measured with a capillary die with diameter of 0.030 in or 0.050 in, and with LID from 33 to 40. At processing temperatures, the effect of the entrance pressure could be neglected. The shear-rate dependence of viscosity is obtained by applying the Rabinowitsch correction. 

The Rabinowitsch correction and the velocity profile are simple analytical functions of the power law exponent n. A schematic diagram of velocity profiles for power law fluids is shown in Figure 13.6. 

Viscosity calculations are done in seconds and corrections such as the Rabinowitsch correction shown below are conveniently used. 

Of course, polymier melts are non-Newtonian due to their shear-thinning behavior. The value calculated from Eq. (6.1) must be corrected for the shear rate at the wall, which is higher for a polymier melt than that calculated by Eq. (6.1). This method is known as the Rabinowitsch correction and is based on determination of viscosity at a location inside the flow channel as opposed to the wall. At a representative location, Newtonian and non-Newtonian shear rates coincide. This location is at r = nR/4, where the pressure transducer should be located to measure the pressure drop. Another correction has to be made for other pressure losses it is called the Bagley correction. PI... 

As mentioned earlier, calculations from measurements are always made on the basis of Newtonian behaviour. This results in apparent quantities which have to be corrected. These corrections are necessary because of the reduced wall adhesion of many polymers (especially with a large filler content), and to this end the Rabinowitsch correction is applied to the shear rate. Also, owing to pressure losses on entry into the capillaries (when measuring with a capillary viscometer), the Bagley correction is applied to the shear stress T. 

Correction to the shear rate is necessitated by the fact that unlike in isothermal Newtonian flow where the velocity distribution from wall to wall in a tube is parabolic, nonparabolic velocity profile develops in non-Newtonian flow. The Rabinowitsch correction [21] is applied to shear rate to eliminate this error as follows ... 

Exatr k 2. The researchers at Crud Chemicals have obtained good data on a polygunk solution from their capillary rheometer. Unfortunately, they don t undeistand the Rabinowitsch correction, so they don t apply it, and the relation that they report as being viscosity vs. shear rate is really apparent viscosity vs. apparent shear rate ... 

Collins et al., (Polymer Handbook, 3d ed., J. Brandrup and E. H. Immergut (eds.), Wiley, New York, 1989, p. V/67-68) give apparent viscosities Va = T /r vs. r for a variety of PVCs at different temperatures. For a particular LVN = [t ] polymer, apply the Rabinowitsch correction at each temperature to get the true viscosity vs. shear rate relation. 

What is the Rabinowitsch correction factor for a power-law fluid ... 

A capillary rheometer was used for the viscosity measurements with a 1.2mm diameter die (L/D of 33) at 250°C. The Rabinowitsch correction was applied on each measurement to calculate true shear rate and viscosity. 

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