Rabinowitsch correction

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. 

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...

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. 

Fig. E3.1 Shear stress vs. shear rate with and without Rabinowitsch correction. [Courtesy of V. Tan, Polymer Processing Institute (PPI), Newark, NJ.]...

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. 

Figure 3. Viscosity data for a commercial polycarbonate resin, LEXAN 135-111, at 250°C. Key , apparent viscosity Rabinowitsch corrected viscosity.

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... 

Rabinowitsch correction, 626, 629 Radiant energy, 614 Radiation, diffuse, 615 Radiation, direct, 614 Radiation, total solar, 615 Radical mechanism, 497 Railing system, 225, 253, 258, 264, 276, 303-310 Ramie, 101, 110... 

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 ... 

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. 

The difference between single and twin-bore capillary rheometers (Fig. 9) cannot be dealt with in this contribution. Basically this is a matter of being able to make the so-called Bagley correction with less effort and fewer errors. Likewise, no reference can be made here as to how dilatant respectively structural viscose behaviour (Rabinowitsch correction) and the strain properties of ceramic bodies or wall slipping effects (according to the Mooney method) can be determined with the capillary rheometer. 

Rabinowitsch correction n. The correction factor derived by Rabinowitsch (1929) applied to the Newtonian shear rate at the wall of a circular tube (including capillary) through which a non-Newtonian liquid is flowing, gives the true shear rate at the wall. For pseudoplastic liquids such as paints and some polymer melts the correction is always an increase. If the fluid obeys the power law it reduces to a simple correction factor (3n+ l)/4n, where n is the flow-behavior index of the liquid. Munson BR, Young DF, Okiishi TH (2005) Fundamentals of fluid mechanics. John Wiley and Sons, New York. Harper CA (ed) (2002) Handbook of plastics, elastomers and composites, 4th edn. McGraw-Hill, New York. 

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 ... 

If the capillary rheometer is used to compare different polymers, it is not necessary to go through the various correction procedures. However, if one wants to know the absolute values of the viscosity, it is important to apply the various correction factors. The most important corrections are the correction of the shear rate for non-Newtonian fluid behavior (often referred to as Rabinowitsch correction) and the correction of the shear stress for entrance effects (often referred to as Bagley correction). These are the most common corrections applied to capillary rheometers. Other corrections that are sometimes considered are corrections for viscous heating, corrections for the effect of pressure on viscosity, corrections for compressibility, correction for time effects, etc. If many corrections are applied to the data, the whole measurement and data analysis procedure can become very complex and time consuming. 

Capillary and slit-die rheometers are used to determine the dependency of viscosity on shear rate. Since most molten polymers exhibit non-Newtonian behavior, it is important to be able to characterize this behavior. Measurements are made using a piston-driven cylinder that drives the molten polymer through a die of precise dimensions. The pressure drop across the die is measured, as is the flow rate through the die. Temperature is precisely controlled throughout the measurement. This test yields precise viscosity measurements as a function of temperature and shear rate. However, measurements tend to have artifacts in them, which need to be corrected in order to obtain true viscosity using Bagley and Rabinowitsch corrections. Capillary rheometers are also used to determine the effects of slip, a phenomenon in which the velocity of the melt at the capillary wall is nonzero. Slip has important implications for highly filled materials. 

The flow behavior of non-Newtonian fluids is usually described by expressing either shear rate or viscosity as a function of shear stress. Absolute viscometers, either capillary or rotational, are used to perform the necessary measurements. In the capillary viscometer, the flow rate is measured as a function of applied pressure. Apparent viscosities calculated by means of Poiseuille s relation [Eq. (9)], are converted to true viscosities using the Weissen-berg-Rabinowitsch correction... 

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 ... 

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