Rabinowitsch

Franck J and Rabinowitsch E 1934 Some remarks about free radicals and the photochemistry of solutions Trans. Faraday Soc. 30 120-31... 

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. 

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. 

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

When the multiplicity of a complex is the same for ionic or ion-dipole bonds and for covalent bonds, the decision as to which extreme bond type is the more closely approached in any actual case must be made with the aid of less straightforward arguments. Sometimes theoretical energy diagrams can be constructed with sufficient accuracy to decide the question. A discussion of crystals based on the Born-Haber thermochemical cycle has been given by Rabinowitsch and Thilo3), and more accurate but less extensive studies have been made by Sherman and Mayer4). 

The power of this technique is two-fold. Firstly, the viscosity can be measured over a wide range of shear rates. At the tube center, symmetry considerations require that the velocity gradient be zero and hence the shear rate. The shear rate increases as r increases until a maximum is reached at the tube wall. On a theoretical basis alone, the viscosity variation with shear rate can be determined from very low shear rates, theoretically zero, to a maximum shear rate at the wall, yw. The corresponding variation in the viscosity was described above for the power-law model, where it was shown that over the tube radius, the viscosity can vary by several orders of magnitude. The wall shear rate can be found using the Weissen-berg-Rabinowitsch equation ... 

This has led to such cases in the history of chemistry that spectroscopic signals have been unidentified till newly discovered elements was found (e.g. rubidium, caesium, indium, helium, rhenium) or new species (highly ionized atoms, e.g. in northern lights [aura borealis], luminous phenomena in cosmic space and sun aura, such as nebulium , coronium , geocoronium , asterium , which was characterized at first to be new elements see Bowen [1927] Grotrian [1928] Rabinowitsch [1928]). 

Rabinowitsch E (1928) Physikalische Methoden im chemischen Laboratorium. IV. Bedeu-tung der Spektroskopie fur die die chemische Forschung. Z Angew Chem 16 555... 

In order to determine the true shear rate at the wall it is necessary to use the Rabinowitsch-Mooney equation ... 

This material is seen to be shear thinning. It is possible that it may exhibit a yield stress but confirmation of this would require measurements at lower shear rates. Note that the Rabinowitsch-Mooney equation is still valid when a non-zero yield stress occurs. 

When data are available in the form of the flow rate-pressure gradient relationship obtained in a small diameter tube, direct scale-up for flow in larger pipes can be done. It is not necessary to determine the r-y curve with the true value of y calculated from the Rabinowitsch-Mooney equation (equation 3.20). 

Equation 3.29 is helpful in showing how the value of the correction factor in the Rabinowitsch-Mooney equation corresponds to different types of flow behaviour. For a Newtonian fluid, n = 1 and therefore the correction factor has the value unity. Shear thinning behaviour corresponds to < 1 and consequently the correction factor has values greater than unity, showing that the wall shear rate yw is of greater magnitude than the value for Newtonian flow. Similarly, for shear thickening behaviour, yw is of a... 

As part of the Rabinowitsch-Mooney analysis, it was shown that the volumetric flow rate can be written in terms of the shear stress distribution ... 

The occurrence of slip invalidates all normal analyses because they assume that the velocity is zero at the wall. Returning to the Rabinowitsch-Mooney analysis, the total volumetric flow rate for laminar flow in a pipe is given by... 

When trying to determine the flow behaviour of a material suspected of exhibiting wall slip, the procedure is first to establish whether slip occurs and how significant it is. The magnitude of slip is then determined and by subtracting the flow due to slip from the measured flow rate, the genuine flow rate can be determined. The standard Rabinowitsch-Mooney equation can then be used with the corrected flow rates to determine the tw-jw curve. Alternatively, the results can be presented as a plot of tw against the corrected flow characteristic, where the latter is calculated from the corrected value of the flow rate. 

This must be done for each of a range of values of the wall shear stress tw. The standard Rabinowitsch-Mooney equation can then be used with the corrected values of uc ... 

Paneth, F., E. Rabinowitsch u. W. Hacken fiber die Gruppe der fliich-... 

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 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]. 

The slope of this function is the Rabinowitsch [12] correction for the shear rate in terms of the power law parameter n ... 

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