Normal stress measurements

Measurements of normal stress differences during steady shear flow, and of normal stress growth approaching steady-state flow and stress relaxation after cessation of flow, provide additional information about nonlinear viscoelastic properties. The conventional identifications of the normal stresses for simple shear have been shown in Fig. 1-16 their orientations in several examples of experimental geometry are sketched in Fig. 5-5. 

Although, in studying linear viscoelastic properties, the geometries of Fig. 5-1 or Fig. 5-5 all yield equivalent information, this is not the case for normal stresses, and different configurations give different combinations of ffn, 0-22, and 0-33. A 

Identification of normal stresses in different experimental geometries, (a), rotation between coaxial cylinders (b), torsion between cone and plate or parallel plates (c) annular axial flow between coaxial cylinders. 

Whorlow [1992] notes that, of the many methods which have been proposed for the measurement of various combinations of the first and second normal stress differences, N and N2 respectively, few can give reliable estimates of N2- Combined pressure gradient and total force measurements in the cone-and-plate geometry, or combined cone-and-plate and plate-plate force measurements, appear to give reliable values [Walters, 1975] and satisfactory results may also be obtained from techniques based on the measurement of the elevation of the surface of a liquid as it fiows down an inclined open duct [Kuo and Tanner, 1974], 

In the work reported by Jackson and Kaye [1966] the spacing, h, between a cone and a plate was varied and the normal force measured as a function of gap size. The same method was used by Marsh and Pearson [1968] who showed that. 

For a detailed and systematic treatment of the various approaches to normal stress measurements, the reader is referred to the text by Walters [1975]. 

---

Description of normal stress measurements on a practical but complex material, paint, is available (150). More recent pubHcations (151—154) give the results of investigations of normal stress differences for a variety of materials. These papers and their references form a useful introduction to the measurement of normal stress differences. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

Figure 5.12 shows JeR obtained by different investigators on a single sample of narrow distribution polystyrene [sample 6a, Mw=860.000, Mw/M = 1.05 (174), polymerized anionically by the Pressure Chemical Company, Pittsburgh, Pennsylvania]. A number of different solvents, temperatures, and methods are represented (175-182). The values rise from below 0.4 at low concentrations, pass through a broad maximum which somewhat exceeds 0.4, then decrease again at high concentrations. Data from dynamic moduli, normal stress measurements, and... 

Again the reader must be warned that a large proportion of the Je° data in the correlation, summarized in Eqs. (5.26) and (5.27) and Tables 5.2 and 5.5, are based on normal stress measurements (total thrust in plate-cone rheometers) with attendant uncertainties about whether limiting behavior was attained. Also, in... 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

Normal stress measurements for some MLC nematics was reported to be consistent with that of a second-order fluid, that the low frequency limit of G /co equaled the low shear limit of N /(dy/dty [36]. Coleman and Markowitz demonstrated that for a second-order fluid in slow Couette flow, the viscoelastic contribution to the normal thrust must have a sign opposite to the inertial contribution on thermodynamic grounds [37]. A textbook by Walters stated that the measurements of first normal stress difference have invariably led to a positive quantity except for one case which was later found to be in error [38]. Adams and Lodge reported the possible observation of a negative value for Nj for solutions of poly isobutylene + decalin [39]. This result was obtained by a combination of obtained from radial... 

Normal stress measurements on concentrated solutions of helical polypeptides were conducted by lizuka [1,42]. However he used these to calculate extinction angles, from which the rotary diffusion constant was deduced, and thence an apparent particle size from tables given by Scheraga [43]. In a personal communication to Kiss and Porter, lizuka commented that he had observed negative normal stresses in solutions of PBLG + Ch Br with concentrations of greater than 10% (i.e. probably liquid crystalline) however he ascribed this to the adhesive force of the solution (E. lizuka, personal communication, April 1977). 

Tomita, Y. and Mochimaru, Y. Normal stress measurement of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 7, (1980) 235-255. 

Correlation Between Steady-Shear and Oscillatory Data. The viscosity function is by far the most widely used and the easiest viscometric function determined experimentally. For dilute polymer solutions dynamic measurements are often preferred over steady-shear normal stress measurements for the determination of fluid elasticity at low deformation rates. The relationship between viscous and elastic properties of polymer liquids is of great interest to polymer rheologists. In recent years, several models have been proposed to predict fluid elasticity from shear viscosity data. 

The shear stress and primary normal stress measurements can be done simultaneously on the sample when it is subjected to unidirectional rotational shear in e gap of a cone and plate viscometer. 

Boger, D.V. and Denn, M.M. (1981) Capillary and slit mefiiods of normal stress measurements, /. Non-Newtonian Fluid Mech., 6,163-85. 

The elasticity of polymer melts is manifested through two material functknis, namely, the primary normal stress coefficient ii and the secondary normal stress coefficient ijia. The secondary normal stress coefficient is not as well duuacter-ized as the primary normal stress coefficient due to its small magnitude. The primary normal stress measurements are themselves difficult and require highly... 

Most common instrument for normal stress measurements Simple working equations homogeneous deformation Nonlinear viscoelasticity G(t, y)... 

Vertical oscillations are always present in rotating members. These can be particularly annoying with normal stress measurements on high viscosity materials. Adams and Lodge give an es-... 

Normal stress measurements versus wall shear stress for a 1 % solution of polyacrylamide at 25°C in annular flows —N2 from axial annular flow, N] from (solid line) tangential annular flow, N from (dashed line) cone and plate, and Ph the hole pressure error. Adapted from Osmers and Lobo (1976),... 

There are two basic designs of drag flow rheometers controlled strain with stress measurement and controlled stress with strain measurement. Below we Hrst discuss strain control and torque measurement (Section 8.2.2) followed by instrument alignment problems (Section 8.2.3) and normal stress measurement (Section 8.2.4). Then we treat special design issues for stress control. Both designs use the same type of environmental control system, as discussed in Section 8.2.6. 

We now present the theory (Davis et al. 1973 Han 1974) that allows one to determine shear stress and first normal stress difference in steady-state shear flow using wall normal stress measurements along the axis of a slit die. Consider a fluid flowing through a slit die having the height h and the width w, and assume that flow has become fully developed. Then, for steady-state fully developed flow, the equations of motion... 

What is the alternative The answer clearly lies in the use of a continuous-flow capillary (or slit) rheometer, which makes use of wall normal stress measurements in the fully developed region of a capillary (or slit) die (see Chapter 5). That is, as long as the wall normal stresses along the axis of a die are linear (i.e., in the fully developed region), a can be calculated from... 

---