Secondary normal stress difference measurement

The normal stresses c,/ cannot be specified on an absolute basis because of the arbitrary hydrostatic pressure in equation 59, but their differences are predicted by continuum mechanics and several molecular theories and can be measured. The primary and secondary normal stress differences are defined as (Th — an and 022 — an respectively. Data are often expressed in terms of the primary normal stress coefficient... 

Thus oscillatory measurements of the primary normal stress difference give the same information as oscillatory shear stress measurements. Oscillatory measurements of the secondary normal stress difference, however, would provide additional... 

For parallel plate geometry, the vertical thrust depends on both primary and secondary normal stress differences. A device for providing this measurement at very high shear rates has been described by Walters. ... 

A combination of these geometries is provided by the plate and truncated cone apparatus of Lxxige, which provides the radial gradient of pressure in the outer cone region as well as the pressure at the center of the truncated (parallel plate) area. From these measurements, both primary and secondary normal stress differences can be obtained in principle preliminary work suggests, however, that the accuracy obtainable for [Pg.107]

Rheological measurements are performed so as to obtain a test fluid s material functions. Under viscometric flows we have seen that the shear viscosity and the primary and secondary normal stress differences suffice to rheologically characterize the fluid. If the flow field is extensional and the material is able to attain a state of dynamic equilibrium, then one measures the extensional viscosity otherwise, we measure the extensional viscosity growth or decay functions. In this section, we will examine steady and dynamic shear plus uniaxial extensional tests, since these make up the majority of routine rheological characterization. 

Most rheological measurements measure quantities associated with simple shear shear viscosity, primary and secondary normal stress differences. There are several test geometries and deformation modes, e.g. parallel-plate simple shear, torsion between parallel plates, torsion between a cone and a plate, rotation between two coaxial cylinders (Couette flow), and axial flow through a capillary (Poiseuille flow). The viscosity can be obtained by simultaneous measurement of the angular velocity of the plate (cylinder, cone) and the torque. The measurements can be carried out at different shear rates under steady-state conditions. A transient experiment is another option from which both y q and ]° can be obtained from creep data (constant stress) or stress relaxation experiment which is often measured after cessation of the steady-state flow (Fig. 6.10). 

Figure 6.11 Cone-plate viscometer allowing measurement of the primary and secondary normal stress differences. Normal force (F) and pressure transducers recording hydrostatic pressures (p,) at different radial positions are shown.

According to this equation, the thrust profile can, in principle, be measured on the upper cone or lower plate. Note that the normal stress differences are assumed to be independent of position. By plotting He0(r) against —ln r/R), a straight line is obtained from whose slope a combination of the primary ( (jxi) - CTee) and secondary (dee - normal stress differences is obtained. Though the pressure profile is difficult to measure, the primary stress difference can be readily determined from the force F exerted on the cone or plate. The value of F is given by... 

Flow into either sharp-edged or tapered die was studied using stress-optical measurements. Distribution of shear stress and normal stress difference was obtained for PS melt — neither stresses nor velocities showed secondary motion. 

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