The proper description of viscoelastic forces

The viscoelastic forces that produce the remarkable manifestations illustrated above are properly characterised in shear flow by the so-called first and second normal-stress differences, Ni and N2, which occur in addition to the shear stress CT (with which we are already familiar) —note that occasionally Ni and N2 are called the primary and secondary normal stress differences. The complete stress distribution in a flowing viscoelastic Hquid may be written down formally as follows, 

The viscoelastic equivalents to viscosity—the stress divided by the shear rate—are the so-called first and second normal-stress coefficients, F,and These are given by the first and second normal-stress differences divided by the shear rate squared, so 

Generally speaking, the second normal-stress difference is a fraction of the first usually less than a quarter—and of the opposite sign. 

There are a number of ways in which Ni and Ni can be measured as a fimction of shear rate. The easiest and most convenient measurements can be made using a combination of rotating cone-and-plate and parallel-plate tests. When a viscoelastic liquid is sheared in these geometries, not only is the customary drag force experienced, but a force now arises that tends to push the plates apart. This force, F, when measured, can be used to evaluate the respective normal-stress differences. The following formulas apply to the cone-and-plate, parallel-plate and 

The normal-force differences are evaluated in every case at the edge shear rate, which is given by y = am h. From a combination of two or more of these measurements, Ni and N2 can be separately determined. 

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