Normal Stresses in a Viscoelastic fluid

Apr 2022

non-Newtonian Flow Viscoelastic Fluid Deviatoric Stress 220419 Simple Shear flow A viscoelastic fluid in a simple shear flow produces unequal normal stresses that have non-zero values.

$$P_{xx}\ne P_{yy}\ne P_{zz}$$

In Practice, it is easier to measure the differences between the stresses.

$$\begin{array}{rl}& \text{Primary normal stress difference, }{N}_1=P_{xx}-P_{yy}\\ & \text{Secondary normal stress difference, }{N}_2=P_{yy}-P_{zz}\end{array}$$

When coupled with the Shear rate, the Stress difference is useful to analyse rheological properties.

$$\begin{array}{rl}& \text{Primary normal stress coefficient, }{\psi }_1=\frac{N_1}{({\dot{\gamma }}_{yx}{)}^2}\\ & \text{Secondary normal stress coefficient, }{\psi }_2=\frac{N_2}{({\dot{\gamma }}_{yx}{)}^2}\end{array}$$

Frage: How does the deviatoric stresses relate?

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References

Visco-elastic fluid behaviour