Reiner- Rivlin equation

The Reiner-Rivlin equation is based on the assumption that the relationship between the stress and the shear rate does not necessarily have to be linear. The constitutive equation can be written as... 

Because the coefficients of the invariants are not specified, the use of the Reiner-Rivlin equation is rather arbitrary. On the other hand, the time-dependent characteristics of viscoelastic fluids are not described by this equation. Neither are normal stresses in Couette flow correctly described by Eq. (13.3). 

This equation is known as the Reiner-Rivlin equation. For a Pseudoplastic ... 

If we choose the coefficients p and s in (6.1.7) to be nonzero constants, then we arrive at the Reiner-Rivlin model, which additively combines the Newton model with a tensor-quadratic component. In this case the constants p and e are called, respectively, the shear and the dilatational (transverse) viscosity. Equation (6.1.7) permits one to give a qualitative description of specific features of the mechanical behavior of viscoelastic fluids, in particular, the Weissenberg effect (a fluid rises along a rotating shaft instead of flowing away under the action of the centrifugal force). 

This constitutive equation is also known as a Reiner-Rivlin fluid. The Newtonian fluid is simply a special case with t , (Iho, 11 ho) = I. a constant, and r 2 = 0. 

The following form of a constitutive equation is referred to as the Reiner-Rivlin fluid ... 

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