Reiner-Rivlin fluid

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). 

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). 

The only other study on flow past spheroidal particles is due to Sigh (1971) who derived an approximate stream function for the flow of a Reiner-Rivlin model fluid. Within the range of applicability, very little departure from the Newtonian kinematics is presented which is consistent with their subsequent experimental observations (Maalouf and Sigli, 1984). 

Sigli. D., Sur le calcul de I ecoulement d un fluide de Reiner-Rivlin autour d un ellipsoide de revolution, C.R. Acad. Sci., Paris 272 1006-1009 (1971). 

The isotropic term in Eq. 79 can be lumped with the pressure, giving the Reiner-Rivlin fluid (RR)... 

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 ... 

---