Epilogue

A unified field theory for viscoelastic, in particular, nonlinear viscoelastic fluids along the lines of the Navier–Stokes equations for Newtonian fluids is still lacking. Several constitutive structures popularly used are subject to Hadamard and dissipative instabilities as a result of the omission of some fundamental continuum mechanics principles in their derivation as well as thermodynamic principles. Naturally, they have a bearing on the ability of the constitutive formulations in predicting flows in general geometries and for high We. A number of constitutive equations that may be stable in the Hadamard and dissipative sense and are compliant with the principles of thermodynamics predict zero second normal stress differences and thereby cannot be used in describing the transversal field in flows in tubes of arbitrary cross-section. © 2014, The Author(s).