Some remarks about the use of Gordon–Schowalter time derivative in rate-type viscoelastic constitutive equations

The present paper is concerned with the analysis of the thermodynamic consistency of rate-type constitutive equations for viscoelastic fluids that adopt the Gordon–Schowalter time derivative. The choice of the objective time derivative is important not only to assure a mathematically correct modelling and physically realistic description of the viscoelastic behaviour, but also to perform a thermodynamically consistent modelling. It is shown that, for some very popular constitutive equations that adopt this particular family of objective time derivatives (such as the upper-convected Oldroyd fluids), it is impossible to automatically assure that the second law of thermodynamics is satisfied in any process.