Second-order fluids and the choice of objective derivative

Abstract

We generalize the second-order fluid constitutive model to accommodate a range of possible frame indifferent time derivatives. Using the Gordon--Schowalter derivative, which contains the upper-convected, lower-convected, and corotational (Jaumann-Zaremba) derivatives as subsets, we show how the subjective choice of derivative may change model predictions and we identify features that remain universal independent of this choice. Writing these models in terms of generic coefficients is non-universal and may lead to misinterpretations of flow predictions. However, writing the models in terms of zero-shear material functions or terminal relaxation time reveals universal and robust representations.