Oldroyd B, and not A?

We examine Oldroyd’s 1950 paper On the Formulation of Rheological Equations of State (Oldroyd, 1950) in which he introduced the upper and lower convected time-derivatives, along with the Oldroyd-A and Oldroyd-B model fluids. Those developments are placed in context of prior ideas and his own subsequent papers on constitutive equations. The choice between the A and B models is addressed by looking at micro-structural studies, finding that something in between is appropriate. Finally some refinements are discussed in terms of the elastic-dumbbell model. •Oldroyd’s 1950 paper.•Derivation of upper and lower convected time-derivatives.•Choice between Oldroyd-B and Oldroyd-A.•Insights from micro-structural studies.•Refinements from elastic-dumbbell model.