Oldroyd B, and not A?

John Hinch

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

Abstract

Oldroyd’s 1950 paper On the Formulation of Rheological Equations of State [1] is examined 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.

[1] J. G. Oldroyd (1950) On the Formulation of Rheological Equations of State. Proc. Royal Soc. A200, 523—541

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