Coleman-Noll second-order fluid

Note that since m(s) and a( i, 2) are functions only of time y, then t]q, y3, and v are constants. A material that can be represented by the constitutive equation given in Eq. (3.76) is called a Coleman-Noll second-order fluid (Coleman and Markovitz 1964 Truesdell and Noll 1965). For steady-state simple shear flow, Eq. (3.76) yields... 

Coleman,B D., Noll,W. Simple fluids with fading memory, pp. 530-552. In Proc. of the International Symposium on Second-Order Effects in Elasticity, Plasticity, and Fluid Dynamics, Haifa. New York Pergamon Press 1962. 

The first of these relations was noted by Lodge [(46), Eq. (6.43)] and by Williams and Bird (77) as a result of the study of two different empirical constitutive equations. Later Spriggs (70) obtained Eqs. (7.22) and (7.23) from the Coleman and Noll (21) theory of second-order viscoelasticity. Eqs. (7.22) and (7.23) indicate that no additional information about fluids can be obtained from normal stress oscillatory measurements than has not already been obtained by shear stress oscillatory data. Eq. (7.24) seems to be new and is probably specific to rigid dumbbell suspensions. 

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