Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions

We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the “paren functions,” we use these for evaluating the normal stress differences for large amplitude oscillatory shear flow. We find the shapes of the first normal stress difference versus shear rate loops predicted to be reasonable [see Fig. 1(a)]. We find that the second normal stress difference is not proportional to the first, and that its shape differs markedly from that of the first [cf. Fig. 1(a) and (b)]. We discover the same remarkable qualitative similarity between the predictions of the rigid dumbbell model and the corotational Maxwell model for the first normal stress difference. We find no qualitative similarities between the dumbbell and the continuum models for any of the predicted coefficients of the second normal stress differences in large-amplitude oscillatory shear flow.