Superposition of Steady-State Shear Flow and Small-Amplitude Oscillations

Having discussed steady-state shear flow in 6 and small-amplitude oscillatory shearing motion in 7, we now consider a superposition of these two types of flow this type of superposed flow has only recently been studied. 

The function K(t) for this problem, and the corresponding shear stress are assumed to have the form  

In order to describe the problem for the rigid dumbbell suspension, we must begin by solving Eq. (5.1) with K(t) given by Eq. (8.1). A solution of the form 

Some sample curves based on these equations are shown in Figs. 4 and 5. 

Experimental data for polymer solutions have been reported by Osaki, Tamura, Kurata, and Kotaka (60), by Booij (12), and by Macdonald (50). Osaki et al. used polystyrene in toluene, polymethylmethacrylate in diethylphthalate, and poly-n-butylmethacrylate in diethylphthalate. Booij s data were for aluminum dilaurate in decalin and a rubbery ethylene-propylene copolymer in decalin. Macdonald s experiments were performed on several polystyrenes in several Aroclors and on polyisobutylene in Primol. Shortly after the original publication of the Japanese group, Macdonald and Bird (51) showed that a nonlinear viscoelastic constitutive equation was capable of describing quantitatively their data on both the non-Newtonian viscosity and the superposed-flow material functions. Other measurements and continuum model calculations have been described by Booij (12 a). 

---

Superposition of Steady-State Shear Flow and Small-Amplitude Oscillations [Evans, Warner, Ramakka, and Bird (25)]... 

---