Abstract." An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namely $12 (7)= 7-a(7-1) (a = 0 for 7 --< 1, a = 1 for 7 => 1) for the mirroring of the viscosities, $12(7 ) = 7-a(7-k2/7) (a = 0 for 7 = k, a = 1 for 7 >-k) for the mirroring of the first normal-stress coefficients, and SI2 (7) = ½ 7 {1 -erf[ln (7/2 I/k)/2V2~k]} for the third relation. Here 7 denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value of k is used.
This investigation concerns the important class of fluids whose rheological properties are described by a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type. The first Cox–Merz relation is closely approximated by such a fluid if its nonlinearity in shear can be described by the strain measure $ S_{12} (\gamma) = \int_0^\gamma {J_0} (\upsilon)dv $, irrespective of the distribution of its relaxation times and, hence, its linear viscoelastic properties. Here γ equals the shear strain and J0 the zeroth‐order Bessel function. The second Cox–Merz relation is met by materials with a different nonlinearity, namely S12(γ) = Si(γ), where Si is the sine integral. Experimental data on melts of a polystyrene and a low‐density polyethylene sample were utilized to demonstrate that both Cox–Merz relations cannot hold simultaneously.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.