A MODEL WITH 2 COUPLED MAXWELL MODES

In an effort to quantitatively examine the effect of coupling between multiple relaxation modes, a new model involving two coupled Maxwell m odes is developed as a generalization of the upper-convected Maxwell a nd the Giesekus models. The model contains, in addition to the paramet ers inherent to a Maxwell model with two uncoupled modes (i.e., lambda (1),lambda(2) and eta(1) = G(1) lambda(1), eta(2) = G(2) lambda(2)), a dimensionless coupling coefficient theta that multiplies a quadratic coupling term. In the two characteristic limits theta = 0 or (eta(1),l ambda(1)) = (eta(2),lambda(2)), the Maxwell model with two uncoupled r elaxation modes or the Giesekus constitutive model is obtained, respec tively. The rheological behavior of the model is investigated in the l inear and nonlinear deformation-rate regimes. Calculation of the linea r viscoelastic behavior shows that the linear stress relaxation modulu s is the sum of two decaying exponentials with characteristic times an d preexponential factors that are quite different from lambda(1), lamb da(2) and G(1), G(2), respectively. In slow, slowly varying flows, the zero shear-rate ratio Psi(2)(0)/Psi(1)(0) assumes small negative valu es when theta takes on small positive values. The nonlinear rheologica l behavior of the model is examined under the imposition of shear and extensional flow fields, from both a steady-state and transient perspe ctive. The qualitative behavior observed is remarkably rich in describ ing the experimental trends seen in polymer melts and Boger fluids for a constant value of theta approximate to 0.1. (C) 1996 Society of Rhe ology.