A Test Case for Predicting the Rheological Properties of Polymeric Liquids: the Multiple Coupled Maxwell Modes Model
In this work, the behavior of the multiple coupled Maxwell modes (MCMM) model is examined with regard to the rheological properties of polymer melts in diverse flow fields, including (i) transient, (ii) steady-state shear flow, (iii) small-amplitude oscillatory shear flow, and (iv) transient uniaxial elongational flow. This model is specialized to the case of pair-wise coupling, i.e., each mode interacts with only one other mode. Consequently, each pair of modes acts independently of the others. For a typical polymer melt of industrial interest, a simple optimization technique is developed for determining the number of independent mode pairs, as well as precise values for the corresponding parameters.
The goal of this ongoing study is to fit the parameters of various rheological models using a limited number of simple, standard experiments, and then to see whether or not the models can predict data taken from more complicated experiments. In this paper, only the first step is taken in this direction: we examine for one particularly promising rheological model, the MCMM model (but herein restricted to pair-wise coupling), whether or not it can achieve this goal. This restricted model is chosen because it mimics the effect of pair-wise coupling between relaxation modes that is prevalent in current rheological models. Using this model as a test case allows the optimization technique and analytical methodology for achieving the overall goal to be developed. The outcome of this study with regard to developing the methodology was successful, but the particular model chosen, written in terms of coupled Maxwell modes with pair-wise coupling, is not general enough to predict well typical polymer melt rheological behavior.
B. Jiang, P. Kamerkar, D. J. Keffer, B. J. Edwards, A test case for predicting the rheological properties of polymeric liquids: the multiple coupled Maxwell modes model, Journal of Non-Newtonian Fluid Mechanics, Volume 120, Issues 1-3, 3rd International workshop on Nonequilibrium Thermodynamics and Complex Fluids, 1 July 2004, Pages 11-32, ISSN 0377-0257, DOI: 10.1016/j.jnnfm.2004.02.007. (http://www.sciencedirect.com/science/article/B6TGV-4CRY6XW-1/2/09b0da7eac64eaa90c26314ef3cf69a9)