A finitely extensible bead-spring chain model for dilute polymer solutions

Abstract The FENE-P dumbbell, that is, the finitely extensible non-linear elastic dumbbell with the Peterlin approximation, has been used extensively to describe the rheological behavior of dilute polymer solutions. The model is, however, severely limited, since it cannot describe the broad distribution of relaxation times that real polymer molecules possess. Hence, it is important to extend the model to a chain of finitely extensible springs. The FENE-P chain, however, has not been as widely used, presumably because of the large number of coupled equations that must be solved simultaneously in order to calculate the stress tensor. We present here a new model, the FENE-PM chain, as an alternative to the FENE-P chain. The stress tensor for the FENE-PM chain is calculated from a much smaller set of equations than the FENE-P and at the same time yields nearly the same results for the material properties in shear and elongational flow as the FENE-P. The reduced number of equations greatly expedites calculations for longer chains.