A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts

Abstract

AbstractIn deriving a constitutive equation from a molecular model of polymers in concentrated solutions and melts, Doi and Edwards used a mathematical approximation, the “independent alignment approximation,” which has recently been shown to produce significant error in the particular case of stress relaxation following a double‐step strain in opposite direction. In the present paper, in order to examine the approximation in general cases, we derive a new constitutive equation without using the independent alignment approximation. The new equation is a nonlinear integro‐differential equation and is solved numerically for several cases, i.e., steady shear and elongational flows, and the transient flows after the start of shear and elongation. It is found that, in the cases examined here, the new constitutive equation gives nearly the same results as the old one: the rheological functions calculated from the two theories differ no more than 30%. This substantiates the expectation that the independent alignment approximation does not produce drastic error as long as the flow direction is not reversed.