Constitutive equations based on the transient network concept

A consitutive theory for polymetric liquids based on the transient network concept is developed, following Wiegel and Jongschaap. The Phan-Thien-Tanner equation is shown to follow from the general theory with two critical assumption, one of these is quasi-equilibrium of the internal structure, which preludes consistency of application in ”fast flows“. The Marrucci model can be made consistent with the general format with a small change in the kinetic equation that can be deduced from asymptotic behaviour and leaves the steady viscometric behavior unchanged. The simplest genaral formulation requires the linear viscoelastic spectrum and two parameters; the latter cannot be determined uniquely from steady viscometric flow data.