Convective nonlinearities for the orientational tensor order parameter in polymeric systems

Abstract

Nonlinear hydrodynamic equations for polymeric fluids with permanent or transient orientational order are discussed. We start from a description that utilizes the well-known nematohydrodynamic equations for low molecular weight uniaxial nematics. We concentrate on the reversible nonlinearities in the dynamic equation for the orientational tensor order parameter. The non-phenomenological part is unambiguously of the 'corotationally convected' or 'Jaumann' type. This holds also for the case of transient orientational order, which occurs in semi-flexible or rigid polymeric systems in the isotropic phase. The phenomenological part of the (nonlinear) reversible dynamics (flow alignment) is different for the isotropic and uniaxial case (the biaxial case is discussed in an Appendix). The corresponding form of the stress tensor is discussed. A comparison with existing phenomenological and mesoscopic models is given.