Flow and mass transport in blends of immiscible viscoelastic polymers

The purpose of this paper is to derive a nonlinear 3D model that investigates, on two levels of description, the flow–diffusion–structure interaction occurring in mixtures consisting of a Newtonian fluid and a blend of immiscible viscoelastic polymers embedding an interface. The internal structure is characterized on the kinetic level of description by two distribution functions and on the mesoscopic level by a scalar and two symmetric second-order tensors. The morphology of the interface and the conformation of the macromolecules are found to be strongly dependent on the flow and diffusion. In return, the behavior of the flow and mass transport are shown to be influenced by the deformation of the internal structure. In the absence of flow, the behavior of diffusion is examined in more detail, and the occurrence of Non-Fickian mass transport is discussed. The dimensionless form of the governing equations includes three Deborah numbers and three coupling constants. The nature of propagation of both nonlinear hyperbolic and linear dispersive waves is examined and explicit formulas for the characteristic speed, phase velocity, and attenuation are provided. The stability conditions determine the range of validity of the kinetic coefficients involved in the model equations.