Flow–diffusion interface interaction in blends of immiscible polymers

The flow–diffusion interface interaction in ternary mixtures consisting of a two-component polymeric immiscible blend and a simple fluid is investigated under isothermal conditions. A non-linear 3D model that explicitly couples the interface dynamics to the Navier–Stokes–Fick governing equations is derived. The interface is characterized on the microscopic level of description by a distribution function of the unit vector normal to the interface and on the mesoscopic level by a second-order tensor. The model shows that the morphology of the embedded interface is modified by the internal diffusion fluxes as well as by the external flow, and in return, the deformation of the interface changes the behavior of diffusion that may deviate from the Fickean mass transport. In a one-dimensional setting, the nature of propagation of both linear dispersive and nonlinear hyperbolic waves is examined, and explicit formulas for the characteristic speed, phase velocity, and attenuation are provided.