Prediction of equilibrium polymer blend morphology in dispersed two-phase flow and comparison with experiment

A theory is developed to predict equilibrium polymer blend morphology in dispersed two-phase flow in terms of the viscosity ratio and blend ratio of the constituent components. We formulated a system of equations for the 'One-Cell Model,' describing the situation where a spherical droplet of one liquid is dispersed in another liquid, by first considering a pair of Newtonian liquids and then a pair of truncated power-law fluids. The question posed was: which of the two Liquids, A or B, will form a droplet dispersed in another liquid? Finite element method was employed to calculate the rate of the energy dissipated per unit volume when a unit cell, having either Morphology I or Morphology II, was subjected to steady-state simple shear flow, where Morphology I has a droplet of liquid A dispersed in the matrix phase of Liquid B and Morphology II has a droplet of liquid B dispersed in the matrix phase of liquid A. We used a criterion that the morphology that requires a lower rate of the energy dissipated per unit volume in dispersed two-phase flow is an equilibrium polymer blend morphology. In so doing, we determined the blend composition, at which a matrix inversion takes place, in terms of the viscosity ratio of the constituent components. Theoretically predicted blend morphologies compared favorably with experimental results.