Effects of Interface Velocity on the Stress Tensor in Immiscible Polymer Blends

The total stress tensor for immiscible polymer blends is calculated based on the theoretical expression by Batchelor (1970), and Mellema and Willemse (1983) in the last stage of the stress relaxation under large step shear strains. In this stage, the shape of droplets is spheroid and the retraction of isolated droplets is calculated according to the theory developed by Okamoto et al. (1999). The calculated results are compared with experimental data for a polyisobutylene/polydimethylsiloxane blend. Contribution of the motion of the interface (the interface velocity term) to the total stress tensor in the theoretical expression for the isolated droplets is 37 % - 50 %, which cannot be neglected compared with the contribution of the pressure difference beyond the interface (the Laplace pressure term). The summation of both terms agrees well with the experimental data at step strain γ = 1, in which effects inherent in multiple droplet systems are the smallest. The γ dependence of the reduced stress appearing in the experimental data, which cannot be predicted by the theoretical calculation for the isolated droplets, is qualitatively explained by considering droplet size distribution in the theoretical calculation.