Numerical simulations of the polydisperse droplet size distribution of disperse blends in complex flow

The blend morphology model developed by Wong et al. (Rheologica Acta, 2019), based on Peters et al. (J Rheol 45(3):659–689, 2001), is used to investigate the development of the polydispersity of the disperse polymer blend morphology in complex flow. First, the model is extended with additional morphological states. The extended model is tested for simple shear flow, where it is found that the droplet size distribution does not simply scale with the shear rate, because this scaling does not hold for coalescing droplets. Subsequently, the model is applied to Poiseuille flow, showing formation of distinct layers, which occurs in realistic pressure-driven flows. Finally, the model is applied on an eccentric cylinder flow, where histograms are made of the average droplet size throughout the domain. It is observed that outer cylinder rotation results in narrow distributions where the small droplets are relatively large, whereas inner cylinder rotation results in broad distributions where the small droplets are significantly smaller than in the case of outer cylinder rotation. Eccentricity seems to only have a minor effect if the maximum shear rate is held constant. The flow profile and history in combination with the maximum shear rate strongly determine how the polydisperse droplet size distribution develops