Batchelor’s theory extended to elongated cylindrical or ellipsoidal particles

Extensions to Batchelor’s theory have been derived to take into account different shaped particles while relating extensional viscosity enhancement to three parameters — shape, volume fraction and particle aspect ratio. The extended theory now allows calculation of the extensional viscosity enhancement, at a given volume fraction of particles, for either ellipsoidal or cylindrical particles. The formula improves the predictive capability of Batchelor’s theory when compared with measurements found in the literature for different rod-like polymer solutions.