Viscosity of capsule suspensions: Effects of internal-external viscosity ratio and capsule rupture release

This work explores the variation of viscosity of capsule suspension during the process of capsule rupture and polymer release using the immersed-boundary lattice Boltzmann method. The variation of viscosity is classified into three stages in the rupture process: the deformation stage, the rupture stage, and the stable stage. In the process of polymer release, two new stages of the variation of viscosity emerge: the diffusion stage and the dilution stage. Furthermore, the influence of viscosity ratio ($\lambda$) on the viscosity is investigated. We find that the effective viscosity grows with $\lambda$ and approaches the solid particle limit for very large $\lambda$, reflecting a similar behavior in the capsule shape. Finally, an available law that relates suspension viscosity to $\lambda$, capillary number ($\mathrm{Ca}$), and volume fraction ($\varphi$) is established. The findings of this research have potential applications in fields such as oil exploration and capsule transportation.