Numerical study of suspensions of nucleated capsules at finite inertia

We study the rheology of suspensions of capsules with a rigid nucleus at negligible and finite flow inertia by means of numerical simulations. The capsule membrane is modeled as a thin Neo-Hookean hyperelastic material and the nucleus as a rigid particle with radius equal to half the radius of the undeformed spherical capsules. The fluid and solid motion are coupled with an immersed boundary method, validated for both the deformable membrane and the rigid nucleus. We examine the effect of the Reynolds number, capillary number, and volume fraction on the macroscopic properties of the suspensions, comparing with the case of capsules without nuclei. To explain the rheological measurables, we examine the mean capsule deformation, the mean orientation with respect to the flow direction, and the stress budget. The results indicate that the relative viscosity decreases with the capillary number, i.e., increasing deformability, and increases with inertia. The presence of a nucleus always reduces the membrane deformation. Capsules align more in the flow direction at higher capillary numbers and at higher volume fractions, where we also see a significant portion of them oriented with their longer deformed axis in the spanwise direction. When increasing inertia, the alignment with the flow decreases while more capsules orient in the spanwise direction. The first normal stress difference increases with the capillary number and it is always less for the nucleated capsules. Finally, the relative viscosity and the first normal stress difference increase with the capsule volume fraction, an effect more pronounced for the first normal stress difference.