Structure and rheology of suspensions of spherical strain-hardening capsules

We investigate the rheology of strain-hardening spherical capsules, from the dilute tothe concentrated regime under a confined shear flow using three-dimensional numericalsimulations. We consider the effect of capillary number, volume fraction and membraneinextensibility on the particle deformation and on the effective suspension viscosity andnormal stress differences of the suspension. The suspension displays a shear-thinningbehaviour that is a characteristic of soft particles such as emulsion droplets, vesicles,strain-softening capsules and red blood cells. We find that the membrane inextensibilityplays a significant role on the rheology and can almost suppress the shear-thinning. Forconcentrated suspensions a non-monotonic dependence of the normal stress differenceson the membrane inextensibility is observed, reflecting a similar behaviour in the particleshape. The effective suspension viscosity, instead, grows and eventually saturates, for verylarge inextensibilities, approaching the solid particle limit. In essence, our results revealthat strain-hardening capsules share rheological features with both soft and solid particlesdepending on the ratio of the area dilatation to shear elastic modulus. Furthermore, thesuspension viscosity exhibits a universal behaviour for the parameter space defined bythe capillary number and the membrane inextensibility, when introducing the particlegeometrical changes at the steady state in the definition of the volume fraction