| Three-dimensional numerical simulations using immersed-boundary methods are performed to study the rheology of capsule suspensions. Two well-known dynamics of the capsules are the tank-treading and tumbling motions. The motivation of the thesis is twofold: first, to study the micro-macro link between the individual cell dynamics and the rheology of the cell suspension under a dilute condition, and, second, to extend the analysis to a dense suspension in which the multi-body interaction also contributes to the suspension rheology.;A recent theoretical study in the limit of small deformation, supported by experimental work, suggested that the effective viscosity of a vesicle suspension in dilute limit exhibits a singularity in the form of a viscosity minimum at the threshold of the transition between the tank-treading and the tumbling motion. In the first part of the thesis, we extend this study to the dilute suspension of capsules undergoing large deformation. The objective here is to relate the time-dependent rheology with the time-dependent capsule dynamics, and study the role of the tank-treading-to-tumbling transition. We find that the time-averaged rheology obtained for the non-spherical capsules undergoing the unsteady motion is qualitatively similar to that obtained for the spherical capsules undergoing the steady tank-treading motion, and that the tank-treading-to-tumbling transition has only a marginal effect. The time-averaged rheology exhibits a shear viscosity minimum when the capsules are in a swinging motion at high shear rates but not at low shear rates unlike that of a vesicle suspension which exhibits a shear viscosity minimum at the point of transition.;In the second part, we extend our study to dense suspension of initially spherical capsules. We find that the shear viscosity minimum gradually diminishes with increasing capsule volume fraction. We explain this result by decomposing the particle shear stress into elastic and viscous components. The elastic component is observed to increase but the viscous component remains constant with respect to increasing volume fraction. It is also shown that the elastic contribution is shear-thinning, but the viscous contribution is shear-thickening. The deformation and orientation dynamics of the capsules in dense suspension are also presented. Non-trivial results for the normal stress differences and particle pressure are also analysed. |
