We study the transient and steady shear rheology of rigid particle suspensions in Boger fluids via complete 3D numerical simulations and experiments. We calculate the transient per-particle extra viscosity and primary stress coefficients for suspensions at different particle volume fractions ϕ for a range of Weissenberg numbers (Wi). The per-particle viscosity (ηp) and the primary normal coefficient (ψ1p) increase monotonically to steady state in body-fitted (BF) simulations (for dilute suspensions) and immersed boundary (IB) simulations (for nondilute suspensions). We also present experimental measurements including small amplitude oscillatory shear, steady shear, and transient shear measurements at different particle volume fraction suspensions in a Boger fluid. The simulations and experiments suggest that longer strains are needed to achieve steady state at higher ϕ and Wi. We also show the comparison of the BF and the IB simulations with experimental data for the per-particle viscosity and find excellent quantitative agreement between simulations and experiments at Wi=3 but the IB simulations underpredict the steady values at higher Wi=6. Nevertheless, the IB simulations show an increase in the per-particle viscosity with ϕ as witnessed in the experiments. To understand this behavior, we examine the particle-induced fluid stress (PIFS) and the stresslet contributions using a novel method developed for the IB simulations in this work. We find that the PIFS is independent of ϕ but the stresslet values increase with ϕ. Thus, the particle-particle hydrodynamic interactions in nondilute suspensions affect the stresslet and, in turn, the per-particle viscosity at a given Wi.

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