Elastic and Flow Properties of Densely Packed Binary Microgel Mixtures with Size and Stiffness Disparities

Densely packed soft microgels (pastes) behave as a yield-stress fluid. They act as soft elastic solids with finite equilibrium shear modulus (G₀) below a critical stress (σ_c) whereas they flow like liquids above σ_c. The effects of size and stiffness heterogeneities in the constituent microgels on the rheological properties of the pastes are revealed using the binary microgel mixtures by an oscillatory rheometer and diffusive wave spectroscopy (DWS). The binary blends with various degrees of size and stiffness disparities are made by mixing the pastes with the same apparent particle-volume fraction (ϕ_eff) at various values of relative weight fraction of soft microgels (f_soft). The G₀–f_soft relations for the soft/hard microgel mixtures are significantly influenced by size disparity: The relations for small size disparities well obey the logarithmic mixing rule, while those for large size disparities have a wide f_soft regime in which G₀ are almost equal to those of the single small-microgel pastes (G_0,small), regardless of whether the small microgels are soft or hard. The characteristic f_soft region with G₀ ≈ G_0,small for the mixtures with large size disparities is attributed to the developed continuous phase of small microgels (overwhelming in number) where the large microgels are discretely dispersed. The steady-state flow behavior of the binary pastes above σ_c obey the classical Hershel–Bulkley (H–B) equation. In each binary paste, the characteristic time (τ_cage) of the fast local dynamics of microgels trapped in the densely packed structures evaluated from DWS is close to the characteristic time (τ_HB) obtained from the parameters in the H–B equation and G₀. This agreement shows that the dynamics of the positional rearrangement of microgels in the steady-state flow is closely related to the fast local dynamics in the quiescent state of the pastes, independently of the size and stiffness disparities in the constituent microgels.