Shear viscosity scaling of granular suspensions across semi-dilute to dense regimes

Herein we present evidence of a semi-dilute-dense behavior transition in suspensions as the result of a thorough study combining both experiments and numerical results. Following an extensive experimental validation, we perform constant-volume shearing simulations of non-Brownian granular suspensions using the discrete element method coupled with the lattice Boltzmann method. We choose a wide range of solid fractions, shear rates, fluid viscosities, particle sizes, and inter-particle frictional coefficients to obtain a scaling solution for the viscous behaviour of suspensions in both dilute and dense regimes. This result demonstrates that, with a proposed dilute-dense transitional solid fraction, $phi_d$, there exists a strong correlation between the inverse relative viscosity and the shear stress. This work incorporates both the $phi$-dependence and the $dot{gamma}$-dependence of suspension viscosity in a universal framework, which provides a scaling solution for granular suspensions across dilute and dense regimes and sheds light on the dilute-dense transition mechanisms. This work also indicates a second order critical phenomenon related to the dilute-dense transition of granular suspensions.