We present evidence of a semi-dilute-dense behaviour transition in suspensions from a thorough study combining both experiments and numerical results. Following an extensive experimental study, where such a transition was observed, we perform constant-volume shearing simulations of non-Brownian granular suspensions using the discrete element method coupled with the lattice Boltzmann method (DEM-LBM). 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 semi-dilute and dense regimes. This result demonstrates that, with a proposed semi-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 semi-dilute and dense regimes and sheds light on the semi-dilute-dense transition mechanisms. This work also gives some evidence of a second-order critical phenomenon related to the semi-dilute-dense transition of granular suspensions.
 

granular suspension,shear viscosity,critical scaling,DEM-LBM simulation