Shear flow dynamics in vibrated granular materials: Analysis of viscosity transitions and non-Newtonian behaviors

In a continuous fluid, the presence of a velocity gradient perpendicular to the flow creates shear stress and shear rate between adjacent layers. The fluid's viscosity can be constant, depending only on temperature (Newtonian fluid), or vary with shear rate (non-Newtonian fluid). However, the viscosity characteristics of shear flows in discrete media, such as vibrated granular materials, remain insufficiently understood. This study experimentally investigated shear flows in vibrated granular media, exploring the relationship between shear stress, shear rate, and the impact of vibration conditions and particle number on granular viscosity. The findings indicate that the viscosity of sheared granular material transitions between dilatant and pseudoplastic non-Newtonian states with increasing vibration strength, shifts from pseudoplastic non-Newtonian fluid to Newtonian fluid with increasing vibration frequency, and remains consistently pseudoplastic non-Newtonian with increasing particle number. Two continuous non-Newtonian fluid models were utilized for comparison with our experimental results. Additionally, ascending curves of granular viscosity against granular temperature reveal gas-like flow characteristics in the sheared granular material, albeit with an abnormal descending viscosity-temperature relationship. These are attributed to volume expansion and oblique collisions in the vibrated granular medium. This study uncovers distinct viscosity properties in a discrete medium under shear flows, markedly different from those in continuous fluids, and highlights potential new applications for granular materials.