Resistance forces on an intruder penetrating partially fluidized granular media

This paper analyzes the forces on a cylindrical straight rod penetrated into a granular bed in the partially fluidized state. As gas flow is blown from the bed bottom, the resistance force decreases linearly with increasing gas flow velocity. After the bed is fluidized, the resistance force is close to zero. When the bed is under the action of vibration, the average resistance force (F_{b,ave}) linearly decreases with increasing vibration acceleration but is barely influenced by the vibration frequency. The bed cannot be completely liquefied under vibration only, and F_{b,ave} constantly exists with increasing vibration acceleration. Based on the equivalent effects of gas flow and vibration, the calculation formula of the resistance force in the partially fluidized bed is established as F_{b,ave}/F_{b,0}=1-u/u_{MF}-0.748Γ, and the minimum vibration liquid velocity is estimated as u_{ML}/u_{MF}=1-0.748Γ.