Drag acting on an intruder in a three-dimensional granular environment

Abstract

The drag acting on an intruder in a threedimensional frictionless dry granular environment is numerically studied. It is found the followings: (i) There is no yield force for the motion of the intruder without the gravity. (ii) The drag is proportional to the cross section of the moving intruder. (iii) If the intruder is larger than surrounding grains, the drag is proportional to the moving speed V of the intruder for dense systems, but it exhibits a crossover from quadratic to linear dependences of the moving speed when the volume fraction of the surrounding grains is much lower than the jamming point. (iv) There is a plateau regime where the drag is almost independent of V if the size of the intruder is identical to those of the environmental grains and the volume fraction is near the jamming point.

Drag of a cylindrical object in a two-dimensional granular environment

“…with F dyn ∝ V 2 , which is also observed in high speed regime in many experiments and simulations [4][5][6]11]. Let us describe the second term F dyn (V) in Eq.…”

“…2, there exists a threshold F Y , and the object cannot move for F drag F Y because the drag force is balanced with the interparticle forces from the surrounding particles. Here, we can regard F Y as the yield force [5,6]. From the simulations, F Y 1.1 × 10 −2 k n d and 1.8 × 10 −2 k n d for ϕ = 0.75 and 0.80, respectively.…”

“…The previous studies [4] reported that the drag is proportional to the square of the moving speed in the high-speed regime. On the other hand, the low-speed regime shows various velocity dependence depending on the density of the system [5,6]. It is also noted that the granular jet experiments [7] and simulations [8] suggest the perfect fluidity of the granular jet flows.…”

“…The force acting on an object in granular materials is known to be different from that in fluids characterized by the drag coefficient. The drag in granular materials is studied in many setups and situations [2][3][4][5][6][7][8]. The previous studies [4] reported that the drag is proportional to the square of the moving speed in the high-speed regime.…”

Particle flows around an intruder

“…We note that our obtained drag forces are proportional to (D + d ) 2 , i.e., the collision cross section [28,47]. The drag force is proportional to the square of the speed for…”