Figure 2
From: Ultrasonic tracking of a sinking ball in a vibrated dense granular suspension
Sinking dynamics of a steel ball of radius R = 5 mm for different vibration intensities Γ. (a) Positions of the ball versus time. (b) Instantaneous sinking velocities versus ball positions. Inset: comparison with the full analytical solution (black line) for Γ = 1.08 (see Eqs 7 and 8 in Methods). (c) Accelerations versus ball positions. (d) Sinking acceleration versus velocity, which shows a transition from a fast decelerating regime to a quasi-steady regime. (dz/dt)* is obtained from the intersection of two sets of linear fits (see dotted lines). (e) The ball positions versus time in the quasi-steady regime. The black lines correspond to the solutions fitted in the quasi-steady regime with Eq. 4. (f) Evolution of the ball position at the lowest acceleration of vibration for various radii.
