Mechanism of Intruder Movement

The sine-wave displacement of the granular bed leads to the displacement of the intruder. Frame-by-frame analysis of video movies made show that the intruder follows a sort of repeated parabolic trajectory as a function of time when displaced, which results in an overall upward or downward movement in the granular bed, depending on the vibration conditions.

In the figure below, extracted from one of the high-speed movies made, a 0.015 m diameter intruder can be seen to be displaced in the granular bed. The horizontal black line in the lower part of the frames indicates a position 3 cm above the base of the granular bed. Observe that the intruder reaches its maximum position when the sine-wave displacement of the container housing the granular bed is approximately at its minimum position. Also observe that a wake is formed below the intruder during its upward movement.

Displacement of intruder in the granular bed.                                         Vibration frequency = 30 Hz                                        Vibration amplitude = 1 mm

The intruder position as a function of time (for the figure above) is shown in the figure below. The position shown corresponds to the point at the bottom of the intruder measured from the base of the granular bed.  Also shown is the relative container position as a function of time, which is a sine-wave displacement. Observe that the intruder traces a series of parabolic paths, rising gradually in the process.

Our interest lies in predicting the rise and/or sink of the intruder in the granular bed by taking into account the forces and parameters responsible for these. In order to achieve these, we resort to the development of mathematical models for describing the phenomena which occur in the bed.