Vertical dynamics of a horizontally oscillating active object in a two-dimensional granular medium

Area of Science:

• Physics
• Granular Mechanics
• Complex Systems

Background:

• Granular materials exhibit complex behaviors due to particle interactions.
• The dynamics of immersed objects in granular media are not fully understood.
• Oscillatory motion can significantly alter particle-fluid interactions.

Purpose of the Study:

• To investigate the vertical dynamics of a self-energized oscillating disk in a 2D granular bed.
• To identify the key parameters governing the rise, sink, or stable depth of the immersed object (IO).
• To develop an analytical model explaining the observed phenomena.

Main Methods:

• Discrete-element method (DEM) simulations were employed.
• Analytical calculations and a cavity model were developed.
• Phase diagrams were constructed based on oscillation frequency and velocity amplitude.

Main Results:

• The IO's vertical motion (rise, sink, or stable depth) depends on oscillation amplitude, frequency, and initial depth.
• A critical frequency (f_c) and minimal amplitude (A_min) were derived, determining the IO's ability to rise.
• A critical acceleration amplitude (g_c) was identified, below which the IO cannot sink.

Conclusions:

• The IO's behavior is governed by competing effects of particle climbing and bed fluidization.
• The analytical cavity model accurately predicts and explains the observed phase diagram.
• Key dimensionless parameters controlling IO dynamics were identified and quantified.