Stability of freely falling granular streams

Area of Science:

• Fluid Dynamics
• Granular Physics
• Computational Physics

Background:

• Understanding the behavior of falling granular streams is crucial in various industrial and natural processes.
• Previous models often simplified particle interactions and stream dynamics.

Purpose of the Study:

• To model and analyze the breakup of freely falling granular particle streams.
• To investigate the relationship between cohesive energy and droplet size.
• To determine the stability of extensional flow in such systems.

Main Methods:

• Event-driven simulations were employed to model granular particle interactions.
• Continuum hydrodynamics, specifically the one-dimensional Navier-Stokes equation, was used for analysis.
• Extensional flow was analyzed as an exact solution to the governing equations.

Main Results:

• Event-driven simulations demonstrated that granular streams break into droplets.
• Droplet size was found to be a function of the cohesive energy of the particles.
• Analysis of extensional flow revealed stability at early times (γ̇(0)t << 1) but instability at later times (γ̇(0)t >> 1) for all wavelengths.
• The growth rate of perturbations varied with time, leading to diverse observable patterns.

Conclusions:

• Freely falling granular streams are inherently unstable and fragment into droplets.
• Cohesive forces play a significant role in determining the size of these droplets.
• The temporal evolution of perturbations dictates the complex and variable patterns observed in granular stream breakup.