Stable Configurations of Charged Sedimenting Particles

Area of Science:

• Physics
• Fluid Dynamics
• Colloid Science

Background:

• Earnshaw's theorem dictates no stable configurations for charged particles in a vacuum.
• Stationary configurations of uncharged particles in viscous fluids are known but unstable.
• Understanding particle interactions is key in dilute particulate systems.

Purpose of the Study:

• To investigate the possibility of asymptotically stable configurations for charged particles in a fluid.
• To demonstrate the existence of stable 'bound states' for settling charged particles.
• To explore the fundamental and practical significance of such configurations.

Main Methods:

• Theoretical analysis and demonstration by example.
• Consideration of charged particles settling in a viscous fluid.
• Analysis across a range of particle charges, radii, and densities.

Main Results:

• Two charged particles settling in a fluid can achieve asymptotically stable configurations.
• These stable 'bound states' exist for a wide range of physical parameters.
• This stability contrasts with the behavior predicted by Earnshaw's theorem in a vacuum.

Conclusions:

• Asymptotically stable configurations of charged particles in a fluid are possible.
• The existence of these 'bound states' has fundamental implications in physics.
• This phenomenon is significant for applications involving dilute charged particulate systems.