Stable Configurations Of Charged Sedimenting Particles

TL;DR

This paper demonstrates that charged sedimenting particles in a viscous fluid can form asymptotically stable configurations, unlike in a vacuum, which has implications for biological, medical, and industrial systems.

Contribution

It introduces the existence of stable bound states of charged particles in a fluid, challenging prior assumptions based on vacuum behavior.

Findings

Charged particles can form stable configurations in a viscous fluid.

Such stable states depend on charge, size, and density parameters.

Potential applications in biological, medical, and industrial systems.

Abstract

The qualitative behavior of charged particles in a vacuum is given by Earnshaw's Theorem which states that there is no steady configuration of charged particles in a vacuum which is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable - they are not attractors. In this paper, it is shown by example that two charged particles settling in a fluid may have a configuration which is asymptotically stable to perturbations, for a wide range of charges, radii and densities. The existence of such "bound states" is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical and industrial contexts.