Soft Matter and Complex Systems Seminar

Earnshaw’s theorem is a fundamental theorem in electrostatics which states that no stationary electrostatic configuration in a vacuum is stable to perturbations. It is also well known that stationary arrangements of electrically neutral particles settling in a viscous fluid are also not stable. However, examining a theoretical model, two charged particles settling in a viscous fluid are shown to have configurations which are asymptotically stable to perturbations. This result was published in [1]. Stable stationary states exist for a wide range of charges, radii and densities. Necessary and sufficient conditions for the existence of such stable states are given and analyzed.

[1] Trombley CI, Ekiel-Jeżewska ML. Physical Review Letters. 2018 Dec 21; 121(25):254502.