Effect of noise on the stability of electrodynamically levitated one or many charged droplets

The theory of the effect of external fluctuations on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using a classical pseudo-potential approach. The theory is supplemented with numerical simulations where the non-homogeneous modified Mathieu equation is solved for single-droplet as well as many-droplet systems. In this essentially non-equilibrium system a pseudo-potential is identified, and a Boltzmann-like pseudo-equilibrium distribution is suggested that describes the variance of the deterministic configuration of particles levitated in a quadrupolar trap. This formalism seems to explain the numerical results in a fairly close and convincing manner. A transition from a well-ordered Coulombic crystal to a randomly distributed liquid-like structure is observed above a threshold value of noise. A surprising finding of the present work is the observation that the strength of the threshold noise for the transition of a 2-particle system into a noise-dominated regime is identical to the critical noise required for a solid melting transition in a 100-particle system. The simulations could prove useful in analysing an ordered assembly of levitated micro- and nano-particles from the air streams using a contactless membrane.