(259e) Lbm Study on Rayleigh Instability of Charged Droplet

Rayleigh instability of charged droplet is well known phenomenon: if a liquid droplet has electrostatic charge, both of electrostatic repulsive force and surface tension work on its surface, and if the electrostatic stress excesses surface tension the droplet cannot be maintained as a sphere and starts to deform and small daughter droplets are generated as a disruption. Lord Rayleigh derived the stability criterion for a spherical droplet. According to his result, the critical charge can be predicted as a function of diameter of droplet and surface tension. Several experimental studies of the Rayleigh limit have been reported. Doyle et al. suspended individual droplets of water or aniline in a Millikan apparatus and observed sudden decreases of specific charge following evaporation: the limit specific charges were close to the Rayleigh limit. Abbas and Latham refined the Doyle's method to obtain particle size from sedimentation speed. The Rayleigh limit was confirmed for water, aniline and toluene droplets with radius between 30 and 200 . They also found that up to 30% of particle mass was lost during the disruption. Schweizer and Hanson suspended volatile oil droplets in air in an electrodynamic levitator. Using the drag force to determine the sizes of the droplets they found that the breakup occurred near the Rayleigh limit: 23% of the charge and 5% of the mass was lost on average. Although the instability condition was revealed by Lord Rayleigh, how the deformation is developed after the unstable state is still remaining as a question because of its dynamic nature. Numerical simulative method, therefore, will be useful to study the phenomenon in more detail. The phenomenon is not only interesting by itself, in terms of scientific interest, but also important as a physical basis to understand the electro atomization for further industrial application. In this work we report a trial applying LBM (Lattice Boltzmann Method) simulation to the Rayleigh instability of a charged droplet. As an advanced numerical simulation method on fluid dynamics, the LBM is attracting interests recently. In particular, the LBM has been successfully applied to problems of fluid flows through porous media, and multi-phase fluid flow. Advantage of the method is its applicability to two phase flow, in which phase separation is automatically produced by the nature of the algorithm and there is no necessity to follow the interface explicitly. In this work we show an interesting extension of the LBM to involve electrostatic repulsive force working on the surface of an individual liquid droplet by means of momentum modification. The method successfully simulates the Rayleigh instability, in which a droplet is stretched its ellipsoidal shape when the electrostatic potential exceeds Rayleigh's threshold, on the contrary, a droplet with a less potential than the threshold deforms back to a spherical shape as a static form.