Dielectric charged drop break-up at sub-Rayleigh limit conditions

The maximum charge a drop may hold, for an electrically isolated, electrically conducting drop, in vacuum, is defined by the Rayleigh Limit. For spray plumes of electrically charged drops this condition is clearly not met due to the space charge field. We would like to simulate such spray plumes and to simulate drop break up within them, using stochastic methods. Since many simulated particles are required a dynamic drop stability analysis is clearly not computationally feasible. Based upon a static analysis, and a thorough review of the previous experimental data on charged drop stability, it is shown that for dielectric drops in the presence of significant electric fields, and particularly those within spray plumes, the maximum charge a drop may hold is less than the Rayleigh Limit. Typical values of stable drop charge of 70-80% of the conducting drop Rayleigh Limit are predicted, and this is supported by a majority of recent experimental work. We present an explanation of the sub-Rayleigh Limit drop fission within charged spray plumes for dielectric drops, based upon a static, rather than a dynamic analysis. This permits sub-Rayleigh Limit drop fission to be incorporated into stochastic particle simulations.