Date of Award


Degree Type


Degree Name

Doctor of Philosophy


To be able to properly predict the breakup of highly charged liquid droplets, a complete understanding of their behavior at the Rayleigh limit is necessary. An analytical model has been developed for a conductive spherical drop charged to its Rayleigh limit which predicts the final state just after the breakup for both single and multi-sibling disintegrations. The numerical analysis of this model involves scanning all the possible radii of the sibling droplets and ensuring that the solutions satisfy the conservation of energy and Rayleigh limit criteria. For a drop unaffected by any external force, the results of this model show that the most probable disintegration satisfies the single sibling breakup. The sibling, under such conditions, carries about 25% of the initial mass and 40% of the initial charge. The results also show that the difference between the final energy, calculated at different sibling mass ratios, and the minimum final energy is very small for a very wide range of sibling mass ratios (0.1 to 0.9) and thus can be easily affected by any external force to produce a multi-sibling disintegration. For the multi-sibling case, the model assumes tree-like secondary breakups which lead to a residual drop and n siblings of different sizes and charges. The results of this model show good agreement with the experimental observations of many other investigators. The numerical results also show that the single sibling exists for all the values of sibling mass ratios greater than 11.1%. For all the values less than this, the multi-sibling disintegration is favoured. This has been verified experimentally by collecting water droplets after their breakup on water sensitive paper and then examining their traces with a microscope.;Since the Rayleigh limit is only valid for spherical droplets unaffected by any external force, general equations describing the drop stability have been derived for both prolate and oblate spheroidal shapes. From the analytical evaluation of these equations, it was concluded that the Rayleigh limit is only valid for small droplet sizes (R {dollar}<{dollar} 50 {dollar}\mu{dollar}m) and for very low levels of external forces. (Abstract shortened with permission of author.)



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