ENERGY CONSIDERATIONS IN THE ELECTROSTATIC DISPERSION OF LIQUIDS

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Abstract
For the dispersion of electrically surface charged liquid drops it is assumed that the final minimum energy state is accessible to the system.Asymmetric division into two drops of radius γ and xr is considered as well as symmetric dispersion into n droplets of equal radius, where n = 2, 3, 4. A parameter y is defined as y = Q2/(16πR3γ), where Q is the charge on the original drop of radius R and surface tension γ. It is shown that if x > 2 in an asymmetric binary division, the smaller of the two droplets formed may be unstable and divide again. Photographic evidence of a secondary division is given. For a symmetric dispersion, at y = 1, the formation of four droplets leads to an energy minimum, with a maximum number, nmax, of allowed droplets of 20. For values of y > 1, nmax rises sharply.Values of y are calculated, below which symmetric division into two, three, or four droplets is forbidden. The conclusion is reached that below y = 0.351 the only permitted process is asymmetric division into two droplets, and that there is no situation for which binary symmetric division leads to a lower final energy of the system than the other modes of dispersion.

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