Observations on the Coulombic fission of isolated drops of diameter D charged near the Rayleigh limit show that they often form where 1 0 is the electric permittivity of vacuum and g is a transient Taylor cone through which many droplets much the surface tension coefficient of the liquid. This prediction smaller than D are emitted. Sometimes, however, the products of agrees approximately with most measurements (3), though the explosion are only a few, and their size is comparable to D. more refined observations indicate that the instability may We argue that the ''fine fission'' mode takes place under the same occur at around 80% of q R (4, 5).
conditions generally leading to the formation of a steady Taylor
When the surface becomes unstable, it ejects a certain cone; namely, D has to be much larger than the charge relaxation mass Dm and charge Dq, which brings q again below q R . length d m Å ( gt 2 /r) 1/3 (t Å 11 0 /K is the electrical relaxation Although a variety of studies have been directed at charactertime; 1 0 is the electrical permittivity of vacuum; 1, K, g, and r
izing the limit of instability, very little is known on the are the dielectric constant, electrical conductivity, surface tension, number, charge, and mass of the liquid fragments liberated and density of the liquid). Otherwise, no Taylor cone may form and the explosion must proceed through a ''rough fission'' mode. in such ''Coulombic explosions.'' Accordingly, this note Consequently, although drops of low conductivity liquids may will consider the Coulombic burst of an isolated drop in a break up into a few large and probably unequal fragments, more field-free region, with an emphasis on the characteristics of conducting drops are bound to explode with little mass loss, prothe fission products. The different problem of the instability ducing many very small and relatively monodisperse daughter of charged or uncharged drops under external fields has been droplets. For the case of polar liquids for which D ӷ d m , we reason investigated by a number of authors (6-11). It will not be that the emissions from the exploding drop must be quasi-steady, pursued further here because information on the features of with characteristics similar to those of steady electrified cone-jets the corresponding fission products is available only for liqsupported on a capillary tube. In addition, the liquid flow rate Q uid-liquid interfaces, while some of the arguments to be through the cone-jet forming on the exploding drop must be near made in this work have experimental basis only for the case the threshold value, which is on the order of Q m Å gt/r. This of liquid-gas interfaces.
fixes approximately the size and charge of the fission products to be on the order of d m and of the Rayleigh limit, respectively. No Most studies on Coulombic fragmentation have reported quantitative data are available for the size of the daughters from relatively small mass losses (Dm/m Ç 2%), together with exploding polar liquids. Furthermore, the electrical conductivity charge losses Dq/q some ten times larger. This situation has K has not been reported for the polar liquids whose Coulombic corresponded generally to the production not just of a few explosions have been studied so far. But the present predictions droplets, but of a cloud of daughter droplets considerably agree qualitatively with available measurements on the relative smaller than the parent drop. Thus, Rayleigh (12) remarked charge over mass loss in Coulomb fissions.