ON THE OUTCOME OF THE COULOMBIC FISSION OF A CHARGED ISOLATED DROP

Observations on the Coulombic fission of isolated drops of diameter D charged near the Rayleigh limit show that they often form a transient Taylor cone through which many droplets much smaller than D are emitte d. Sometimes, however, the products of the explosion are only a few, a nd their size is comparable to D. We argue that the ''fine fission'' m ode takes place under the same conditions generally leading to the for mation of a steady Taylor cone; namely, D has to be much larger than t he charge relaxation length d(m) = (gamma tau(2)/rho)(1/3) (tau = epsi lon epsilon(0)/K is the electrical relaxation time; epsilon(0) is the electrical permittivity of vacuum; epsilon, K, gamma, and rho are the dielectric constant, electrical conductivity, surface tension, and den sity of the liquid). Otherwise, no Taylor cone may form and the explos ion must proceed through a ''rough fission'' mode. Consequently, altho ugh drops of low conductivity liquids may break up into a few large an d probably unequal fragments, more conducting drops are bound to explo de with little mass loss, producing many very small and relatively mon odisperse daughter droplets. For the case of polar liquids for which D much greater than d(m), we reason that the emissions from the explodi ng drop must be quasi-steady, with characteristics similar to those of steady electrified cone-jets supported on a capillary tube. In additi on, the liquid flow rate Q through the cone-jet forming on the explodi ng drop must be near the threshold value, which is on the order of Q(m ) = gamma tau/rho. This 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 quantitative data are available for the size of the daughters from exploding polar liquids. Furthermore, the electrical c onductivity K has not been reported for the polar liquids whose Coulom bic explosions have been studied so far. But the present predictions a gree qualitatively with available measurements on the relative charge over mass loss in Coulomb fissions. (C) 1996 Academic Press, Inc.