Simulations of Coulombic Fission of Charged Inviscid Drops

Simulations of coulombic fission of charged inviscid drops.

We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small perturbations are unstable and eventually lead to the formation of a lemon-shaped drop with very sharp tips. For perfectly conducting drops, the tip forms a self-similar cone shape with a subtended angle identical to that of a Taylor cone, and quantities such as pressure and veloci...

Inviscid coalescence of drops

We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than ℓ ν = ρν 2 /σ, which is 10nm for water. Using a high-precision boundary integral method, we show that the walls of the thin retractin...

Electrically Charged Conducting Drops Revisited

Since its publication in 1882, Rayleigh's work on electrically charged conducting drops has been widely quoted, but its rigorous derivation has not been given in the literature. By means of the domain perturbation technique, this work presents a rigorous derivation of Rayleigh's results, following his approach with Lagrange's equation. With the systematic procedure, it becomes explicit that the...

Existence and Stability of Charged Drops

We consider a variational problem related to the shape of charged liquid drops at equilibrium. We show that this problem never admits global minimizers with respect to L perturbations preserving the volume. This leads us to study it in more regular classes of competitors, for which we show existence of minimizers. We then prove that the ball is the unique solution for sufficiently small charges.

Vlasov simulations of parallel potential drops