Exact solutions for equilibrium configurations of charged conducting liquid jets

Abstract

A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a round jet. A critical value of the linear electric charge density is determined, for which the jet surface becomes self-intersecting, and the jet splits into two. It exceeds the density value required for the excitation of the linear azimuthal instability of the round jet. Hence, there exists a range of linear charge density values, where our solutions may be stable with respect to small azimuthal perturbations.

Random matrices in 2D, Laplacian growth and operator theory

“…Numerous non-equilibrium physical processes of apparently different nature are examples of Laplacian growth: viscous fingering [51], slow freezing of fluids (Stefan problem) [53], growth of snowflakes [54], crystal growth, amorphous solidification [55], electrodeposition [56], bacterial colony growth [57], diffusion-limited aggregation (DLA) [58], motion of a charged surface in liquid Helium [59], and secondary petroleum production [60], to name just a few.…”

Symmetry breaking bifurcations for an overdetermined boundary value problem on an exterior domain issued from electrodynamics

“…The authors show that for the cylindrical geometry the Coulomb force has a stabilizing effect for axisymmetric sinusoidal perturbations with long wavelength and a destabilizing effect for non-axisymmetric perturbations. In [8] the authors find a wide class of equilibrium configurations of electrically charged fluid jets. These configurations correspond to the finite amplitude azimuthal deformations of the surface of the cylindrical jet.…”

“…We shall show the existence of bifurcation branches for special values γ ls of γ, see (8) if s > 0 and (10) if s = 0.…”