Korteweg–de Vries solitons on electrified liquid jets - Wang,Q; Papageorgiou,DT; Vanden-Broeck,J-M (Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 2015)
The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric fieldis considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jetconcentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivialinteraction arises between the hydrodynamics and the electric field in the annulus, resulting in the formationof electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of suchaxisymmetric waves in the weakly nonlinear regime, which is valid for long waves relative to the undisturbedjet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and theapplied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and aweakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical systemthat arises is the Kortweg–de Vries equation with coefficients that vary as the electric field and the electroderadius are varied. Interestingly, the coefficient of the highest-order third derivative term does not change sign andremains strictly positive, whereas the coefficient α of the nonlinear term can change sign for certain values of theparameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevationfor α > 0 and of depression for α < 0. Regions in parameter space are identified where such waves are found.