TY - JOUR

T1 - Axisymmetric waves in electrohydrodynamic flows

AU - Grandison, Scott

AU - Vanden-Broeck, Jean-Marc

AU - Papageorgiou, Demetrios T.

AU - Miloh, Touvia

AU - Spivak, Boaz

PY - 2008

Y1 - 2008

N2 - The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of
radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic
waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is
paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet
inside a hollowcylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet
is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically
passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant
voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode
placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid
dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial
waves influenced by surface tension and electrical stresses are computed in both cases. The computations are
capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface
pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that,
for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case
the electric field promotes bubble formation, all other parameters being equal.

AB - The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of
radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic
waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is
paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet
inside a hollowcylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet
is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically
passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant
voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode
placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid
dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial
waves influenced by surface tension and electrical stresses are computed in both cases. The computations are
capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface
pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that,
for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case
the electric field promotes bubble formation, all other parameters being equal.

U2 - 10.1007/s10665-007-9183-1

DO - 10.1007/s10665-007-9183-1

M3 - Article

VL - 62

SP - 133

EP - 148

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 2

ER -