Static and Dynamic Behavior of Liquid Drops in Electric Fields

摘要

The problem considered is the behavior of an uncharged, conducting liquid drop in a uniform electric field. The liquid is assumed to be homogeneous, non-viscous, and incompressible. The shape of the drop is expressed as an infinite series of Legendre polynomial, and expressions, correct to second order in the Legendre polynomials, coefficients, are obtained for the surface tension potential energy and electrostatic potential energy of the system. The total system potential energy is then minimized with respect to variations in the coefficients, thereby yielding the equilibrium shape of the drop in a d-c field. This theoretically predicted drop distortion is shown to be in close agreement with all experimental data. The coefficients are then considered to be time varying, and a second order expression for the kinetic energy of the liquid is obtained. This expression is combined with the total potential energy to yield the Lagrange formulation of the equations of motion for the coefficients. The equations of motion are used to obtain solutions for the characteristic oscillatory frequencies (eigenvalues) and corresponding characteristic deformations (eigenvectors) for the drop. A stability criterion for the drop is formulated in terms of the eigenvalues, and is shown to be in close agreement with experimental evidence. (Author)