Instability of Slender Liquid Jet in AC Electric Field of Arbitrary Frequency |
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Authors: | Evgeny A Demekhin Sergey V Polyanskikh |
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Affiliation: | 1.Department of Mathematical Methods and Models,Kuban State University,Krasnodar,Russian Federation |
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Abstract: | In the present work stability of capillary micro-jet of electrolyte solution in alternating longitudinal electric field is
investigated theoretically. The gravity effects are neglected. The problem is described by strongly coupled nonlinear system
of PDEs for ion transport, electric field and fluid flow under assumption of a viscous Newtonian liquid. The Debye layer thickness
is supposed to be small compared with initial jet radius. The Peclet number based on the Debye layer thickness is assumed
to be small. These assumptions lead to substantial simplification of the problem. Slender-body theory is used to further simplification
of initial statement. Used asymptotic method allows to reduce initially infinite system to three-dimensional ODE with time-periodic
coefficients. It is shown that monodromy operator has the only real unstable multiplier. In the case of high-frequency alternating
electric field the results showed good agreement with the ones provided by averaging theory. |
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