Stability of Non-axisymmetric Electrolyte Jet in High-frequency AC Electric Field

Abstract

In the present work linear instability of capillary non-axisymmetric micro-jets of electrolyte solutions in a high-frequency alternating axial electric field is investigated theoretically. The gravity affects are neglected. The problem is described by strongly coupled nonlinear system of PDEs for ion transport, electrical field and fluid flow. Viscous liquid is taken. The problem can be divided into outer and inner ones. Solution for the unsteady double ion layer is obtained in Debye-Huckel approximation provided that the oscillation frequency is sufficiently high while Pecklet number based on the Debye layer thickness is sufficiently small. The unsteady double ion layer produces additional normal and tangential stresses on the liquid-gas interface; the latter can either stabilize or destabilize the flow. It is shown that only axisymmetric mode is unstable while non-axisymmetric perturbations are always stable. It is also shown that in unstable case there is an essential dependence of the main stability characteristics on the parameter proportional to the frequency of external field. There are two threshold values of the parameter The research was partially financed by the Russian Foundation for Basic Research grants No 08-01-00005-à and 06-08-96637-r_ug_a.at which a bifurcation of stability parameters occurs. In particular, the size of the formed drops suffers a jump at increase of amplitude of fluctuation of an electric field. The problem is solved in a broad region of its parameters. There is a qualitative agreement of the theory developed with the available experimental data.

Instability of Slender Liquid Jet in AC Electric Field of Arbitrary Frequency

“…It is easy to show that in this case there is no depence on Reynolds number in complete analogy with the classical Rayleigh case of electric field absence, The results were also compared with the ones obtained from the averaging theory (Polyanskikh and Demekhin 2009). It was shown that the latter gives very good approximation even at dimensionless frequency ω greater than 1 ÷ 2 for arbitrary values of other parameters (see Fig.…”

“…In Polyanskikh and Demekhin (2009) it was shown that non-axisymmetric perturbations are always stable in the case of uncharged electrolyte jet in longitudinal electric field. This justifies consideration of the most important axisymmetric case.…”

“…allow to separate electrodynamic part of the problem in a thin Debye layer from outer hydrodynamic part (see Polyanskikh and Demekhin 2009;Demekhin et al 2006). The assumptions (12) are in a good agreement with experimental data in Yeo et al (2004), Gneist and Bart (2002), and Malloggi et al (2008) in a wide range of external parameters (see Table 1).…”

“…which represents the charge conservation law (see Polyanskikh and Demekhin (2009) and Demekhin et al (2006) for details). The relation (18) also takes into account the change in the fundamental metric coefficients of the free surface in addition to ohmic and convective effects.…”

“…The paper Polyanskikh and Demekhin (2009) deals with the stability of liquid electrolyte jet in case of high-frequency alternating external electric field. In the present paper we investigate the stability of a jet in case of external AC electric field without any restrictions on the field frequency in slender body approximation.…”