Absolute and convective instability of a charged viscoelastic liquid jet

Abstract

The absolute and convective instability of an electrically charged viscoelastic liquid jet is studied. The liquid is assumed to be (i) a dilute polymer solution described by the Oldroyd-B viscoelastic model, and also and (ii) a leaky dielectric defined by the Taylor–Melcher leaky dielectric theory. A generalized eigenvalue equation is obtained and solved numerically. Two different viscoelastic liquids, i.e. a PEO aqueous solution and a PIB Boger fluid, are taken as examples to study the effect of electric field and elasticity on the absolute and convective instability characteristic of the axisymmetric and first non-axisymmetric modes of a viscoelastic jet. The analysis shows that normal electric field may induce absolute instability of both axisymmetric and non-axisymmetric modes, being the effect of electric field larger on the latter. Elasticity has a profound destabilizing effect on the absolute and convective instability of the axisymmetric mode while its effect on the non-axisymmetric mode is quite limited. Strategies for suppressing absolute instability of an electrically charged viscoelastic jet are explored. The result indicates that increasing jet velocity or decreasing jet radius may effectively avoid the occurrence of absolute instability.