Dynamics of a charged drop in a quadrupole electric field

Abstract

Quadrupole electric fields are commonly employed for confining charged conducting drops in Paul traps for studying Rayleigh instability characteristics. We investigate the effect of these fields on the deformation and stability characteristics of a charged liquid drop, using the axisymmetric boundary integral method (BIM). Different combinations of the amount of charge and strength of the electric field give rise to different equilibrium shapes. Interestingly, unlike in the case of uniform fields, stable oblate equilibrium drop shapes are sustained in quadrupole fields. In a positive endcap configuration of the quadrupole setup a drop carrying a small negative charge displays a transition from oblate to prolate as the field strength increases. On the other hand, for the case of a highly charged drop, a shift in the Rayleigh critical charge is observed in the presence of a weak quadrupole field. The Rayleigh instability displays imperfect transcritical bifurcation characteristics with respect to imposed prolate and oblate perturbations. Results are of significance in i) interpreting deformation and the Rayleigh stability effects using Paul traps with quadrupole fields, ii) designing more efficient quadrupole-field–based technologies for emulsification of water in oil.