Deformation dynamics of Oldroyd B drop in alternating electric field

Abstract

The deformation of viscoelastic drops in alternating electric fields is relevant to electrohydrodynamic applications such as microfluidics, inkjet printing, and drop manipulation. We investigate the dynamics of a neutrally buoyant Oldroyd-B drop subjected to a uniform alternating electric field using asymptotic analysis and direct numerical simulations with the open-source solver Basilisk. An analytical solution is derived for small deformation and weak elasticity for an Oldroyd-B drop suspended in an Oldroyd-B medium, with both fluids modeled as leaky dielectrics under axisymmetric Stokes flow. Depending on the conductivity and permittivity ratios, six electrohydrodynamic regions are identified, characterized by distinct deformation modes, flow directions, and nonlinear responses; while some exhibit stable spheroidal deformation, others undergo pointed-tip, multi-lobed, or oblate breakup beyond a critical electric capillary number. Across high-, intermediate-, and low-frequency regimes, the deformation oscillates at twice the applied field frequency, with its mean and amplitude governed by the field frequency and viscoelasticity. For cases that produce prolate deformation under a steady field, the drop remains prolate at high frequency, exhibits brief oblate excursions at intermediate frequency, and undergoes large-amplitude oscillations between near-spherical and highly deformed states at low frequency. The mean deformation varies monotonically or non-monotonically with $De$, depending on frequency and electrical property ratios. For cases producing oblate deformation under a steady field, the drop remains oblate at high frequency, develops dimples at intermediate frequency, and breaks up at low frequency for sufficiently large $De$ and $Ca_E$; the mean deformation increases monotonically with $De$.