A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops

A weakly conducting liquid droplet immersed in another leaky dielectric can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, nonlinear coupling interfacial charge transport fluid flow trigger electrohydrodynamic instabilities that lead to shape deformations complex dynamics. We present a spectral boundary integral method simulate electrohydrodynamics uniform All physical variables, such as drop density, are represented using spherical harmonic expansions. In addition its exponential accuracy, representation affords nondissipative dealiasing required for numerical stability. comprehensive model, valid wide range strengths, accounts relaxation, Ohmic conduction, surface convection by flow. reparametrization technique enables exploration significant deformation regimes. For low-viscosity drops, drives steep gradients near equator. This introduces ringing artifacts we treat via weighted expansion, resulting solution convergence. The simulations validated against experimental data analytical predictions axisymmetric Taylor Quincke electrorotation