The equilibrium shape of a liquid drop in mutually perpendicular electrostatic and hydrodynamic fields

An analysis of the balance of pressures on the surface of a drop of an ideal incompressible liquid, exposed to a homogeneous electrostatic field and streamlined by a laminar flow of an ideal incompressible fluid perpendicular to the field, shows that, in the approximation linear with respect to the deformation amplitude, the equilibrium drop shape represents a triaxial ellipsoid.