Structure of Taylor cone-jets: limit of low flow rates

In this paper the structure of the Taylor meniscus and emitted jet is studied by perturbation methods in the limit of low flow rates. An asymptotic system of governing equations is derived from the basic equations of electrohydrodynamics. They rigorously take into account the inertia and viscosity of the liquid as well as the surface ion mobility. The solutions to the asymptotic equations in the meniscus, jet and surrounding gas regions are found, matched with each other, and applied to study distributions of electric and hydrodynamic variables. Such an approach allows the liquid velocity, surface charge, and meniscus-jet radius as well as electric potential inside and outside the liquid to be calculated. We also derive the theoretical dependences of the current carried by the jet and its diameter on the liquid properties and how rate. These dependences are consistent with the scaling laws found experimentally by Fernandez de la Mora & Loscertales (1994) and data obtained by Chen & Pui (1997).