Electrohydrodynamics

Electrohydrodynamics (EHD) is the study of the interactions between electric fields and fluid motion. It considers how electric forces act on charged or polar liquids, how charge distributions evolve in fluids, and how fluids in turn affect electric fields and currents. EHD spans phenomena at solid–liquid and liquid–liquid interfaces and is central to electrokinetic transport, dielectrics in flow, and electrohydrodynamic spraying. Practical areas include microfluidics, inkjet printing, electrospray ionization, and propulsion devices based on ionic wind.

The governing picture combines fluid dynamics with electromagnetism. In many problems the fluid obeys the Navier–Stokes equations with an electric body force f_e, often written as f_e = rho_e E, where rho_e is the free charge density and E is the electric field. The field is derived from a potential via E = -grad phi, and charge conservation is captured by partial_t rho_e + div J = 0. The current density J typically includes conduction and convection, J = sigma E + rho v. Electric stresses at interfaces are described by the Maxwell stress tensor T^M = epsilon( E E - 1/2 E^2 I ), contributing to boundary conditions in balance of stresses. Dielectrophoresis, electroosmosis, and electrowetting arise from field gradients, surface charges, and capillary forces.

Applications range from microfluidic pumps and mixers to particle manipulation, droplet actuation, and mass spectrometry. Electrospray ionization forms charged liquid jets that produce ions in vacuum. Dielectrophoretic devices separate or concentrate particles, while electrowetting enables digital microfluidics and programmable droplet motion. Limitations include charge relaxation, interfacial instabilities such as Taylor cone formation, and the need to manage heating and electrochemical reactions in conductive liquids.