Electrohydrodynamics

Electrohydrodynamics (EHD), also known as electro-fluid-dynamics (EFD) or electrokinetics, is the study of the dynamics of electrically charged fluids.^[1][2] Electrohydrodynamics (EHD) is a joint domain of electrodynamics and fluid dynamics mainly focused on the fluid motion induced by electric fields. EHD, in its simplest form, involves the application of an electric field to a fluid medium, resulting in fluid flow, form, or properties manipulation. These mechanisms arise from the interaction between the electric fields and charged particles or polarization effects within the fluid.^[2] The generation and movement of charge carriers (ions) in a fluid subjected to an electric field are the underlying physics of all EHD-based technologies.

The electric forces acting on particles consist of electrostatic (Coulomb) and electrophoresis force (first term in the following equation)., dielectrophoretic force (second term in the following equation), and electrostrictive force (third term in the following equation):

${\displaystyle F_{e}=\rho _{e}{\overrightarrow {E}}-{1 \over 2}\varepsilon _{0}{\overrightarrow {E}}^{2}\triangledown \varepsilon _{r}+{1 \over 2}\varepsilon _{0}\triangledown {\Bigl (}{\overrightarrow {E}}^{2}\rho _{f}\left({\frac {\partial \varepsilon _{r}}{\partial \rho _{f}}}\right){\Bigr )}}$^[2]

This electrical force is then inserted in Navier-Stokes equation, as a body (volumetric) force.

EHD covers the following types of particle and fluid transport mechanisms: electrophoresis, electrokinesis, dielectrophoresis, electro-osmosis, and electrorotation. In general, the phenomena relate to the direct conversion of electrical energy into kinetic energy, and vice versa.

In the first instance, shaped electrostatic fields (ESF's) create hydrostatic pressure (HSP, or motion) in dielectric media. When such media are fluids, a flow is produced. If the dielectric is a vacuum or a solid, no flow is produced. Such flow can be directed against the electrodes, generally to move the electrodes. In such case, the moving structure acts as an electric motor. Practical fields of interest of EHD are the common air ioniser, electrohydrodynamic thrusters and EHD cooling systems.

In the second instance, the converse takes place. A powered flow of medium within a shaped electrostatic field adds energy to the system which is picked up as a potential difference by electrodes. In such case, the structure acts as an electrical generator.