Electrohydrodynamics

Part I | Part II | Part III | Supplement A | Supplement B

The term "electrohydrodynamics" has come into use recently to distinguish a certain class of phenomena from the more general regime of "magnetohydrodynamics". The term may be considered to be synonymous with the rather elaborate term "electrostrictive hydrodynamics".

In general, the phenomena relate to the conversion of electrical energy into kinetic energy and vice versa.

In the first instance, shaped electrostatic fields create hydrostatic pressure (or motion) in dielectric media. When such media are fluids, a flow is produced. The flow can be directed against the electrodes, generally to move the electrodes. In such case, the moving structure acts as a "motor".

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 a "generator".

THEORY:

The theory underlying these phenomena is not entirely clear. An appropriate reference *1 discloses the following:

"The system of stresses in dielectric media may be supposed to consist of:

(i) - A tension KR²/8 per unit area in the direction of the lines of force;

(ii) - A pressure KR²/8 per unit area perpendicular to the lines of force;

(iii) - A hydrostatic pressure R²/8 2K/2 of amount in all directions."

Sir James Jeans further notes:

"this system of stresses . . . was first given by Helmholtz. The system differs from that given by Maxwell by including the pressure:

-R²/8 2K/2

It is to be pointed out that in (iii) a hydrostatic pressure results from an electric field which, if the term 2K/2 is negative, acts outwardly "in all directions".

A gradient in plasma density and, hence, a gradient in K unquestionably exists throughout the shaped electric fields present in these experiments. This may be sufficient to account for a part, at least, of the observed forces. Polarization of certain molecules of the fluid must also be considered where dielectrophoresis is involved, but these forces are generally contra-directional. Additional direct-acting, not represented in the above, result from the transfer of momentum from ions to the host medium.

ELECTRODE GEOMETRY:

Regardless of the adequacy of the theory at this stage, the experimental results show the need of a unique geometry in the "shape" of the electrostatic field.

These fields must be non-uniform, such as those created by arcuate or annular electrodes of differing size, for the specific purpose of causing maximum electrostriction in the fluid medium.

In applying the principles of electrostrictive hydrodynamics (electrohydrodynamics) it is immediately clear to the aeronautical engineer that a large electrode area is required. Just as a sailboat uses a sail, any vehicle utilizing electrohydrodynamic propulsion must employ a large ballistic electrode to integrate the pressure of plasma "winds" to provide lift or forward thrust.

These so-called "electric winds" are ion flows, moving at relatively high velocity. The flows may take various patterns determined by:

1) The manner in which the flows are generated, and
2) The curvature of the surfaces which confine them.

Hydrostatic pressure (or aerodynamic pressure, if one prefers) is exerted against the entire inner surface of the large arcuate electrode, and the integrated pressure creates a mechanical force which propels the entire structure in one direction.

It is conceivable that the electrohydrodynamic drive will be effective wherever an ambient plasma is present. Hence, according to latest concepts, this includes a great part of outer space where the attenuated solar corona is believed to extend. In every case, momentum is transferred to the surrounding medium however tenuous. The surrounding medium would be influenced for some distance on all sides of the proposed craft and would be propelled in the opposite direction. Thus it may be concluded that, in outer space, momentum is conserved without the expenditure of a working fluid.