Notes on Magneto-Hydrodynamics, Vol. 4: Ohm's Law (Classic Reprint) - Softcover

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Excerpt from Notes on Magneto-Hydrodynamics, Vol. 4: Ohm's Law

Next, let us consider a two-fluid theory. The simplest such theory involves two mass-conservation equations, while retaining a single momentum and a single energy equation for the total fluid. We assume that a single equation of state involving energy, pressure, and both densities is given. Counting variables, compared to the one-fluid theory, we have an extra density (matched by an extra mass conservation equation) and also an extra velocity vector, e.g., the difference or diffusion velocity. In ordinary fluid dynamics, this extra velocity is taken care of by supplementing the system of conservation equations by a diffusion relation, e.g., an assertion that the difference velocity is proportional to the concentration gradient.

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