Maxwell, electromagnetism, and fluid flow in resistive media



Common wisdom has it that Darcy [1856] founded the modern field of fluid flow through porous media with his celebrated 1856 experiment on the steady flow of water through a sand column. For considerable time, Darcy's empirical observation, in conjunction with Fourier's [1807] heat equation, was used to analyze fluid flow in porous media simply by mathematical analogy. Hubbert [1940] is credited with placing Darcy's work on sound hydrodynamic foundations. Among other things, he defined an energy potential, interpreted permeability in the context of balancing impelling and resistive forces, and derived an expression for the refraction of flow lines. In 1856, James Clerk Maxwell constructed a theory for the flow of an incompressible fluid in a resistive medium as a metaphor for comprehending the emerging field of electromagnetism [Maxwell, 1890].