Electrohydrodynamics of real fluids

Prevailing theories of interactions between electric fields and fluids often incorporate an assumption of constant fluid properties in the development of couplings between the equations of motion and Maxwell's equations of electrodynamics. This is a severe limitation in that two of the three electric body forces acting on the fluid arise from gradients in fluid properties (mass density and electric permittivity). These effects are included in the theory by describing property variations with Taylor series expansions about a datum value. This introduces a number of additional terms beyond those described by a zeroth-order theory. Some of these terms are neglected on the basis of physical estimates, leading to an electrohydrodynamic analog to the Boussinesq approximation of classical fluid mechanics. The interactions described by the theory include natural convection due to Joule heating. Coulombic, and electrostrictive body forces and interfacial tractions associated with permittivity gradients. The significance of these effects is discussed for static and dynamic regimes. This discussion includes development of first-order EHD analogs of Bernoulli's Theorem, Kelvin's Circulation Theorem and Crocco's Theorem. The theory is then illustrated with a new, exact solution to the coupled first-order equations of electrohydrodynamics