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Maxwell's Equations for Electricity and Magnetism for Two-Phase Systems: The Concept of Local Electrodynamic Equilibrium and Its Failure
Applied Math| Speaker: | Stephen Whitaker, Dept.of Chemical Engineering, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Nov 16 2001, 4:10PM |
The form of Maxwell's equations is explored for a two-phase system such as an emulsion or a porous medium. The point equations for the electric and magnetic fields are well understood for single-phase systems; however, this is not the case for multiphase systems where some form of upscaled equation must be used. In this lecture we consider two questions: 1. Can one describe electrodynamic phenomena in a two-phase system with single equations for the volume averaged magnetic and electric fields? 2. If not why not? We begin by developing separate volume averaged equations for each phase and then identify the condition of local electrodynamic equilibrium. When this condition is satisfied, single equations for the electric and magnetic fields can be used to describe multiphase phenomena; however, the constraints associated with local electrodynamic equilibrium are rarely satisfied for real systems. This leads to the necessity of using coupled, two-equation models in order to accurately describe electrodynamic phenomena in two-phase systems.
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