Nonlocal electromagnetic theory of fluids with applications to surface waves in a dielectric fluid Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1n79h749s

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  • The last two decades have seen many new continuum models for electromagnetic materials which were constructed by merely adding terms to the classical balance laws and constitutive equations. Nonlocal theories, such as the one developed by A. C. Eringen., however, depart from the traditional approaches by accounting for the effects of distant atomic, molecular and granular interactions. Although some attention has been given to nonlocal electromagnetic solids no work has been done on nonlocal electromagnetic fluids. The natural occurrence of electromagnetic fluids (atmospheric and oceanic circulations, the earth's core as well as its mantle) and their applications to certain mundane problems such as energy conversion, biofluids, medicine, nuclear and electrical engineering make electromagnetic fluids an important field of study. Moreover, in many laboratory devices the electromagnetic fluids are preferred over electromagnetic solids since they readily deform and flow as compared to the latter. In the present thesis, based on Eringents approach, we develop a nonlocal theory of fluids with electromagnetic constitution, capable of exhibiting electromagnetic interactions. Though the approach is nonrelativistic in nature it is in agreement with relativistic Lorentz theories up to terms of 0(v²/c²), where v is the speed of the material; c is the speed of light in vacuum. A generalized Clausius- Duhem thermodynamic inequality which encompasses nonlocal effects is derived and is applied to obtain specific forms of the constitutive equations, including the total electromagnetic momentum, stress, and energy without any a priori assumption as to their nature or form. Both local and nonlocal electromagnetic variables, including their time rates are incorporated into the constitutive theory. Full thermodynamic restrictions and admissibility of the constitutive equations is investigated. In order to facilitate practical applications a completely linear constitutive theory is also derived, again including thermodynamic restrictions as well as the full field equations with appropriate boundary conditions. Surface effects, such as surface waves and surface tension, which occur on free surfaces and between stratified layers are of great importance in many applied fields. Consequently, the linear theory developed above is used to analyze the problem of surface waves in a dielectric fluid medium. A theory of nonlocal polar electromagnetic fluids is also developed. Such a theory takes into account internal orientational effects with electromagnetic interactions in a material with internal substructures, e. g. liquid crystals and animal blood.
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