Abstract:
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.
