We develop a continuum theory of fluids that consist of orientable permanent dipoles of identical geometry subject to the influences of rotary diffusion and externally applied fields. The average alignment of the dipoles may vary in magnitude and in direction. Fundamental to our approach is an extended kinematic description wherein each material element has associated with it a position in space and a distribution of orientations on the unit sphere-the former describing the center of mass of an assembly of dipoles and the latter describing the manner in which the dipoles are oriented about their center of mass. By incorporating transport due to the translatory motion of the mass centers and also to the rotary motion of the dipoles, our proposed balance laws reflect this extended kinematic description. In addition to a rotary mass balance, we formulate separate momentum balances associated with the translatory and the rotary degrees of freedom and a moment of momentum balance that incorporates both translatory and rotary ingredients. For simplicity, we suppress thermal effects, so that the first and second laws of thermodynamics are expressed by an energy imbalance. Our final governing equations result on combining the fundamental balances with constitutive relations restricted to satisfy the energy imbalance in all thermodynamic processes. These partial differential equations provide a framework that encompasses, as specializations reflecting certain idealized constitutive assumptions, equations arising in common statistical models for dipolar fluids, such as the Debye theory of rotary diffusion and various straightforward generalizations thereof.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
TAM R 888
1998-6014
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112594
Copyright and License Information
Copyright 1998 Board of Trustees of the University of Illinois
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.
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