The Debye Theory of Rotary Diffusion: History, Derivation, and Generalizations |
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Authors: | Eliot Fried Shaun Sellers |
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Institution: | Department of Theoretical and Applied Mechanics?University of Illinois at Urbana-Champaign?Urbana, IL 61801-2935, USA, US Department of Geological Sciences?University College London?Gower Street?London WC1E 5BT, UK, GB
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Abstract: | Motivated by the Debye theory of rotary diffusion in a dipolar fluid, we systematically develop a continuum mechanical theory
of rotary diffusion. This theory generalizes classical kinematics to include continuous rotary degrees of freedom and introduces
an additional balance law associated with the rotary degrees of freedom. Various constitutive relations are proposed in accordance
with standard procedures of nonlinear continuum mechanics. The resulting set of equations provides a properly invariant and
thermodynamically consistent theory that allows for constitutive nonlinearities. In particular, the classical Debye theory
along with the Nernst-Einstein relations are shown to follow from a special case of linear constitutive relations and an assumption
of ideality in which the free energy consists only of a classical entropic contribution. Within our theory, the notion of
osmotic pressure arises naturally as a consequence of accounting for
forces that act conjugate to the rotary degrees of freedom and serves as the driving force for rotary diffusion.
Accepted November 18, 2000?Published online April 23, 2001 |
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