ACH - Models in Chemistry 135. (1998)

6. szám - RESEARCH ARTICLES - Nettleton, R. E.: Shear-dependent binary liquid diffusion

920 NETTLETON: Shear-dependent binary liquid diffusion where ux = 0. Given values of aap and Caß, which are ensemble averages of operators aap and Cap , the maximum entropy formalism of Jaynes [5] gives the phase-space distribution at the phase point x: p[x) = Z"1 exp[~ß{H + X óap + vlßCaß +1• (1) aß а and 'У}ф are thermodynamic forces associated with a^ß and C\p, respectively; ф^ is the force belonging to the diffusion flow and Z normalizes p to unity. The forces Q\p and f^p, and ф^ can be calculated from the matching conditions, e.g., Jda-\p^daáx' ^ Using Eqs (1) and (2), we obtain an expansion for ф^ in terms of Jd, and C^p. This expansion is substituted into Jda - ^Kaß0dß > (3) ß where the tensor Kap is determined to make Eq. (3) an identity. Kap is related via an Onsager reciprocity relation to the diffusion tensor, Dap, for which we obtain in this way an expansion. In steady shear, axy and Cxy are proportional to the shear-rate, and the terms in Daß involving these tensors exhibit the shear-induced anisotropy. To use Eq. (1), we need operators aap and Cap. These need not be traceless when tracelessness applies to the forces in Eq. (1). Other authors on extended thermodynamics of viscoelasticity have invariably followed Kluitenberg [6] in using inelastic rather than elastic strain as a variable. The only existing expression [7] for uaß supposed that we can select a point R within the small volume V and let crap(R) characterize the strain throughout V. This should work from an information-theoretic point of view but, with this parametrization, it is difficult in a natural way to make the information-theoretic entropy extensive, as required if it is to be a model for thermodynamic entropy. Here we modify the definition [7] of aap(R) in such a way that it can be averaged over all points R in V, which leads easily to an extensive entropy. We also introduce an operator Caß never previously used. This is based on a picture of inelastic particle displacement in which a particle moves to a new postion within a localized region where mean inter-molecular separation increases to the point where the particle can cross a potential barrier and escape from its cage. The model for elastic displacement of a particle used here is the same as the one proposed previously [7]. The elastic displacements are superpositions of high­­frequency hypersound modes near the top of the phonon dispersion curve which 'V' Ц - models in Chemistry 135. 1998

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