ACH - Models in Chemistry 135. (1998)
6. szám - RESEARCH ARTICLES - Nettleton, R. E.: Shear-dependent binary liquid diffusion
ЛС Ц- MODELS IN CHEMISTRY 135 (6), pp 919-930 (1998) Shear-dependent binary liquid diffusion Richard E. Nettleton Department of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa Received February 4, 1998 Binary diffusion in a liquid undergoing Couette flow at high shear-rate is parametrized via a traceless elastic strain tensor cr^ß and an inelastic strain-rate C^. Corresponding operators cr^ and are introduced for which the variables are ensemble averages. The operators are used to set up a Jaynesian distribution from which one can calculate entropy and its derivatives. One obtains the thermodynamic force associated with diffusion as an expansion in the variables, from which the a^ß- and C^g-dependence of the diffusion tensor Daß can be extracted via a reciprocity relation. The predicted anisotropies Dxx > D^ and 0 > DXy are in qualitative agreement with limited computer data. Introduction An extended thermodynamics of viscoelasticity in simple liquids has been developed [1,2] which associates with a macroscopically-small volume V, immersed in a large homogeneous fluid phase, a set of strain and creep-rate variables. These include a traceless elastic strain crj^ proportional to traceless pressure and a traceless inelastic strain-rate CjU Thermodynamic potentials for V depend on these variables, on temperature T, and on the number TV,- of particles of constituent i. One may also need one or more scalar parameters characterizing liquid structure. By coupling the scalars to the relaxation equations for and C\ß one can explain non-analyticities [3] seen at high shear-rates. Anisotropies [4] arising in Couette flow at high rates-ofshear stem from dependence of the diffusion tensor on cr^ and C\p They have been studied by molecular dynamic simulation which removes frictional heat to make possible an observation at constant T. The binary mixture we consider here has N\ particles of mass mi which constitute a dilute solute mixed with Nj particles of mass m2■ The N\ particles are the diffusing component. X\=N\ IN, with N = N\ +N2, will be a small fraction independent of N. In the present paper, we seek to predict the anisotropy of the diffusion tensor at high shear-rate, dux/dy, for mass flow in the ^-direction, varying with y. For our theoretical treatment, we select a point at у = 0 in the middle of the diffusion cell, 1217-8969/98/$ 5.00 0 1998 Akadémiai Kiadó, Budapest