Critical diffusion in a bounded fluid. II. Temperature-dependent effects.

Abstract

The mode-mode coupling formalism is applied to calculate the nonlocal critical diffusion coefficient for a binary-mixture film close to the consolute point. The system is confined between two parallel walls, of infinite extent, separated by a distance 2L. Assuming that the mixture exhibits no preferential wetting to the walls, the boundary effects are calculated. These boundaries are assumed to constrain the fluid on contact with them to remain stationary and, therefore, modify the transport properties of the hydrodynamic shear modes and, consequently, the diffusion coefficient. The Fourier transform of this coefficient is expanded in inverse powers of L(${q}^{2}$+${\ensuremath{\kappa}}^{2}$${)}^{1/2}$, where q is the Fourier wave vector and \ensuremath{\kappa} is the inverse of the concentration correlation length. The term of order [L(${q}^{2}$+${\ensuremath{\kappa}}^{2}$${)}^{1/2}$${]}^{\mathrm{\ensuremath{-}}1}$, yielding the first correction to the bulk value, is calculated explicitly giving an expression which is valid for L(${q}^{2}$+${\ensuremath{\kappa}}^{2}$${)}^{1/2}$\ensuremath{\gg}1 but for arbitrary \ensuremath{\kappa}/q. It is found that the walls always suppress the diffusion coefficient and have their maximal effect at the critical point, \ensuremath{\kappa}=0. For \ensuremath{\kappa}g0 and fixed q, the suppression effect decreases monotonically with increasing \ensuremath{\kappa}.