Isothermal transport of a near-critical binary fluid mixture through a capillary tube with the preferential adsorption

Abstract

We study isothermal transport of a binary fluid mixture, which lies in the homogeneous phase near the demixing critical point, through a capillary tube. A short-range interaction is assumed between each mixture component and the tube's wall surface, which usually attracts one component more than the other. The resulting preferential adsorption becomes significant owing to large osmotic susceptibility. The mixture flowing out of the tube is rich in the preferred component when flow is driven by the pressure difference between the reservoirs. When flow is driven by the mass-fraction difference, the total mass flow occurs in the presence of the preferential adsorption. These phenomena can be regarded as cross-effects linked by the reciprocal relation. The latter implies that diffusioosmosis arises from the free energy of the bulk of the mixture not involving the surface potential, unlike usual diffusioosmosis far from the critical point. We also study these phenomena numerically by using the hydrodynamics based on the coarse-grained free-energy functional, which was previously obtained to reveal near-critical static properties, and using material constants that were previously obtained in some experimental studies. Influence of the critical enhancement of the transport coefficients is found to be negligible because of off-critical composition in the tube. It is also shown that the conductance, or the total mass flow rate under a given mass-fraction difference, can change non-monotonically with the temperature. The change is well expected to be large enough to be detected experimentally.