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 in the homogeneous phase near the demixing critical point through a capillary tube connecting two reservoirs. It is usual that one component is preferentially adsorbed by the tube wall, and its influence is amplified because of the near-criticality. We consider the resultant inhomogeneous composition in terms of the renormalized local functional theory, which was previously devised to explain the interaction between two plates immersed in a near-critical binary fluid mixture. The inhomogeneity causes that of the correlation length, and then that of the transport coefficients. How the mass flow rates of the components through the tube depend on the temperature cannot be explained by the critical enhancement of the transport coefficients because of the off-critical composition in the tube. Deriving formulae of the Onsager coefficients, we numerically calculate the mass flow rates for a mixture of 2,6-lutidine and water and for a mixture of nitroethane and 3-methylpentane. When the flow is driven by pressure difference between the reservoirs, the composition of the mixture flowing out of the tube is modified by the preferential adsorption. When the flow is driven by mass-fraction difference, the total mass flow rate is raised distinctly by convection emerging in the presence of the preferential adsorption. These phenomena can be regarded as representing cross effects linked with each other via the reciprocal relation.