Effect of surface curvature on critical adsorption

Thermo-osmosis of a near-critical binary fluid mixture: A general formulation and universal flow direction

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis-mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980)PHYADX0378-437110.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ(r), where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ(r) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h_{1}, where the surface order parameter ψ(a) is determined by h_{1} and is independent of the radius a. If r considerably exceeds a, ψ(r) decays as r^{-(1+η)} for a sphere and r^{-(1+η)/2} for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.