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

Abstract

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, de Gennes, and Au-Yang ($[$C. R. Acad. Sci. Paris Ser. B {\bf 287}, 207 (1978)$]$ and $[$Physica {\bf 101}A, 255 (1980)$]$). We calculate the mean order parameter profile $\psi (r)$, where $r$ is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for $\psi (r)$ 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 $\psi (a)$ is determined by $h_1$ and is independent of the radius $a$. If $r$ considerably exceeds $a$, $\psi (r)$ decays as $r^{-(1+\eta )}$ for a sphere and $r^{-(1+\eta )/2}$ for a cylinder in three dimensions, where $\eta$ is the critical exponent in the order parameter correlation at bulk criticality.

arXiv comment8 pages, 4 figures, accepted for publication in Phys. Rev. E

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• The Theory of Boundary Critical Phenomena
• Nonequilibrium critical Casimir interactions in binary fluids
• Near-Surface Long-Range Order at the Ordinary Transition
• Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory
• Critical adsorption on curved objects
• Attractive interaction and bridging transition between neutral colloidal particles due to preferential adsorption in a near-critical binary mixture
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