TY - JOUR

T1 - Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality

T2 - Local functional theory

AU - Yabunaka, Shunsuke

AU - Onuki, Akira

N1 - Funding Information:
This work was supported by KAKENHI Grant No. 15K05256. A.O. would like to thank D. Beysens for informative correspondence. S.Y. was supported by Grant-in-Aid for Young Scientists (B) (Grant No. 15K17737), Grants-in-Aid for Japan Society for Promotion of Science (JSPS) Fellows (Grant No. 14J03111), and the JSPS Core-to-Core Program “Non-equilibrium dynamics of soft matter and information”.

PY - 2017/9/18

Y1 - 2017/9/18

N2 - 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 h1, where the surface order parameter ψ(a) is determined by h1 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.

AB - 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 h1, where the surface order parameter ψ(a) is determined by h1 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.

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U2 - 10.1103/PhysRevE.96.032127

DO - 10.1103/PhysRevE.96.032127

M3 - Article

C2 - 29346888

AN - SCOPUS:85029843547

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

M1 - 032127

ER -