Model fluid in a porous medium: Results for a Bethe lattice

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 2 2, 2003, Pages

  Sokolovskii, R O ^a,b   Cates, M E ^a   Sokolovska, T G ^a,b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b INSTITUTE FOR CONDENSED MATTER PHYSICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; POROUS MATERIALS; QUENCHING; THERMAL EFFECTS; WETTING;

BETHE LATTICE; MACROSCOPIC VOLUME;

FLUID MECHANICS;

EID: 42749109136     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

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11. Of course, we are interested in the thermodynamic limit: V → ∞.
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13. This corresponds to the case when the matrix-fluid attraction equals one half of the fluid-fluid attraction: K = I/2. In this case the model is spin-flip symmetric at H = 0, which results in the symmetric binodal with critical point at n = 1/2.
14. z.
15. There is a one-to-one correspondence between s(h) and s̃(ξ) through Eq. (36).
16. max)], but even this procedure does not result in exact bounds.
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20. R. O. Sokolovskii, M.E. Cates, and T. G. Sokolovska (unpublished); for the Bethe approximation treatment of the special case H; = 0, see Ref. [17].
21. H remains unchanged when all spins and fields (H, H;) change sign simultaneously.
22. If q(h) really has step discontinuities, it is incorrect to call it a "continuous spectrum." But we are not sure there are any real discontinuities (only very steep slopes that our numerics cannot resolve) and hence continue to use this term throughout the paper to emphasize distinction between q(h) and s(h).
23. 17.
24. H = -J.