Crossover from the hydrodynamic regime to the thermal fluctuation regime in a two-dimensional phase-separating binary fluid containing surfactants

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 1 B, 2000, Pages 766-774

  Roan, Jiunn Ren ^a,b   Hu, Chin Kun ^a  

^a INSTITUTE OF PHYSICS   (Taiwan)

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY MIXTURES; HYDRODYNAMICS; PHASE SEPARATION; SURFACE ACTIVE AGENTS;

CAHN-HILLARD-COOK REGIME;

STATISTICAL MECHANICS;

EID: 0034229109     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.766     Document Type: Article

References (24)

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8. H. Tanaka and T. Araki [Phys. Rev. Lett. 81, 389 (1998)] reported that dynamic scaling could not be observed under high-fluidity. It is not clear how much the free boundary condition used, which in two dimensions leads to a fictitious hydrodynamic interaction that varies with logarithmically spatial separation, is responsible for this result. It is interesting to note that H. Chen and A. Chakrabarti, [J. Chem. Phys. 108, 6006 (1998)] used this divergent hydrodynamic interaction and obtained results that look "normal."
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10. The estimation of surface tension used in Ref. [8] may seem pathological. It was based on the following consideration. The amount of surfactants at the interfaces is expected to be roughly proportional to 〈ρ〉. ρR can serve as a measure of this amount, so ρR∝〈ρ〉. This estimation of course breaks down in the early stage, which was not the concern of Ref. [8].
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21. Figures 3(c) and 3(d) may suggest to some readers that there is a systematic drift when more samples are included. This is, however, not the case. As stated in the text, an individual sample's growth curve can be roughly retrieved. The reader can then see that there is no systematic drift that drives the growth curve downward.
22. In Ref. [8] it is shown that logarithmic growth laws and algebraic growth laws work equally well because the true growth law is far more complicated and contains many parameters. Both can be used to fit the data.
23. The two methods are complementary. When two slopes can be clearly seen in the growth curve regardless of the number of samples included, there is no point in using the other method. When the second slope cannot be unambiguously determined for all ensembles, using the slopes to locate the crossover is not reliable. We find the borderline between these two methods is around 〈ρ〉 = 0.35. The locations of the crossover determined at different 〈ρ〉 are consistent with the theoretical expectation given in Sec. III A. However, the crossover is probably not sharp and what these methods give is an estimation of the lower bound and the upper bound, respectively, so it is difficult to make an unequivocal quantitative analysis.
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