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On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
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10.1063/1.3054346
/content/aip/journal/jcp/130/1/10.1063/1.3054346
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/1/10.1063/1.3054346

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the fluctuating density profile as a function of ; the height is the distance over which the intrinsic density profile (dashed line) is shifted.

Image of FIG. 2.
FIG. 2.

MC results by Vink et al. (Ref. 3) for the surface structure factor (in units of ) vs (in units of ) for various values of the integration limit , 2, 3, 4. The dashed line is the CW model. In this example, , , and the colloidal particles are used to define .

Image of FIG. 3.
FIG. 3.

MC results by Vink et al. (Ref. 3) for the surface structure factor (in units of ) vs (in units of ). The dotted line is the CW model, the dashed line is the combination of the CW model and the bulk correlation function, and the drawn line is the combination of the ECW model and the bulk correlation function. In this example, , , , and the colloidal particles are used to define .

Image of FIG. 4.
FIG. 4.

MC results by Vink et al. (Ref. 3) for the surface structure factor (in units of ) vs (in units of ) using the colloidal particles (circles) and polymer particles (triangles) to define . The dotted line is the CW model and the drawn lines are the combination of the ECW model and the bulk correlation function. In this example, , , and .

Image of FIG. 5.
FIG. 5.

Surface tension in units of vs the volume fraction difference, . In this example, ; the symbols are numerical results, the drawn line is the gradient expansion approximation, and the filled symbols are results from the MC simulations by Vink et al. (Ref. 3).

Image of FIG. 6.
FIG. 6.

Curvature correction to the volume fraction profile as a function of (in units of ) using the ic (circles) and the cc (squares). In this example, and ; the symbols are numerical results and the drawn lines are the analytical profiles from the gradient expansion.

Image of FIG. 7.
FIG. 7.

Contributions to the bending rigidity and in units of vs the volume fraction difference, . In this example, ; the symbols are numerical results and the drawn lines are the gradient expansion approximation.

Image of FIG. 8.
FIG. 8.

Bending rigidity in units of vs the volume fraction difference, , using the ic (circles) and the cc (squares). In this example, ; the open symbols are numerical results, the drawn lines are the gradient expansion approximation, and the filled circles are the MC results by Vink et al. (Ref. 3); the dashed line is the fit .

Image of FIG. 9.
FIG. 9.

Bending rigidity in units of vs the volume fraction difference, . In this example, ; the filled circles are the MC results by Vink et al. (Ref. 3), the drawn line is the virial expression with the sharp-profile approximation, the dashed line is the equilibrium result, and the dotted line is the Mecke and Dietrich result (Ref. 19) with .

Image of FIG. 10.
FIG. 10.

Contributions to the bending rigidity and in units of vs the reduced temperature distance to the critical point, . The symbols are numerical results and the drawn lines are the gradient expansion approximation.

Image of FIG. 11.
FIG. 11.

The bending length (in units of ) vs the reduced temperature distance to the critical point, , using the ic (circles) and the cc (squares). The open symbols are numerical results and the drawn lines are the gradient expansion approximation. The dashed line is the correlation length and the dotted line is the Mecke and Dietrich result (Ref. 19) with .

Tables

Generic image for table
Table I.

Listed are the simulation results (Ref. 3) for the polymer volume fraction , liquid and vapor colloidal volume fractions, and , surface tension (in units of ), bending rigidity (in units of ; in parentheses is the estimated error in the last digit), and (in units of ).

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/content/aip/journal/jcp/130/1/10.1063/1.3054346
2009-01-07
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/1/10.1063/1.3054346
10.1063/1.3054346
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