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A maximum-entropy approach to the adiabatic freezing of a supercooled liquid
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10.1063/1.4801864
/content/aip/journal/jcp/138/16/10.1063/1.4801864
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4801864
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Theoretical phase diagram for a system of particles interacting through the potential (2.2) with ϕ(x) = x −6 and z 1 = 12. T c is the critical temperature and β c = (k B T c )−1. The critical-point coordinates, ρ c and T c , follow from requiring that the first- and second-order density derivatives of the fluid pressure be simultaneously zero. One thus finds ρ c = ρ0/3 and k B T c = (8/27)aρ0, with a = (2π/3)εσ3. Top: phase diagram on the density-temperature plane, showing the extent of the coexistence regions; the triple temperature is between 0.6 and 0.65 of T c . Bottom: phase diagram on the temperature-pressure plane, reporting as blue crosses also the (T, P) points characterizing the solid-liquid coexistence states borne out of the decay of the metastable-liquid states at various T in values, for x g = 0.001 (see Sec. III B ).

Image of FIG. 2.
FIG. 2.

Final equilibrium state after the adiabatic decay of the metastable liquid under constant-volume conditions, for T m = 0.8 T c . Top: temperature; bottom: pressure.

Image of FIG. 3.
FIG. 3.

Final equilibrium state after the adiabatic decay of the metastable liquid under constant-volume conditions, for T m = 0.8 T c and for two different amounts of foreign gas in the vessel (crosses, x g = 0.001; squares, x g = 0.1). Top: temperature; bottom: pressure.

Image of FIG. 4.
FIG. 4.

Top: Solid fraction in the equilibrium state resulting from the adiabatic decay of the metastable liquid under constant-volume conditions, for T m = 0.8 T c and for two different amounts of foreign gas in the vessel (crosses, x g = 0.001; squares, x g = 0.1). Bottom: Entropy of the solid-liquid mixture at T fin (solid lines) vs. entropy of the supercooled liquid at T in (dotted lines).

Image of FIG. 5.
FIG. 5.

Final equilibrium state after the adiabatic decay of the metastable liquid under constant-volume conditions, for T m = 0.8 T c and for two different amounts of foreign gas in the vessel (top panel, x g = 0.001; bottom panel, x g = 0.1). Volume of the solid-liquid mixture (solid lines) vs. volume of the supercooled liquid at T in (dotted lines).

Image of FIG. 6.
FIG. 6.

Final equilibrium state after the adiabatic decay of the metastable liquid at constant pressure, for T m = 0.8 T c . Top: volume of the solid-liquid mixture at T m (solid line) vs. volume of the liquid at T in (dotted line); bottom: solid fraction in the mixture.

Image of FIG. 7.
FIG. 7.

Difference in specific entropy between the droplet-liquid mixture at T fin and the original metastable liquid at T in, as a function of the droplet “radius,” . Two values of N are considered, 1000 (red curves, left) and 10 000 (blue curves, right), for T m = 0.8 T c . For each N, various T in/T c values were considered: from top to bottom, 0.57, 0.60, 0.63 for N = 103; and 0.60, 0.65, 0.70 for N = 104.

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/content/aip/journal/jcp/138/16/10.1063/1.4801864
2013-04-22
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A maximum-entropy approach to the adiabatic freezing of a supercooled liquid
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4801864
10.1063/1.4801864
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