Classical equations of state are continuous functions of the density. At subcritical conditions, they exhibit a van der Waals loop, signaling phase coexistence as determined from the Maxwell construction. Here it is described how such loops may be observed in computer simulation studies, and how they depend on the system size. For small systems with dimensions close to the fluid's correlation length, a continuous van der Waals loop is observed which clearly resembles the expected mean field equation of state. As the system size increases, the loop gradually developes a series of discontinuities, corresponding to the formation of condensed domains. In our systems in three dimensions and periodic boundary conditions, systems develope sequentally a slab domain, then a cylindrical domain and finally a spherical condensed domain as system size increases. When the domain forms in the vapor phase, it is a droplet. When it grows within a liquid mother phase, it is a cavity or bubble. It is shown that the sequence of transitions that develop depend on a scaled system size, which is a function of the system's temperature. Close to the critical temperature, the scaled system size remains small even for very large systems, and the formation of condensed domains is supressed. For finite temperatures, the slope of the discontinuities becomes infinite at the thermodynamic limit, and the smooth van der Waals loop gradually becomes the expected flat tie line of zero slope. This slideshow has been presented in: 1. Contributted talk, Liblice Conference, June 2006. 2. Invited Seminar, Johannes Gutenberg Universitat, Mainz, February 2007.

1. Nucleation and cavitation of
spherical, cylindrical and slab like
droplets and bubbles
Slideshow for an invited seminar at the Condensed Matter Theory Group,
Johannes Gutenberg Universit¨at Mainz, February 2007.
by
Luis Gonz´alez MacDowell
References:
√
MacDowell, Virnau, Muller, Binder, J. Chem. Phys. 120, 5293 (2004).
√
MacDowell, Shen, Errington, J. Chem. Phys. 125, 034705 (2006).
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.1/23

2. Nucleation and cavitation of
spherical, cylindrical and slab like
droplets and bubbles
Luis González MacDowell1
, Vincent Shen2
, Jeff Errington3
Peter Virnau4
, Marcus Müller4
, Kurt Binder4
1. Universidad Complutense de Madrid.
2. National Institute for Standards and Technology.
3. University of New York at Buffalo.
4. Johannes Gutenberg Universität, Mainz.
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.2/23

3. Subcritical isotherm
−0.1 0.1 0.3 0.5 0.7 0.9
ρ
−1.5
−0.5
0.5
1.5
µ
Equilibrium curve
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.3/23

4. Subcritical isotherm
−0.1 0.1 0.3 0.5 0.7 0.9
ρ
−1.5
−0.5
0.5
1.5
µ
‘Metastable’ branch
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.3/23

5. Subcritical isotherm
−0.1 0.1 0.3 0.5 0.7 0.9
ρ
−1.5
−0.5
0.5
1.5
µ
‘Unstable’ branch
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.3/23

6. Grand Canonical Simulations (µVT)
WµV T (N) = −kBT ln P(N)
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.4/23

7. Grand Canonical Simulations (µVT)
WµV T (N) = −kBT ln P(N)
N
WµVT
WµVT
180 N
g l
g
l
g
l
∆ΩVT
∆ΩVT
−(pl−pg)V
b)
c) d)
a)
−(pl−pg)V
Nspin
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.4/23

8. Grand Canonical Simulations (µVT)
WµV T (N) = −kBT ln P(N)
N
WµVT
WµVT
180 N
g l
g
l
g
l
∆ΩVT
∆ΩVT
−(pl−pg)V
b)
c) d)
a)
−(pl−pg)V
Nspin
Wµ′V T (N) ∝ WµV T (N) − (µ′
− µ)N
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.4/23

9. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

10. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

11. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

12. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

13. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

14. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

15. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

16. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

17. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

18. Chemical potential v density loops
0 0.2 0.4 0.6
ρ
−0.5
0
0.5
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.5/23

19. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

20. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

21. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

22. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

23. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
∆A
∆A
R R
ρ<ρ
*
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

24. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
∆A
∆A
R R
ρ<ρ
*
ρ=ρ
*
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

25. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
∆A
∆A
R R
ρ<ρ
*
ρ=ρ
*
ρ>ρ
*
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

26. Capillary drop model in a closed
system
A(Vl) = av[V − Vl] + alVl + γS
∆A
∆A
R R
ρ<ρ
*
ρ=ρ
*
ρ>ρ
*
ρ>>ρ
*
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.6/23

27. Resulting equation of state
0 2 4 6 8 10
ρ
0
0.2
0.4
0.6
0.8
1
µ
√
Homogeneous branch for ρ < ρt
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.7/23

28. Resulting equation of state
0 2 4 6 8 10
ρ
0
0.2
0.4
0.6
0.8
1
µ
√
Homogeneous branch for ρ < ρt
√
Inhomogeneous branch for ρ > ρt
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.7/23

29. Taking into account the fluctuations
Two states model:
√
system is in homogeneous state with weight 1
√
system is in inhomogeneous state with weight exp(−β∆A)
µ(ρ) =
µ(ρ) + µ(ρg)e−β∆A
1 + e−β∆A
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.8/23

30. Taking into account the fluctuations
Two states model:
√
system is in homogeneous state with weight 1
√
system is in inhomogeneous state with weight exp(−β∆A)
µ(ρ) =
µ(ρ) + µ(ρg)e−β∆A
1 + e−β∆A
Quantitative description:
√
MSA equation of state for the LJ fluid
√
Simulation result for the surface tension
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.8/23

31. Predicting the equation of state
0 0,02 0,04 0,06 0,08 0,1 0,12
ρ-ρc
0
0,2
0,4
0,6
0,8
1
1,2
1,4
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.9/23

32. Predicting the equation of state
0 0,02 0,04 0,06 0,08 0,1 0,12
ρ-ρc
0
0,2
0,4
0,6
0,8
1
1,2
1,4
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.9/23

33. Predicting the equation of state
0 0,02 0,04 0,06 0,08 0,1 0,12
ρ-ρc
0
0,2
0,4
0,6
0,8
1
1,2
1,4
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.9/23

34. Some simulated subcritical
isotherms
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.10/23

35. Some simulated subcritical
isotherms
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.10/23

36. Some simulated subcritical
isotherms
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.10/23

37. Some simulated subcritical
isotherms
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
β∆µ
0 0.2 0.4 0.6 0.8
ρ
−1.6
−0.8
0
0.8
1.6
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.10/23

38. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

39. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

40. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

41. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

42. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

43. Low temperature isotherm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.11/23

44. The Laplace Equation



∂Ainh
∂Vl
= ∆p − γ ∂S
∂Vl
ρV = ρv[V − Vl] + ρlVl + ΓS
Generalization: S = kgV
(q−2)/(q−1)
l
q Domain kg
4 spherical (36π)1/3
3 cylindrical 2(πL)1/2
2 slab 2L2
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.12/23

45. Simplified liquid model
√
Density increments are linear in the chemical
potential
√
The fluid is symmetric, χv = χl
√
The surface tension is constant
√
Adsorption at the surface of tension is negligible
Solution:
χl∆µq
− ∆ρ∆µq−1
+
nkgγ
∆ρn
c V 1/(q−1)
q−1
= 0
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.13/23

46. Scaling form of the solutions
x = χl
∆ρ∆µ Kq =
nkgγχl
∆ρn
c ∆ρq/(q−1)V 1/(q−1)
q−1
xq
− xq−1
+ Kq = 0
∆a = 1
2
χl
∆ρ2
∆A
V ω = 1
2(1 − x) n = q−2
q−1
∆a(ω) = ω2
− ω + 2n−1
n K1−n
q ωn
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.14/23

47. Solutions for different domain
shapes
transition transition density
hom → sph ρt
= ρc
v + 2 · 33/4
∆ρc
ξsph
V
1/4
hom → cyl ρt
= ρc
v + 3 · 21/3
∆ρc
ξcyl
V
2/9
hom → slb ρt
= ρc
v + ∆ρc
ξslb
V
1/6
ξ ∝ γ3χ3
v
∆ρ6
c
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.15/23

48. System size features of the isotherm
volume range stable domains observed
V
ξsph
> 43
π4 (4
3
)41
hom → sph → cyl → slab
43
π4 (4
3
)41
< V
ξsph
< π5
27 (3
2
)22
hom → cyl → slab
π5
27 (3
2
)22
< V
ξsph
< 3427
π
hom → slab
V
ξsph
< 3427
π
hom
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.16/23

49. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

50. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

51. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

52. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

53. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

54. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

55. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

56. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

57. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

58. Large system, low temperature
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ρ
−1
−0.6
−0.2
0.2
0.6
1
µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.17/23

59. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

60. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

61. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

62. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

63. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
0 0.1 0.2 0.3 0.4
ρ
−50
−20
10
40
χ
−1
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

64. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
0 0.1 0.2 0.3 0.4
ρ
−50
−20
10
40
χ
−1
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

65. Increasing system size (low T)
0 0.2 0.4 0.6 0.8
ρ
−1.6
−1
−0.4
0.2
0.8
1.4
2
β∆µ
0 0.1 0.2 0.3 0.4
ρ
−50
−20
10
40
χ
−1
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.18/23

66. Increasing system size (high T)
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.19/23

67. Increasing system size (high T)
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.19/23

68. Increasing system size (high T)
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.19/23

69. Increasing system size (high T)
0.05 0.25 0.45 0.65
ρ
−0.2
−0.1
0
0.1
0.2
β∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.19/23

70. A look at the volume scale
Properties are governed by scaled volume V/ξ, with
ξ ∝ χ2
γ3
∆ρ−6
c
For the temperature approaching Tc:
ξ ∝ |T − Tc|−3ν
ξ1/3
is a meassure of the correlation length
The scaled volume decreases as T approaches Tc
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.20/23

71. Increasing Temperature =
Decreasing volume
−0.5 −0.25 0 0.25 0.5
(ρ−ρ1/2)/∆ρc
−1
−0.5
0
0.5
1
∆µ/∆µs
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.21/23

72. Increasing Temperature =
Decreasing volume
−0.5 −0.25 0 0.25 0.5
(ρ−ρ1/2)/∆ρc
−1
−0.5
0
0.5
1
∆µ/∆µs
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.21/23

73. Increasing Temperature =
Decreasing volume
−0.5 −0.25 0 0.25 0.5
(ρ−ρ1/2)/∆ρc
−1
−0.5
0
0.5
1
∆µ/∆µs
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.21/23

74. Increasing Temperature =
Decreasing volume
−0.5 −0.25 0 0.25 0.5
(ρ−ρ1/2)/∆ρc
−1
−0.5
0
0.5
1
∆µ/∆µs
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.21/23

75. Approaching infinite system size ...
0 0.2 0.4 0.6 0.8
ρ
−2
0
2
∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.22/23

76. Approaching infinite system size ...
0 0.2 0.4 0.6 0.8
ρ
−2
0
2
∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.22/23

77. Approaching infinite system size ...
0 0.2 0.4 0.6 0.8
ρ
−2
0
2
∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.22/23

78. Approaching infinite system size ...
0 0.2 0.4 0.6 0.8
ρ
−2
0
2
∆µ
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.22/23

79. Approaching infinite system size ...
0 0.2 0.4 0.6 0.8
ρ
−2
0
2
∆µ
∆A∗
=
∆ρ2
c
χl
ξsph
V
ξsph
1/2
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.22/23

80. Conclusions
√
Droplet states obey a universal scaling law
√
Different sequences of domain transitions occur
depending on V/ξ
√
Small ‘scaled’ systems follow a continuous loop
isotherm
√
Stable states are possible inside coexistence loop
(for small systems)
√
Apparent spinodal points are small system dew
and bubble points
√
Young-Laplace equation (capillary model)
provides accurate description
Nucleation and cavitation ofspherical, cylindrical and slab likedroplets and bubbles – p.23/23