In the high density liquid phase, particles gain much potential energy because
they are close together and are located in the attractive parts of the
interparticle potential.

J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd edition,
Academic Press, 1986



Fluid systems that can undergo a phase transition are best described as a
grand canonical ensemble in which the system volume V, the temperature T and
the chemical potential μ are fixed. 

L.D. Landau and E.M Lifshitz, Course of Theoretical Physics, Volume 5:
Statistical Physics, 3rd edition, Butterworth Heinemann, 1996.

Furthermore, it is known REF that the pressure in a stable bulk liquid is
larger than in the gas phase at the same chemical potential, ...

D. Chandler, Introduction to modern statistical mechanics, Oxford Univ. Press
(1987).

To study bubbles in a complex geometry like Fig. 4 we use a morphometric
approach to separate the role of geometrical confinement and thermodynamics in
capillary evaporation for ‘capillaries’ of different size, ranging from atomic
to macroscopic.{Roth, 2002 #5004; Roth, 2005 #5005; Roth, 2006 #5376}

R. Evans, FLUIDS ADSORBED IN NARROW PORES - PHASE-EQUILIBRIA AND STRUCTURE,
J. Phys.: Condens. Matter 2, 8989 (1990).

The geometrical measures C and X are the integrated (over the surface area)
mean and Gaussian curvatures of the wall COMMENT: Roland and Dirk, please give
me any other references you want to include here, and the corresponding
thermodynamic coefficients κ and κ are bending rigidities COMMENT: WE NEED A
REFERENCE OR TWO TO TEXTBOOKS THAT DEFINE BENDING RIGIDITIES. 

K.R. Mecke, Morphological thermodynamics of composite media, Fluid Phase
Equilibria 150, 591 (1998).

K.R. Mecke, Integral geometry in statistical physics, Int. J. Mod. Phys. B 12,
861 (1998).

P.-M. Koenig, R. Roth, and K.R. Mecke, Morphological Thermodynamic of Fluids:
Shape Dependence of Free Energies, Phys. Rev. Lett. 93, 160601 (2004).

R. Roth, Fluid mixtures at curved walls, J. Phys. Condes. Matter 17 S3463
(2005). 

Until that is settled, and the interaction of fluid and protein inside a
channel are measured, we use a simple square well model of fluids used in
Density Functional Theory to describe our solvent

R. Evans, NATURE OF THE LIQUID-VAPOR INTERFACE AND OTHER TOPICS IN THE
STATISTICAL-MECHANICS OF NONUNIFORM, CLASSICAL FLUIDS, Adv. Phys. 28,
143 (1979).

Y. Rosenfeld, FREE-ENERGY MODEL FOR THE INHOMOGENEOUS HARD-SPHERE FLUID
MIXTURE AND DENSITY-FUNCTIONAL THEORY OF FREEZING, Phys. Rev. Lett. 63,
980 (1989).

R. Roth, R. Evans, A. Lang, and G. Kahl, Fundamental measure theory for
hard-sphere mixtures revisited: the White Bear version, J. Phys.:
Condens. Matter 14, 12063 (2002).

Y.X. Wu and J. Wu, Structures of hard-sphere fluids from a modified
fundamental-measure theory, J. Chem. Phys. 117, 10156 (2002).

H. Hansen-Goos and R. Roth, Density functional theory for hard-sphere
mixtures: the White Bear version mark II, J. Phys.: Condens. Matter 18, 8413
(2006).