Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations

The theory of second gradient fluids (which are able to exert shear stresses also in equilibrium conditions) allows us: (i) to describe both the thermodynamical and the mechanical behavior of systems in which an interface is present; (ii) to express the surface tension and the radius of microscopic bubbles in terms of a functional of the chemical potential; (iii) to predict the existence of a (minimal) nucleation radius for bubbles. Moreover, the above theory supplies a 3D-continuum model which is endowed with sufficient structure to allow the construction of a 2D-shell-like continuum representing a consistent approximate 2D-model for the interface between phases. In this paper we use numerical simulations in the framework of second gradient theory to obtain explicit relationships for the surface quantities typical of 2D-models. In particular, for some of the most general two-parameter equations of state, it is possible to obtain the curves describing the relationship between the surface tension, the thickness, the surface mass density and the radius of the spherical interfaces between fluid phases of the same substance. These results allow us to predict the (minimal) nucleation radii for this class of equations of state.

[1]  James Serrin,et al.  Mathematical Principles of Classical Fluid Mechanics , 1959 .

[2]  M. Slemrod,et al.  Stability of spherical isothermal liquid-vapor interfaces , 1995 .

[3]  A. H. Falls,et al.  Structure and stress in spherical microstructures , 1981 .

[4]  J. Israelachvili,et al.  Determination of the Capillary pressure in menisci of molecular dimensions , 1980 .

[5]  V. Carey.  Liquid-Vapor Phase-Change Phenomena , 2020 .

[6]  Jerome K. Percus,et al.  Analysis of Classical Statistical Mechanics by Means of Collective Coordinates , 1958 .

[7]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[8]  J. Serrin.  New Perspectives in Thermodynamics , 1986 .

[9]  J. E. Dunn,et al.  On the Thermodynamics of Interstitial Working , 1983 .

[10]  F. dell’Isola,et al.  Deduction of thermodynamic balance laws for bidimensional nonmaterial directed continua modelling interphase layers , 1993 .

[11]  E. Killmann.  Adsorption and the Gibbs Surface Excess , 1984 .

[12]  K. Hutter,et al.  Continuum Description of the Dynamics and Thermodynamics of Phase Boundaries Between Ice and Water, Part II. Thermodynamics , 1988 .

[13]  M. Gurtin.  Thermodynamics and the possibility of spatial interaction in elastic materials , 1965 .

[14]  Pierre Seppecher,et al.  Radius and surface tension of microscopic bubbles by second gradient theory , 1995, 0808.0312.

[15]  P. Ramasamy,et al.  Curvature dependence of surface free energy and nucleation kinetics of CCl4 and C2H2Cl4 vapours , 1991 .

[16]  E. D. Cyan.  Handbook of Chemistry and Physics , 1970 .

[17]  Jean-Baptiste Lully,et al.  The collected works , 1996 .

[18]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[19]  P. G. de Gennes,et al.  Some effects of long range forces on interfacial phenomena , 1981 .

[20]  N. Kampen,et al.  CONDENSATION OF A CLASSICAL GAS WITH LONG-RANGE ATTRACTION , 1964 .

[21]  Lambertus A. Peletier,et al.  Uniqueness of non-negative solutions of semilinear equations in Rn , 1986 .

[22]  D. Kenning.  Liquid—vapor phase-change phenomena , 1993 .

[23]  R. Tolman.  The Effect of Droplet Size on Surface Tension , 1949 .

[24]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[25]  H. Gouin,et al.  Relation entre l'équation de l'énergie et l'équation du mouvement en théorie de Korteweg de la capillarité , 1985 .

[26]  D. Stroud,et al.  Density-functional theory of simple classical fluids. I. Surfaces , 1976 .

[27]  William H. Press,et al.  Numerical recipes , 1990 .

[28]  V. Lamer,et al.  Surface Tension of Small Droplets from Volmer and Flood's Nucleation Data , 1949 .

[29]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[30]  R. Tolman.  Consideration of the Gibbs Theory of Surface Tension , 1948 .