Metastable wetting layers

Bruce M. Law

doi:10.1103/PhysRevE.48.2760

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Metastable wetting layers

Bruce M. Law

Department of Physics, Kansas State University, Manhattan, Kansas 66506-2601

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Phys. Rev. E 48, 2760 – Published 1 October, 1993Erratum Phys. Rev. E 50, 627 (1994)

DOI: https://doi.org/10.1103/PhysRevE.48.2760

Abstract

In the two-phase region of a critical binary liquid mixture a wetting layer of the heavier phase can occur at the upper liquid-vapor surface sufficiently close to the critical temperature. This wetting layer can be either stable or metastable to long-wavelength capillary wave fluctuations on the adjacent critical interface. The stability depends upon the sign and slope of the dispersion force curve F(d). We classify the four main generic shapes for F(d), which determines the stability or metastability of the wetting layer, in terms of the relative magnitudes of the static and visible dielectric constants for the two liquid components. For realistic values of the liquid-mixture parameters we calculate the critical wavelength beyond which fluctuations are unstable and also determine the lifetime of the metastable state. The lifetime can vary from seconds to many hours.

Erratum

Erratum: Metastable wetting layers

Bruce M. Law

Phys. Rev. E 50, 627 (1994)

References (24)

For reviews see S. Dietrich, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic, London, 1987), Vol. 12; D. E. Sullivan and M. M. Telo da Gama, in Fluid Interfacial Phenomena, edited by C. A. Croxton (Wiley, New York, 1985); M. Schick, in Liquids at Interfaces, Proceedings of the Les Houches Summer School Session XLVIII, Haute-Savoie, 1988, edited by J. Charvolin, J. F. Joanny, and J. Zinn-Justin (North-Holland, Amsterdam, 1990).
J. W. Cahn, J. Chem. Phys. 66, 3667 (1977).
J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Oxford University Press, London, 1982).
P. G. de Gennes, J. Phys. (Paris) Lett. 42, L377 (1981).
R. F. Kayser, Phys. Rev. B 34, 3254 (1986).
M. E. Fisher and P.-G. de Gennes, C. R. Acad. Sci. B 287, 207 (1978).
A. J. Liu and M. E. Fisher, Phys. Rev. A 40, 7202 (1989).
H. Kellay, J. Meunier and B. P. Binks, Phys. Rev. Lett. 69, 1220 (1992).
A. Vrij, Discuss. Faraday Soc. 42, 23 (1966); A. Vrij and J. Th. G. Overbeek, J. Am. Chem. Soc. 90, 3074 (1968).
D. B. Hough and L. R. White, Adv. Colloid Interface Sci. 14, 3 (1980).
I. E. Dzyaloshinskii, E. M. Lifshitz and L. P. Pitaevskii, Adv. Phys. 10, 165 (1961).
J. N. Israelachvili, Intermolecular and Surface Forces (Academic, London, 1985), p. 144.
R. Lipowsky and D. A. Huse, Phys. Rev. Lett. 57, 353 (1986).
B. M. Law (unpublished).
In the calculations for Fig. 2 we retain all the liquid parameters for the mixture hexadecane plus acetone; however, we have interchanged ( $ε_{i 0}$ / $ε_{i o +}$ ) and $ε_{iv}$ for the various curves (i)–(iv). Specifically, for curve (i) $ε_{A 0}$ , $ε_{A o +}$ , $ε_{Av}$ , $ε_{B 0}$ , $ε_{B o +}$ , and $ε_{Bv}$ were taken as 21.2, 2.2, 2.025, 2.04, 2.04, and 1.819, respectively; for curve (ii) the respective values are 2.04, 2.04, 2.025, 21.2, 2.2, and 1.819; for curve (iii) the respective values are 21.2, 2.2, 1.819, 2.04, 2.04, and 2.025; and for curve (iv) the respective values are 2.04, 2.04, 1.819, 21.2, 2.2, and 2.025.
R. C. Haskell, D. C. Petersen and M. W. Johnson, Phys. Rev. E 47, 439 (1993).
A. W. Adamson, Physical Chemistry of Surfaces, 4th ed. (Wiley, New York, 1982).
A. Vrij, J. G. H. Joosten and H. M. Fijnaut, Adv. Chem. Phys. 48, 329 (1981).
S. Dietrich and A. Latz, Phys. Rev. B 40, 9204 (1989).
T. Getta and S. Dietrich, Phys. Rev. E 47, 1856 (1993).
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961), Chap. X.
J. Lucassen, M. van den Tempel, A. Vrij and F. Th. Hesselink, K. Ned. Akad. Wet. Proc., Ser. B 73, 109 (1970); A. Vrij, F. Th. Hesselink, J. Lucassen, and M. van den Tempel, ibid. 73, 124 (1970).
This dispersion relation is similar to that quoted by S. Chatterjee, V. Vani, S. Guha, and E. S. R. Gopal, J. Phys. (Paris) 46, 1533 (1985), for the same physical situation, except that they omit the partial F/ partial d term and also do not have the term tanh (kd) in the denominator. The tanh (kd) term in the denominator is required. For example, consider the case when $ρ_{β}$ = 0 and F = 0 in (A6); then the dispersion relation must reduce to that of a free liquid surface. They also state in their paper that wetting layers are unstable to the Rayleigh-Taylor instability on the α beta interface sufficiently close to $T_{c}$ . This may be true for very thick wetting layers far from the equilibrium thickness where partial F/ partial d is small. However, for equilibrium wetting layers described by Eqs. (1) and (2), partial F/ partial d = 3 Δ ρ gL/ $d_{0}$ , which always dominates the gravitational term in (A6) so that $ω^{2}$ > 0 and, in this situation, the wetting layer is never unstable to capillary-wave fluctuations on the critical interface.
J. L. Harden and R. F. Kayser, J. Colloid Interface Sci. 127, 548 (1989).

[c1] For reviews see S. Dietrich, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic, London, 1987), Vol. 12; D. E. Sullivan and M. M. Telo da Gama, in Fluid Interfacial Phenomena, edited by C. A. Croxton (Wiley, New York, 1985); M. Schick, in Liquids at Interfaces, Proceedings of the Les Houches Summer School Session XLVIII, Haute-Savoie, 1988, edited by J. Charvolin, J. F. Joanny, and J. Zinn-Justin (North-Holland, Amsterdam, 1990).

[c2] J. W. Cahn, J. Chem. Phys. 66, 3667 (1977).

[c3] J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Oxford University Press, London, 1982).

[c4] P. G. de Gennes, J. Phys. (Paris) Lett. 42, L377 (1981).

[c5] R. F. Kayser, Phys. Rev. B 34, 3254 (1986).

[c6] M. E. Fisher and P.-G. de Gennes, C. R. Acad. Sci. B 287, 207 (1978).

[c7] A. J. Liu and M. E. Fisher, Phys. Rev. A 40, 7202 (1989).

[c8] H. Kellay, J. Meunier and B. P. Binks, Phys. Rev. Lett. 69, 1220 (1992).

[c9] A. Vrij, Discuss. Faraday Soc. 42, 23 (1966); A. Vrij and J. Th. G. Overbeek, J. Am. Chem. Soc. 90, 3074 (1968).

[c10] D. B. Hough and L. R. White, Adv. Colloid Interface Sci. 14, 3 (1980).

[c11] I. E. Dzyaloshinskii, E. M. Lifshitz and L. P. Pitaevskii, Adv. Phys. 10, 165 (1961).

[c12] J. N. Israelachvili, Intermolecular and Surface Forces (Academic, London, 1985), p. 144.

[c13] R. Lipowsky and D. A. Huse, Phys. Rev. Lett. 57, 353 (1986).

[c14] B. M. Law (unpublished).

[c15] In the calculations for Fig. 2 we retain all the liquid parameters for the mixture hexadecane plus acetone; however, we have interchanged ( $ε_{i 0}$ / $ε_{i o +}$ ) and $ε_{iv}$ for the various curves (i)–(iv). Specifically, for curve (i) $ε_{A 0}$ , $ε_{A o +}$ , $ε_{Av}$ , $ε_{B 0}$ , $ε_{B o +}$ , and $ε_{Bv}$ were taken as 21.2, 2.2, 2.025, 2.04, 2.04, and 1.819, respectively; for curve (ii) the respective values are 2.04, 2.04, 2.025, 21.2, 2.2, and 1.819; for curve (iii) the respective values are 21.2, 2.2, 1.819, 2.04, 2.04, and 2.025; and for curve (iv) the respective values are 2.04, 2.04, 1.819, 21.2, 2.2, and 2.025.

[c16] R. C. Haskell, D. C. Petersen and M. W. Johnson, Phys. Rev. E 47, 439 (1993).

[c17] A. W. Adamson, Physical Chemistry of Surfaces, 4th ed. (Wiley, New York, 1982).

[c18] A. Vrij, J. G. H. Joosten and H. M. Fijnaut, Adv. Chem. Phys. 48, 329 (1981).

[c19] S. Dietrich and A. Latz, Phys. Rev. B 40, 9204 (1989).

[c20] T. Getta and S. Dietrich, Phys. Rev. E 47, 1856 (1993).

[c21] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961), Chap. X.

[c22] J. Lucassen, M. van den Tempel, A. Vrij and F. Th. Hesselink, K. Ned. Akad. Wet. Proc., Ser. B 73, 109 (1970); A. Vrij, F. Th. Hesselink, J. Lucassen, and M. van den Tempel, ibid. 73, 124 (1970).

[c23] This dispersion relation is similar to that quoted by S. Chatterjee, V. Vani, S. Guha, and E. S. R. Gopal, J. Phys. (Paris) 46, 1533 (1985), for the same physical situation, except that they omit the partial F/ partial d term and also do not have the term tanh (kd) in the denominator. The tanh (kd) term in the denominator is required. For example, consider the case when $ρ_{β}$ = 0 and F = 0 in (A6); then the dispersion relation must reduce to that of a free liquid surface. They also state in their paper that wetting layers are unstable to the Rayleigh-Taylor instability on the α beta interface sufficiently close to $T_{c}$ . This may be true for very thick wetting layers far from the equilibrium thickness where partial F/ partial d is small. However, for equilibrium wetting layers described by Eqs. (1) and (2), partial F/ partial d = 3 Δ ρ gL/ $d_{0}$ , which always dominates the gravitational term in (A6) so that $ω^{2}$ > 0 and, in this situation, the wetting layer is never unstable to capillary-wave fluctuations on the critical interface.

[c24] J. L. Harden and R. F. Kayser, J. Colloid Interface Sci. 127, 548 (1989).

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Metastable wetting layers

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