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Continuum description of the dynamics and thermodynamics of phase boundaries between ice and water. III: Thermostatics and its consequences. (English) Zbl 0728.73007

Summary: This paper continues the exploitation of the thermodynamic theory of phase change surfaces commenced by the authors [parts I, II, ibid. 13, No.3, 221-280 (1988; Zbl 0671.73003)]. All possible inferences are drawn from the residual entropy production inequality regarding thermostatic equilibrium and linearized transport equations.
It is shown that in thermostatic equilibrium: - the temperatures of the phase change surface and the adjacent bulk materials at the surface are necessarily the same, - the specific free enthalpies of the surface and the adjacent bulk materials have the same values, - the surface tension, the pressures, the equilibrium densities, entropies and internal energies of the bulk materials and isotropic phase boundaries are functions of the temperature and local mean curvature, - isotropic phase change surfaces are spheres or cylinders when gravity can be ignored.
We analyze equilibrium phase change surfaces under change of curvature at constant temperature and under change of temperature at constant curvature and find this way that freezing and melting are not the same processes at curved phase change surfces because they are governed by different Clausius-Clapeyron equations.
For phase change surfaces whose temperature is the same as that of the adjacent bulk materials we define the reversible phase change surface to be one with zero surface entropy production. We find the corresponding linearized flux transport equations, whose coefficients can be expressed as known functions of geometry and temperature. The results also suggest the simplest extension for constitutive equations of transport relations of irreversible phase change surfaces, and constitute generalized boundary conditions at phase-interfaces.

MSC:

74A15 Thermodynamics in solid mechanics
80A22 Stefan problems, phase changes, etc.
76N20 Boundary-layer theory for compressible fluids and gas dynamics
82B26 Phase transitions (general) in equilibrium statistical mechanics
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[1] Alts T., Part II: Thermodynamics. J. Non-Equilib. Thermodyn. 13 pp 259– (1988) · doi:10.1515/jnet.1988.13.3.259
[2] DOI: 10.1515/jnet.1988.13.3.221 · Zbl 0671.73003 · doi:10.1515/jnet.1988.13.3.221
[3] DOI: 10.1515/jnet.1985.10.2.145 · Zbl 0567.76009 · doi:10.1515/jnet.1985.10.2.145
[4] Alts T., J. Non-Equilib. Thermodyn. 14 (1989)
[5] Mantis H.T., University of Minnesota, Institute of Technology, Engineering Experiment Station, SIPRE Report pp 4– (1951)
[6] DOI: 10.1021/je60064a005 · doi:10.1021/je60064a005
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