Surface critical behavior of water

The presence of a boundary breaks the translational invariance of a bulk system and introduces an anisotropy. As a consequence, all system properties become local, that is dependent on the position of the elementary volume considered relative to the boundary. In the simplest case of a single planar surface, all properties depend on the distance z to the boundary. The surface perturbs the bulk properties of a fluid over some distance from the surface, whereas the system remains undisturbed (bulk-like) far from the surface. The critical behavior of fluids near the surface strongly differs from the bulk behavior [254]. On approaching the bulk critical point, the surface critical behavior intrudes deeply into the bulk, as the range of the surface perturbation is governed by the bulk correlation length [255]. Knowledge of the laws of the surface critical behavior makes it possible to describe the fluid density profiles at various thermodynamic conditions. 

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Surface critical behavior of water has been studied by computer simulations of the liquid-vapor coexistence curves in pores of various sizes and geometries [28, 205, 250, 262]. The behavior of the local order... 

So, the water density profiles near the surfaces and their temperature evolution follow the laws of the surface critical behavior, which are universal for fluids and Ising magnets [254]. Nothing peculiar can be found in the surface critical behavior of water in comparison with LJ fluid (see Section 3.1). Many questions concerning the surface critical behavior of fluids and Ising magnets remain open [262] and should be studied. This may provide the possibility to describe the density profiles of water and other fluids analytically in a wide range of thermodynamic conditions near various surfaces. 

Knowledge of the surface critical behavior of the order parameter and diameter allows description of the local density of liquid water and vapor in a universal way. According to the equation (9), the local densities of water in the surface layer (A = 0) may be written as... 

Surface critical behavior does not disturb notably the order parameter in the second water layer up to about 425 K. Starting from this temperature, the surface perturbation spreads over the surface water layers and intrudes deep into the confined water. Using the values of the correlation length obtained from the fits of the order parameter profile, we notice that Api deviates from the bulk behavior when achieves approximately the outer border Azi of the ith. layer. The temperatures when 2 is equal to the distance of the outer border of the second water layer to the surface (A 2 3.5 A), third layer (Az3 6.5 A), and fifth layer (outer border of inner water Azi 12.5 A) are indicated by arrows in Fig. 48 (right panel). 

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

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