Wetting density profile

Second-Order Integral Equations for Associating Fluids As mentioned above in Sec. II A, the second-order theory consists of simultaneous evaluation of the one-particle (density profile) and two-particle distribution functions. Consequently, the theory yields a much more detailed description of the interfacial phenomena. In the case of confined simple fluids, the PY2 and HNC2 approaches are able to describe surface phase transitions, such as wetting and layering transitions, in particular see, e.g.. Ref. 84. 

In order to demonstrate that the systems in question exhibit nonzero wetting temperature, we have displayed the results of calculations for one of the systems (with =1 at T = 0.7). Fig. 12 testifies that only a thin (monolayer) film develops even at densities extremely close to the bulk coexistence density (p/,(T — 0.7) — 0.001 664). In Fig. 13(a) we show the density profiles obtained at temperature 0.9 evaluated for = 7. Part (b) of this figure presents the fraction of nonassociated particles, x( )- We... 

In Fig. 15 we show similar results, but for = 10. Part (a) displays some examples of the adsorption isotherms at three temperatures. The highest temperature, T = 1.27, is the critical temperature for this system. At any T > 0.7 the layering transition is not observed, always the condensation in the pore is via an instantaneous filling of the entire pore. Part (b) shows the density profiles at T = 1. The transition from gas to hquid occurs at p/, = 0.004 15. Before the capillary condensation point, only a thin film adjacent to a pore wall is formed. The capillary condensation is now competing with wetting. 

This approximation amounts to truncating the functional expansion of the excess free energy at second order in the density profile. This approach is accurate for Lennard-Jones fluids under some conditions, but has fallen out of favor because it is not capable of describing wetting transitions and coexisting liquid-vapor phases [105-107]. Incidentally, this approximation is identical to the hypemetted chain closure to the wall-OZ equation [103]. 

Wet/Wet Pressing, Representative press cycles, conceptual schematics of mass transfer in the sheet, and density profiles through the thickness of the sheet are portrayed in Figure 7, Pressing of wet mats starts with a steady pressure rise to 400 psi platen pressure so as to compress the mat to minimum void volume and express water retained from cold pressing. Platen steam pressures up to 400 psig heat the mat and reduce water viscosity and raise its vapor pressure. This high-presstire inversion cycle is followed by a period of low platen pressure intended to dry the sheet to anhydrous condition. 

Figure 7. Conceptualizations of pressing pressure/time schedules (left), volatiles movement in the board (center), and density profiles through the board thickness (right) for wet- and dry-pressed boards...

Fig. 5. Density profile p z) for a fluid at a surface near a wetting transition. In the nun-wet state of the surface the local density p at the surface is less than the density piiq at the liquid branch of the coexistence curve describing gas-liquid condensation (upper part). Then the density profile p(z) decays to the gas density pgas in the bulk at a microscopic distance which is of the order of the correlation length f). In the wet state of the surface (lower part), the bulk gas is saturated must have the value of the gas branch of the coexistence curve) and /q > piiq, and a (macroscopic) liquid layer condenses at the surface, separated at large distances from the gas by a liquid-gas interface centered at z = h(x, y).

Teletzke et al. (1982) used Equation 2.50 and the Peng-Rohinson equation of state (Peng and Robinson, 1976) to calculate density profiles for various values of the temperature T and bulk density n. They found that below the saturation density n ° relatively thick films can form near the solid when the temperature is below but not too far from the critical temperature of the fluid. Under these conditions the gradient energy contribution is relatively small, as would be expected in the neighborhood of the critical point. For densities above b°. where the bulk phase is a liquid-vapor mixture, the liquid completely wets the solid (i.e., there is no equilibrium contact angle). 

Density profiles in the wetting phase (liquid near a strongly attractive surface) and in the drying phase (vapor near a weakly attractive surface) are not affected by the surface transitions. These profiles reflect the competition between the missing neighbor effect and the fluid-wall interaction and may be described in the framework of the theory of the surface critical behavior (see Section 3). In particular, a gradual density adsorption or a density depletion decays exponentially toward the bulk... 

The simplest way to detect if a crystal phase wets the surface is to measure the density profile of the particles between the two walls. In Fig. 32a we show the ob-... 

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