The Nature of Fluid Flow - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 40

Figure 1.20 Phase regions for adsorption filling of a pore.
dimensionality, which alters the behaviour due to the long-range interactions. This
can result in a first-order change of phase within such a cluster due to the pres-
ence of neighbouring tubes. These interpore effects are difficult to characterize
in real materials and are therefore not, at present, widely investigated by simula-
tions [28]. The filling of a pore involves three basic components, a high density
phase representing the filled part of the pore, a low density part representing the
multilayer adsorption and the interface between the two, as shown in Figure 1.20.
As would be expected from continuum scale observations of surface tension,
the interface between the 'wet' walls of the pore and the 'filled' region is almost
hemispherical. Higher temperature adsorption results in a thicker layer at the walls
through the adsorption layer, resulting in a lower surface tension and an increase
in the number of interfaces within the pore. The effect of inhomogeneity of phases
along the length of a pore becomes negligible when there is no hysteresis present
between adsorption and desorption, and leads to a rounding-off of the phase tran-
sition, similar to the effect of periodic boundaries on bulk fluid [38]. It is therefore
acceptable to think of the phase transition within nano scale pores as almost first
order and apply standard transition thermodynamics, as long as the temperature
does not approach the critical point and the distance between phase interfaces is
comparable to the pore diameter. The term 'critical point' used in capillary con-
fined fluids has a different meaning to that of a bulk fluid, and is used to describe
the point at which adsorption/desorption hysteresis disappears. As a consequence
of the inhomogeneity along the pore, it is not possible to observe a critical point
in the bulk fluid sense, or its associated properties. At lower temperatures, the ad-
sorption layer is thinner and the interfaces are further apart, so small periodic cells
are used whereas, for very high temperatures, the adsorption layer grows to such
an extent and the interfaces are so close together that only one phase is present.
The hysteresis, with respect to chemical potential during filling and emptying, is
present in both experiment and simulation, but its effects are more pronounced
in simulation, possibly due to the short time scale accessible. Longer pores have
more capacity to exhibit inhomogeneity along their length which can present dif-
ferences in nucleation on new phases and hysteresis loops. Pores with closed ends
can have the effect of the closed end acting as an already nucleated dense phase
while filling and affect the hysteresis loop.
The simulations performed by Gelb [38] were for adsorption of xeon on silica.
A simplified model for silica was used, with the surface molecules modelled by