Micropore fluid

The density profile for the micropore fluid was determined as In the equilibrium simulations. In a similar way the flow velocity profile for both systems was determined by dividing the liquid slab Into ten slices and calculating the average velocity of the particles In each slice. The velocity profile for the bulk system must be linear as macroscopic fluid mechanics predict. 

Figure 8. Density and local avers e density profiles of the micropore fluid...

Ill) Velocity profiles. The velocity profiles for the bulk fluid and the micropore fluid are shown In Figures 9 and 10. The profile for the bulk system Is linear In agreement with the macroscopic prediction of fluid mechanics. This fact shows that the flow properties of our first system are Identical with the ones of a bulk fluid, despite the presence of the reservoirs. 

Figure 10. Theoretical and simulation velocity profiles for the micropore fluid.

Finally the knowledge of the velocity profiles allows the determination of the actual shear rate exerted upon the liquid slab. For the bulk system some slip Is observed at the reservoir walls. No slip Is observed for the micropore fluid as a result of the high density close to the reservoir walls, which facilitates the momentum transfer between the reservoir and the liquid slab particles. 

If one Insists on Equation 55 for the micropore fluid an effective viscosity (which Is an experimental observable) must be used Instead, l.e.. 

Movement in supercapillary pores is obeyed on macroscopic hydrodynamic laws. On the contrary in micropores fluids are immobile practically. Movement in mesopores is defined by a balance between hydrodynamical and intermolecular forces. Interactions of molecules... 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Fig. 15. Schematic of the interfacial polymerization process. The microporous film is first impregnated with an aqueous amine solution. The film is then treated with a multivalent cross-linking agent dissolved in a water-immiscible organic fluid, such as hexane or Freon-113. An extremely thin polymer film...

M. Schoen, D. J. Diestler, J. H. Cushman. Fluids in micropores. I. Structure of a simple classical fluid in a slit-pore. J Chem Phys 27 5464-5476, 1987. 

Z. Tang, L. E. Scriven, H. T. Davis. Size selectivity in adsorptions of poly-disperse hard-rod fluids in micropores. J Chem Phys 97 5732-5737, 1992. 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

Adsorption of hard sphere fluid mixtures in disordered hard sphere matrices has not been studied profoundly and the accuracy of the ROZ-type theory in the description of the structure and thermodynamics of simple mixtures is difficult to discuss. Adsorption of mixtures consisting of argon with ethane and methane in a matrix mimicking silica xerogel has been simulated by Kaminsky and Monson [42,43] in the framework of the Lennard-Jones model. A comparison with experimentally measured properties has also been performed. However, we are not aware of similar studies for simpler hard sphere mixtures, but the work from our laboratory has focused on a two-dimensional partly quenched model of hard discs [44]. That makes it impossible to judge the accuracy of theoretical approaches even for simple binary mixtures in disordered microporous media. 

However, before proceeding with the description of simulation data, we would like to comment the theoretical background. Similarly to the previous example, in order to obtain the pair correlation function of matrix spheres we solve the common Ornstein-Zernike equation complemented by the PY closure. Next, we would like to consider the adsorption of a hard sphere fluid in a microporous environment provided by a disordered matrix of permeable species. The fluid to be adsorbed is considered at density pj = pj-Of. The equilibrium between an adsorbed fluid and its bulk counterpart (i.e., in the absence of the matrix) occurs at constant chemical potential. However, in the theoretical procedure we need to choose the value for the fluid density first, and calculate the chemical potential afterwards. The ROZ equations, (22) and (23), are applied to decribe the fluid-matrix and fluid-fluid correlations. These correlations are considered by using the PY closure, such that the ROZ equations take the Madden-Glandt form as in the previous example. The structural properties in terms of the pair correlation functions (the fluid-matrix function is of special interest for models with permeabihty) cannot represent the only issue to investigate. Moreover, to perform comparisons of the structure under different conditions we need to calculate the adsorption isotherms pf jSpf). The chemical potential of a... 

From the theoretical point of view, a density functional type theory for systems confined to microporous media is lacking. This seems to be one of the reasons why the problem of crystallization of fluids in disordered media has not been solved so far. Further work in future is needed, however, to solve this and relevant problems. Our expectation is that a combined application of theoretical methods and simulation would provide faster progress in studies of fluids and mixtures in microporous media. At present, the models studied in theory and simulations are quite far from the systems of experimental focus. Hopefully, favorable changes will occur in future. 

S. Murad, P. Ravi, J. G. Powles. A computer simulation study of fluids in model slit, tubular and cubic micropores. J Chem Phys 95 9771, 1993. 

Theory and Computer Simulation of Structure, Transport, and Flow of Fluid in Micropores... 

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