Planar Pores Research Articles

Adsorption of a Binary Mixture of Adhesive Fluids in Planar Pores: A Monte Carlo Study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.

Modificações na matriz de um Argissolo Amarelo Coeso sob diferentes sistemas de manejo com cana-de-açúcar

Os sistemas de manejo com cana-de-açúcar em solos de tabuleiros costeiros podem causar alterações importantes na matriz do solo. Foram estudados os efeitos de diferentes sistemas de manejo com cana-de-açúcar na organização da matriz de um Argissolo Amarelo Coeso, na usina Triunfo, Estado de Alagoas. Os sistemas de manejo consistiram de uma área não irrigada, uma área irrigada, uma com aplicação de vinhaça e uma sob floresta nativa como condição original. Amostras foram retiradas de cada área a 0-0,2, 0,2-0,4 e 0,4-0,8 m de profundidade para determinar as alterações na estrutura do solo, no sistema de poros e no arranjamento de partículas dos solos cultivados com cana-de-açúcar, em relação ao solo da mata. Os solos cultivados apresentaram associação da porosidade natural com poros aplanados e um arranjamento mais compacto das partículas na matriz solo. Nos agregados dos solos cultivados constatou-se um aspecto maciço e orientação de partículas de argila, em relação ao solo da mata.

Effect of wetting on the transverse diffusion of non-homogeneous fluids

The diffusion dynamics of a Yukawa fluid confined in an attractive planar slit pore was studied by solving the Smoluchowski/Hypernneted-chain equation for the mean first passage times. We show how the time it takes for a particle to get adsorbed at the wall surface is modulated by the effective potential barrier originated by the fluid local density profile. The effect of wetting layering on the apparent constant for the transverse diffusion towards an attractive pore wall is evaluated.

Direct recoil radon emanation from crystalline phases. Influence of moisture content

This paper is devoted to the study of the radon emanation coefficient vs. water mass fraction for mineral samples. Modeling is performed considering only the direct recoil phenomena and assuming planar pores with high lengths-to-width aspect ratios. Water is assumed either to fill the pore alternatively with air or to form a continuous film on the pore surface. This modeling is applied to uranium mine tailings for which the pore size distribution was experimentally measured. It enables a good description of the change of the experimental radon emanation coefficients with the moisture content of the studied samples.

Sedimentation Equilibrium of Colloidal Suspensions in a Planar Pore Based on Density Functional Theory and the Hard-Core Attractive Yukawa Model

The sedimentation equilibrium of colloidal suspensions modeled by hard-core attractive Yukawa (HCAY) fluids in a planar pore is studied. The density profile of the HCAY fluid in a gravitational field and its distribution between the pore and uniform phases are investigated by a density functional theory (DFT) approach, which results from employing a recently proposed parameter-free version of the Lagrangian theorem-based density functional approximation (Zhou, S. Phys. Lett. A 2003, 319, 279) for hard-sphere fluids to the hard-core part of the HCAY fluid, and the second-order functional perturbation expansion approximation to the tail part as was done in a recent partitioned density functional approximation (Zhou, S. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 061201). The resultant DFT approach is, thus, the first adjustable parameter-free DFT for HCAY fluids. The validity of the present DFT for HCAY fluids of reduced range parameter z(red) = 1.8 under various external potentials is established in the first of the papers cited previously. The present DFT for HCAY fluids can predict the radial distribution function for the bulk HCAY fluid accurately in the colloidal limit (large value of z(red)), and in the hard-sphere limit, its prediction for the density profile of the hard-sphere fluid in a gravitational field is in very good agreement with the existing simulation data. The dependence of the density profile and distribution coefficient on the magnitude of the interparticle attraction, gravitational field, and degree of confinement is investigated in detail by the present DFT approach. Intuitive and qualitative analyses are also compared with the quantitative DFT calculational results.

A density functional perturbative approach for simple fluids: the structure of a nonuniformLennard-Jones fluid at interfaces

A density functional perturbation approximation (DFPT), which is based both on thefundamental-measure theory (FMT) to the hard-sphere repulsion and on theweighted-density approximations (WDAs) to the attractive contribution, has been proposedfor studying the structural properties of model fluids with an attractive part of thepotential. The advantage of the present theory is the simplicity of the calculation of theweight function due to the attractive contribution. It has been applied to predict theequilibrium particle density distributions and adsorption isotherms of Lennard-Jones fluidsat interfaces. The theoretical results show that the present theory describes quite well theadsorption isotherms of a Lennard-Jones ethane in a graphite slit pore as well as theequilibrium particle density distributions of a Lennard-Jones fluid near a planar slit pore.

Correlation of the two-phase flow coefficients of porous media with the rheology of shear-thinning fluids

The macroscopic equations of the two-phase flow in porous media are generalized for the case that the displacing non-wetting phase (NWP) is a shear-thinning fluid, and a numerical scheme of inverse modeling is developed to estimate simultaneously the capillary pressure, P c( S nw), non-wetting phase, k rnw( S nw), and wetting phase, k rw( S nw), relative permeability curves, from unsteady-state experiments. The parameter estimation procedure is demonstrated by using transient experimental data of the immiscible displacement of a Newtonian wetting phase (WP) by a shear-thinning NWP from a glass-etched planar pore network. Scaling laws are developed for the width of the frontal region, by extending concepts of the gradient invasion percolation to the rate-controlled displacement of a Newtonian fluid by a power-law fluid. These scaling laws are coupled with the macroscopic fractional flow equations in order to express the width of the frontal region and macroscopic parameters of P c( S nw), k rnw( S nw) and k rw( S nw) as functions of the capillary number ( Ca), in terms of universal scaling exponents. Two parameter estimation procedures are adopted: (i) in the first approach, the NWP is treated as a mixed Meter-and-power-law fluid and a non-Darcian flow model is used; and (ii) in the second approach, the NWP is treated as a pseudo-Newtonian fluid and classical Darcy law with a constant apparent viscosity are used. The variation of the front width with Ca follows a power law, the exponent of which agrees satisfactorily with that predicted by scaling relationships. The estimated P c( S nw) and k rw( S nw) are increasing functions of Ca. The estimated P c( S nw) is a strongly increasing function of Ca, even at high values of this parameter, and almost independent on the flow model considered. The shape of k rnw( S nw) changes from concave at low Ca values, where the width of the frontal region is large, to convex at increasing Ca values, where the front width is small and the displacement is dominated by viscous forces at gradually larger scales. The variation of the parameters of P c( S nw), k rnw( S nw), k rw( S nw) with Ca agrees semi-quantitatively with the scaling relations only in the first approach, where the non-Darcian flow model is used.

Small-angle neutron scattering study of the role of feedstock particle size on the microstructural behavior of plasma-sprayed yttria-stabilized zirconia deposits

The microstructures of thick plasma-sprayed yttria-stabilized zirconia (8% mass fraction yttria) deposits were studied in a series of Porod small-angle neutron scattering (SANS) and multiple small-angle neutron scattering (MSANS) experiments. Three main void components were identified in the deposits: intrasplat cracks, interlamellar planar pores, and globular pores. The SANS and MSANS measurements were analyzed using the traditional theory for Porod scattering and a recently developed three-component model for MSANS evaluation. The average size, volume fraction, internal surface area, and orientation distribution for each void component within the deposits were determined. This study focused on gaining a better understanding of the effects of initial feedstock particle size and annealing temperatures on the microstructure of deposits sprayed under equivalent particle-impact conditions. Quantitative results are presented for each of four deposit samples: one prepared using the as-received feedstock particle wide-size distribution and three prepared from feedstock powder of different and relatively narrow particle size ranges with average sizes of 32, 47, and 88 μm. Except for the coarse (88 μm) feedstock powder, only mild monotonic variations were found in the microstructural anisotropies, the porosities (13 ± 1%), and the internal surface areas in the as-sprayed deposits. The internal surface area was independent of the feedstock particle size, even with the coarse feedstock. When the deposits were annealed at high temperatures (1100 and 1400 °C), the microstructures were altered with a reduction of the total internal surface area and a mild coarsening of the voids. These changes in the microstructural evolution were well-captured and described by the three-component model. The results were compared and related with those obtained from scanning electron microscopy images and elastic moduli measurements.

Sedimentation equilibrium of a suspension of adhesive colloidal particles in a planar slit: A density functional approach

The sedimentation equilibrium of a colloidal suspension modeled as a collection of adhesive hard-sphere particles confined in a planar slit pore is studied by using a density functional approach with a newly developed approximation in which the repulsive part of the adhesive hard-sphere interaction potential is treated within weighted density functional theory while the attractive part is evaluated by a third-order perturbative approach. The calculated density profiles obtained from this approach for the adhesive hard-sphere fluid confined in a slit pore in the absence of gravitational field is in excellent agreement with the available computer simulation results for varying pore sizes and stickiness parameters of the potential. The same approach applied to the study of the effect of gravitational field on the equilibrium structure of the system predicts density profiles exhibiting strong oscillation at the bottom of the pore with a decreasing tail approaching the upper wall. The interplay between the packing effect due to confinement by the walls, gravitational field, and attractive forces among the particles determines the structure of the density profiles. The effect of all these parameters on the distribution of the colloidal particles in the confined environment is investigated.

Solvation of a wedge

The solvation of a wedge can be related to that of planar pores by employing an interface displacement or Derjaguin analysis. This approach implies that the line tension and solvation force for a wedge are proportional to an amplitude defined from averaging the planar pore solvation potential over all possible pore widths, times simple monotonic functions of the wedge angle θ. At small values of θ all sensible choices lead to the same angular dependence. The amplitude is a well known quantity in colloidal science, linked directly to the barrier for flocculation by the depletion effect.

Fluids absorbed in structured pores

A model of fluids absorbed in a pore with walls patterned with parallel channels is used to demonstrate some of the unity that can be proved to hold between the statistical mechanics of fluids absorbed in structured pores and of fluids adsorbed at unstructured walls and at edges/wedges where walls meet. In particular, the work done to reversibly shear a corrugated pore immersed in liquid is related to the difference in the density profile structure of liquid adsorbed near the edges of the channels. When the channel dimensions are mesoscopic or macroscopic but the minimum pore width is microscopic, statistical mechanics generates remarkable links between the surface tension of planar wall-fluid interfaces or, more generally, the solvation free energy of a planar pore, and the density profile at the sides of a channel wall in the vicinity of edges and wedges.

Structure of a two-component mixture of sticky hard-sphere fluids in a planar gap

The structural properties of nonuniform, binary, sticky hard-sphere (SHS) fluid mixture (the particular components being denoted by SHS1 and SHS2) within a planar pore, maintaining the equilibrium with the bulk phase, were investigated. The wall–SHS1 and wall–SHS2 correlations of the SHS mixture confined in the pore, and its distribution between the pore and the bulk phase were studied on the basis of the solution to the Percus–Yevick/Ornstein–Zernike equation, obtained by using the analytic results for the direct correlation functions of the bulk SHS mixture. The density profiles of particular components with the hard core diameters σ1 and σ2 revealed distinct layering, a characteristic feature being the discontinuities in the slopes of the profiles at the distances n⋅σ1+m⋅σ2 (n=0,1,…;m=0,1,…) from the wall–SHS1 and wall–SHS2 contact planes. It was shown that narrowing of the pore considerably affects the partitioning of both components between the bulk phase and the interior of the pore, the effects being more pronounced in the case of a more adhesive component. As the individual components of the binary mixture are selectively partitioned between the bulk phase and narrow pore, the porous material, i.e., a network of narrow pores, makes possible a partial separation of both components from the bulk SHS mixture.

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ ∼a2/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.

Simulations of coexistence between layered phases in planar slits

Layering transitions of a simple fluid in a planar pore with structureless attractive surfaces are investigated, using both simulations and density functional theory. The thermodynamic conditions for coexistence between three different layered phases, denoted 1, 2 and 3 in order of increasing average density, are determined, and coexistence curves are presented. The simulations are performed in the isotension ensemble at low temperatures, while the recently developed restricted isotension ensemble was used at elevated temperatures, in order to avoid phase transitions. According to the simulation results, 1–2 and 2–3 coexistences exist between stable phases at low temperatures, but the 2-phase is truncated by a triple point at which all three phases coexist. Above this triple point, 1–3 coexistence is the only stable one. These results are not confirmed by the density functional calculations, according to which 1–3 coexistence at low temperatures is replaced by a simple thin—thick coexistence at higher temperatures. With a slightly increased surface—fluid potential, the density functional calculations do predict the existence of a 1-2-3 triple point. However, in this case the relative stability of the layered phases above and below the triple point is reversed, as compared with the simulation results. Since the differences in the coexistence quantities are small, we have to consider the possibility that this unexpected behaviour is not a true effect, but rather a result of statistical fluctuations. At any rate, the occurrence of 1–3 coexistence together with a triple point is, to the best of our knowledge, a novel observation and is confirmed by density functional theory. Furthermore, the simulations show that the 1–2, 2–3 and 1–3 coexistence curves are very similar.

Suspensions of adhesive colloidal particles in sedimentation equilibrium in a planar pore

The sedimentation equilibrium of adhesive spheres mimicking a system of interacting spherical colloidal particles in suspensions in planar pores is considered. The density profiles of the adhesive fluid in a gravitational field, and its distribution between the pores and the homogeneous phase are studied on the basis of the solution to the hypernetted chain/Ornstein–Zernike equation, obtained by using the analytic results for the direct correlation function of the bulk fluid. In a few cases, the Percus–Yevick closure is also used. In the hard sphere limit, both integral equation approaches are compared with the results of a grand canonical ensemble Monte Carlo simulation. This comparison shows, in particular in narrow pores, that the hypernetted chain approximation provides a better estimate for the structure of the hard sphere fluid in the pore, as well as for its partitioning between the bulk and the confined system. The calculated density profiles consist of an oscillatory part near the lower wall revealing layering, and a monotonically decreasing tail approaching the upper wall, their shapes being very sensitive to the strength of interparticle attraction, the strength of the gravitational field, and the degree of confinement. Increasing interparticle adhesive attraction together with gravity results in the particles occupying the region of lower altitudes in the gap and being partly squeezed out from the pore.

Sedimentation equilibrium of adhesive spheres in a planar gap

The sedimentation equilibrium of adhesive spheres mimicking a system of interacting spherical colloidal particles in suspensions in planar pores is studied on the basis of the solution to the hypernetted chain/Ornstein–Zernike equation. The increasing interparticle adhesive attraction together with the gravity lead to the overall effect on particles to occupy the region of lower altitudes. It is found that at sufficiently strong stickiness the adhesive fluid in the gap behaves as a `condensation nucleus' for the condensation of particles from the bulk phase, the effect predominating the natural tendency of strongly adhesive particles to avoid the confined system.

Monte Carlo simulation of hard sphere fluids in planar slits with molecularly rough surfaces

The structural and thermodynamic behaviour of hard-sphere fluids confined in planar slit-like pores with hard rough walls is investigated by canonical Monte Carlo simulations. The surfaces of the pores are modelled by means of parallel impenetrable walls. Additionally a molecular “roughness” of the pore surfaces is introduced using several models of randomly distributed hard spheres located (fixed or restricted in motion) at the walls. The density distribution of the hard spheres in the pore and the pressure normal to the walls are estimated and compared with the behaviour of fluids in slit-like pores with smooth hard walls. The results are discussed in the context of experimental studies of fluids confined in the polar interfaces of bilayers.

Effective Porosity and Flow Rate with Infiltration at Low Tensions into a Well-structured Subsoil

A combination of tension infiltrometers and dye tracers was used to investigate the extent and nature of water movement at low tensions through the well-structured subsoil of Ships clay (very-fine, mixed, thermic, Chromic Hapluderts). Dyed-water was placed in the reservoirs of tension infiltrometers and allowed to infiltrate into the soil under seven tension sequences to separate different size pores effective in transmitting water. Flow patterns were then revealed by exposing dye-stained soil after each infiltration sequence. The results showed that, when water was supplied at tensions <24 cm, the effective porosity (fraction of pores that were stained) in this subsoil was primarily macro- and mesoporosity, which constituted about 5% of the total soil porosity. Under flow at 0-cm tension, macropores =0.5 mm and mesopores from 0.06 to 0.5 mm (radius for cylindrical pores or width for planar pores) contributed about 89% and 10% of the total water flux, respectively. Micropores <0.06 mm contributed the remaining 1% of the total water flux, but constituted about 95% of the total soil porosity. Dye stain patterns showed that water flow at tensions <24 cm in this structured subsoil was primarily controlled by slickenside fissures, root channels, and vertical fissures. The nonuniform flow pattern caused water to penetrate to depths as much as 11 times deeper than expected from a Green-Ampt model that considered the total soil porosity to be active in transmitting water. By replacing the air-filled porosity in the Green-Ampt model with the active macro- plus mesoporosity, calculated wetting front depths were close to the observed maximum dye depths.

Sticky spheres in adhesive pores

The structure of Baxter’s adhesive fluid [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)] in planar pores with adsorbing walls maintaining the equilibrium with the bulk fluid is considered. The wall–fluid correlations are studied on the basis of the solution to the Percus–Yevick/Ornstein–Zernike equation, obtained by using the analytic results for the direct correlation function of the bulk fluid. In the case of strongly adsorbing walls, the density profiles of hard sphere fluid resemble those in the pore with nonadsorbing walls but with the width decreased by the thickness of the adsorbed monolayers. The profiles of strongly adhesive fluid show maxima at the distances from the wall–fluid contact plane which correspond to the most probable configurations of strongly adhered successive molecular layers. A characteristic feature observed in all cases is the discontinuity in the slope of the profile at the distance one molecular diameter below the wall–fluid contact plane as the consequence of the exclusion volume of adsorbed monolayer. The distribution of the fluid between the bulk phase and the interior of the pore is oppositely affected by the strength of the wall–fluid and the fluid–fluid adhesion. Its dependence on the degree of confinement is more pronounced in narrow pores than at bigger separation between the walls.