Nonwetting Liquid Research Articles

Modeling mercury porosimetry using statistical mechanics.

We consider mercury porosimetry from the perspective of the statistical thermodynamics of penetration of a nonwetting liquid into a porous material under an external pressure. We apply density functional theory to a lattice gas model of the system and use this to compute intrusion/extrusion curves. We focus on the specific example of a Vycor glass and show that essential features of mercury porosimetry experiments can be modeled in this way. The lattice model exhibits a symmetry that provides a direct relationship between intrusion/extrusion curves for a nonwetting fluid and adsorption/desorption isotherms for a wetting fluid. This relationship clarifies the status of methods that are used for transforming mercury intrusion/extrusion curves into gas adsorption/desorption isotherms. We also use Monte Carlo simulations to investigate the nature of the intrusion and extrusion processes.

Phénomènes de glissement à l'interface liquide–solide

The problem of liquid–solid slip is described here, in a simplified manner. Today, several experiments have shown that substantial slip appears when a non-wetting liquid flows along a surface which is smooth on an atomic scale. This phenomena is characterised by a length, called the slip length, or Navier length, generally denoted by L s . A number of experiments indicate that this quantity may be as large as several hundreds of nanometers. Numerical simulations also show the existence of slip in non-wetting conditions, but the corresponding lengths found here are much smaller than those found experimentally. A theory, based on the existence of a gas film of nanometre thickness has been proposed, but has not yet been experimentally confirmed. Experiments on this are difficult, and sometimes controversial. To cite this article: P. Tabeling, C. R. Physique 5 (2004).

Evaluation of a lattice-Boltzmann method for mercury intrusion porosimetry simulations

We have simulated intrusion of a non-wetting liquid into pores of varying shape and size. Simulations were based on the lattice-Boltzmann method and the Shan–Chen multiphase model. The liquid–solid contact angle for pores with circular cross-section was found to be equal to that for pores with square cross-section, and constant even for small pore sizes if the discretised shape of the circular cross-section was taken into account. For comparison, contact angle was also determined for a liquid column descending in a capillary tube, and the results were found to be consistent. Application of the method to mercury intrusion porosimetry is discussed.

Effect of surface mobility on the particle sliding along a bubble or a solid sphere

The sliding velocity of glass beads on a spherical surface, made either of an air bubble or of a glass sphere held stationary, is measured to investigate the effect of surface mobility on the particle sliding velocity. The sliding process is recorded with a digital camera and analyzed frame by frame. The sliding glass bead was found to accelerate with increasing angular position on the collector's surface. It reaches a maximum velocity at an angular position of about 100° and then, under certain conditions, the glass bead leaves the surface of the collector. The sliding velocity of the glass bead depends strongly on the surface mobility of a bubble, decreasing with decreasing surface mobility. By a mobile surface we mean one which cannot set up resistive forces to an applied stress on the surface. The sliding velocity on a rigid surface, such as a glass sphere, is much lower than that on a mobile bubble surface. The sliding velocity can be described through a modified Stokes equation. A numerical factor in the modified Stokes equation is determined by fitting the experimental data and is found to increase with decreasing surface mobility. Hydrophobic glass beads sliding on a hydrophobic glass sphere were found to stick at the point of impact without sliding if the initial angular position of the impact is less than some specific angle, which is defined as the critical sticking angle. The sticking of the glass beads can be attributed to the capillary contracting force created by the formation of a cavity due to spontaneous receding of the nonwetting liquid from the contact zone. The relationship between the critical sticking angle and the particle size is established based on the Yushchenko [J. Colloid Interface Sci. 96 (1983) 307] analysis.

Two regimes of thermal resistance at a liquid–solid interface

Using nonequilibrium molecular dynamics simulations in which a temperature gradient is imposed, we determine the thermal resistance of a model liquid–solid interface. Our simulations reveal that the strength of the bonding between liquid and solid atoms plays a key role in determining interfacial thermal resistance. Moreover, we find that the functional dependence of the thermal resistance on the strength of the liquid–solid interactions exhibits two distinct regimes: (i) exponential dependence for weak bonding (nonwetting liquid) and (ii) power law dependence for strong bonding (wetting liquid). The identification of the two regimes of the Kapitza resistance has profound implications for understanding and designing the thermal properties of nanocomposite materials.

Wetting transitions at soft, sliding interfaces.

We observe (by optical interferometry) the contact of a rubber cap squeezing a nonwetting liquid against a plate moving at velocity U. At low velocities, the contact is dry. It becomes partially wet above a threshold velocity V(c1), with two symmetrical dry patches on the rear part. Above a second velocity V(c2), the contact is totally wet. This regime U>V(c2) corresponds to the hydroplaning of a car (decelerating on a wet road). We interpret the transitions at V(c1), V(c2) in terms of a competition between (a) liquid invasion induced by shear (b) spontaneous dewetting of the liquid (between nonwettable surfaces).

Investigation of the percolation transition in a nonwetting liquid-nanoporous medium system

The flows of liquid into and out of a nanoporous medium are studied as processes leading to the fluctuation formation and the growth of fractal clusters of filled and empty pores, respectively. The conditions for stable growth of such fluctuations are analyzed as a function of the interfacial energy between the liquid and the porous medium and the surface energy of the liquid. Expressions are obtained for the pressure at which the barrier for fluctuation filling and emptying of the pores vanishes. In general, it is shown for porous media with a pore-size distribution that these processes can be interpreted as a percolation phase transition. The volume and susceptibility of a liquid-porous medium system near the transition points with inflow and outflow of the liquid are calculated. The phenomenon of nonoutflow of a nonwetting liquid from a porous medium and hysteresis of the flow of liquid into and out of a porous medium are explained on the basis of the mechanism considered. The results of an experimental investigation of these processes in the system liquid Wood’s alloy-silochrome 80 and silochrome 120 are presented. The experimental data obtained can be described on the basis of the proposed mechanism.

Determining the Contact Angle of a Nonwetting Liquid in Pores by Liquid Intrusion Calorimetry

A microcalorimetric method is proposed to determine the contact angle of a nonwetting liquid within a mesoporous solid. It is based on the simultaneous measurement of the heat and work of wetting, as the pressure is raised. The method simply requires a previous determination of the surface area to be wetted. It allows one to carry out liquid intrusion porosimetry without any a priori assumption on the contact angle. This method is, in principle, applicable to mercury porosimetry. Its feasibility is shown here for water in porous hydrophobic silicas.

Statics and dynamics of contact lines of nematic liquid crystals on mica

Small drops (1–10μl) of two nematic liquid crystals were spread on the surface of freshly cleaved mica. Their rates of spreading and the apparent dynamic contact angles were measured as functions of time using a contact angle goniometer. From the experimental results, we argue that the elastic effects influence spreading rates for both wetting and nonwetting liquids. In addition, the apparent discontinuity in the orientation of the director at the contact line appears to represent a key feature that influences wettability and wetting rates. In particular, they tend to change a wetting liquid to a nonwetting liquid, provide added volume dependence in the wetting rates and can show in a few cases a reversal in wettability during spreading.

Rolling droplets

A droplet of nonwetting viscous liquid moves on an inclined plane by rolling along it. We give a scaling law for the uniform speed of such a droplet. We then analyze the flow in the contact region and show that the classical stress singularity at the contact line is alleviated in this case.

Simultaneous measurement of capillary pressure, saturation, and effective permeability of immiscible liquids in porous media

In many studies involving a liquid and air, the effective permeability of the wetting phase (kw) is determined from the capillary pressure (Pc)–saturation (S) relation and a corresponding, measured kw value. The movement, and therefore the effective permeability, knw, of air in an air‐liquid system is often ignored, especially by those who consider only the flow of water in soils. However, if a wetting and a nonwetting liquid coexist (two immiscible liquids), the effective permeability function of the nonwetting liquid must be determined as well. Rather than using some indirect method to determine the knw (Pc) or knw (S) relationship of the nonwetting liquid, we propose a direct measurement technique by using a permeameter which allows for steady state flow of the nonwetting liquid over a range of Pc and S values. During each steady state flow condition of the nonwetting liquid, Pc and S are constant and uniform throughout the permeameter, while the wetting liquid is at rest. The nonwetting liquid can either be a dense non–aqueous phase liquid (DNAPL) or a light non–aqueous phase liquid (LNAPL). The knw values are calculated as a function of Pc and S from the measured flow rates and the density difference between the wetting and nonwetting liquid. The proposed technique can be applied during drainage as well as imbibition. The S values are determined by recording the amount of water being displaced from the cell each time the Pc is changed. Results are discussed for the DNAPL perchloroethylene (PCE) and the LNAPL Soltrol.

MODELING SURFACTANT-ENHANCED NONAQUEOUS-PHASE LIQUID REMEDIATION OF POROUS MEDIA

A mathematical model is developed to investigate the main processes associated with surfactant-enhanced nonaqueous-phase liquid (NAPL) remediation of porous media. The model couples four nonlinear mass balance conservation equations (i.e., water, NAPL-phase organic, aqueous-phase organic, and aqueous-phase surfactant) that incorporate aqueous- and NAPL-phase migration and transport of aqueous-phase dissolved surfactant and organics. Rate-limited solubilization of the organic into the aqueous phase is represented by a linear driving force expression and is dependent on the surfactant-enhanced equilibrium concentration. Surfactant-enhanced mobilization of the NAPL phase is incorporated using surfactant concentration-dependent interfacial tension lowering, scaled relative permeability-saturation-capillary pressure relations, and trapping number-dependent effective residual saturations for the nonwetting liquid. Sorption of surfactant is assumed to conform to a Langmuir isotherm model, whereas organic sorption is modeled using a linear isotherm with a surfactant and soil-organic content-dependent retardation coefficient. The model is used to simulate experiments described by Pennell et al. (1996) in which the NAPL perchloroethylene was flushed from sand columns using different surfactant solutions.

Geometric Effects in the Dynamics of a Nonwetting Liquid in Microconfinement: An Optical Kerr Effect Study of Methyl Iodide in Nanporous Glasses

Optical Kerr effect spectroscopy has been used to study the orientational dynamics of liquid methyl iodide in bulk and confined in nanoporous glasses of several different pore sizes. Consistent with the behavior of other nonwetting or weakly wetting liquids, the decays of confined methyl iodide are described well by the sum of two exponentials, the faster of which has the same decay rate as the bulk liquid. The slower exponential is interpreted as arising from the hindered reorientational dynamics of liquid molecules on or near the surfaces of the pores. The rate of surface reorientation depends significantly on the pore diameter, which along with other evidence suggests that the retardation of surface dynamics arises through geometric effects.

New perspectives in mercury porosimetry

Seventy-six years ago, Washburn pioneered the concept that the structure of porous solids could be characterized by forcing a non-wetting liquid to penetrate their pores. At that time Washburn postulated that the minimum pressure P required to force a non-wetting liquid like mercury to penetrate pores of size R is given by P= K/ R, where K is a constant. Nowadays that very same concept constitutes the backbone of mercury porosimetry, a technique applied routinely to the characterization of all kinds of solids. Despite its perceived fundamental and practical limitations, mercury porosimetry will continue to be regarded as a standard measure of macro- and mesopore size distributions for years to come. This is so because this time-tested technique is (1) conceptually much simpler, (2) experimentally much faster, and (3) unique in its ability to evaluate a much wider range of pore sizes, than any alternative method practised currently (e.g. gas sorption, calorimetry, thermoporometry, etc.). Clearly it would be desirable to derive as much structural information as possible from simple mercury porosimetry experiments. Surprisingly, relatively few attempts have been made in the open literature to extract much information beyond pore size distributions from mercury porosimetry data. This contribution emphasizes the need to develop concerted efforts towards expanding the interpretation of mercury porosimetry data by examining the virtues and flaws of various reported attempts to generate particle size distributions, inter- and intraparticle porosities, pore tortuosities, permeabilities, throat/pore ratios, fractal dimensions and compressibilities from mercury intrusion and/or extrusion curves.

Nonwetting flow of a liquid through a packed bed with gas cross-flow

In this study, the effect of a cross-flow gas field on the percolating flow of a non-wetting liquid through a packed bed was investigated. Experiments were conducted to measure the liquid shift, due to the cross-flow of air, for the flow of aqueous barium chloride solutions and mercury percolating through beds of polyethylene and expanded polystyrene particles. An X-ray technique was used to visualize the liquid flow pattern through the packed bed. The liquid percolates through a packed bed as a series of rivulets and droplets which are continuously breaking up and coalescing. A mathematical model to predict the direction of the liquid rivulet/droplet flow under the influence of a gas flow field was developed. The model treats the liquid as a discrete phase and includes the effects of gravity, gas drag, and inertial and viscous bed resistance. The effective droplet/rivulet size is an important model parameter, and the model postulates that the droplet/rivulet size is a function of both the effective capillary size of the bed and the liquid flow rate. A simplified population balance analysis for droplet coalescence is used to predict the effect of liquid flow rate on droplet/rivulet size. The model predictions are consistent with the experiments.

Variability of point source infiltration rates for two‐phase flow in heterogeneous porous media

This study examines the influence of source release location, size, and strength on the infiltration rate and degree of lateral spreading of a dense nonwetting liquid infiltrating into an initially wetting liquid saturated, heterogeneous porous medium. It is demonstrated through numerical simulation in 25 realizations of a spatially correlated random hydraulic conductivity field that infiltration rates for point source releases are lognormally distributed with a variance equal to that of the underlying hydraulic conductivity distribution. The variability in infiltration rates is shown to decrease for sources larger than the correlation scale of hydraulic conductivity. In all cases, individual infiltration rates showed no tendency to converge to the ensemble average. A moment analysis demonstrates that the degree of lateral spreading of the nonwetting body for individual realizations varied greatly and also did not display a tendency to converge to an ensemble average. Numerical simulations carried out in an equivalent homogeneous porous medium incorporating large‐scale anisotropy of intrinsic permeability provided infiltration rates below the ensemble average. For point source releases the degree of lateral spreading exhibited in the equivalent homogeneous porous medium was below the entire ensemble of heterogeneous results. A series of 10 simulations conducted in a single realization demonstrates that the degree of lateral spreading (second moment) along main drainage is a function of the average nonwetting phase saturation with greater degrees of lateral spreading at low capillary pressures. The practical implication of this study is that in addition to fluid and media properties the specific order of encounter of varying permeability lenses must be known in the immediate vicinity of a nonwetting phase release if infiltration rates are to be accurately predicted.

Static Electrification by Nonwetting Liquids. Contact Charging and Contact Angles

A glass slide hydrophobized with dimethyldichlorosilane appears to be electrostatically charged when a nonwetting liquid recedes from its surface. The surface charge has negative polarity. The density of the charge which arises on retraction from water is 10 -4 C/m 2 . The half-life of the charge on the surface in air is 0.5 h. The charging effect is observed with different liquids and solutions for which contact angle and surface tension are high. A correlation of the value of the charge with the conductivity and double layer parameters is not pronounced. The electrification leads to a long range attraction between the plate and the liquid and influences the wetting of the substrate.

Numerical modeling of capillary hysteresis

The statement of the problem and result of numerical simulation of the processes occurring in the flow of a nonwetting liquid in thin capillaries of closed and open types are presented.

Suppression of Rupture in Thin, Nonwetting Liquid Films

Stabilization against the rupture and breakup of thin, nonwetting liquid films spread on surfaces is generally sought by modification of equilibrium interfacial properties. A mechanism for suppressing rupture in such films that uses surface-attached polymers togetherwithfree chains in the bulk of the film is reported. Films of an oligostyrene liquid, which rupture within several minutes when spread on a silicon wafer, may be stabilized for many months by a polystyrene brush attached to the substrate, together with some free polystyrene in the liquid. The effect may arise from entanglements of the free chains with the immobilized brush.

Capillary-gravity waves in the presence of infinite porous plates

The wave motion generated by a porous plate immersed in a non-wetting liquid of infinite depth is investigated. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the plate and a contact-line condition that accounts for the dynamic variation of the angle of contact and the vorticity there. The amplitude of the radiated waves and the energy dissipated are calculated both when the plate is oscillating horizontally and vertically with a prescribed velocity. Also the scattering of a harmonic wave incident normally to the plate is considered and the reflexion and transmission coefficients are obtained.