Confinement of fluids in porous media leads to the presence of solid-fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid-fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability. [GRAPHICS]

We have determined the interfacial properties of tetrahydrofuran (THF) from direct simulation of the vapor-liquid interface. The molecules are modeled using six different molecular models, three of them based on the united-atom approach and the other three based on a coarse-grained (CG) approach. In the first case, THF is modeled using the transferable parameters potential functions approach proposed by Chandrasekhar and Jorgensen [J. Chem. Phys. 77, 5073 (1982)] and a new parametrization of the TraPPE force fields for cyclic alkanes and ethers [S. J. Keasler et al., J. Phys. Chem. B 115, 11234 (2012)]. In both cases, dispersive and coulombic intermolecular interactions are explicitly taken into account. In the second case, THF is modeled as a single sphere, a diatomic molecule, and a ring formed from three Mie monomers according to the SAFT-γ Mie top-down approach [V. Papaioannou et al., J. Chem. Phys. 140, 054107 (2014)]. Simulations were performed in the molecular dynamics canonical ensemble and the vapor-liquid surface tension is evaluated from the normal and tangential components of the pressure tensor along the simulation box. In addition to the surface tension, we have also obtained density profiles, coexistence densities, critical temperature, density, and pressure, and interfacial thickness as functions of temperature, paying special attention to the comparison between the estimations obtained from different models and literature experimental data. The simulation results obtained from the three CG models as described by the SAFT-γ Mie approach are able to predict accurately the vapor-liquid phase envelope of THF, in excellent agreement with estimations obtained from TraPPE model and experimental data in the whole range of coexistence. However, Chandrasekhar and Jorgensen model presents significant deviations from experimental results. We also compare the predictions for surface tension as obtained from simulation results for all the models with experimental data. The three CG models predict reasonably well (but only qualitatively) the surface tension of THF, as a function of temperature, from the triple point to the critical temperature. On the other hand, only the TraPPE united-atoms models are able to predict accurately the experimental surface tension of the system in the whole temperature range.

The high-pressure phase diagrams of the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) mixtures are examined using the SAFT-VR approach. Carbon dioxide molecule is modeled as two spherical segments tangentially bonded, water is modeled as a spherical segment with four associating sites to represent the hydrogen bonding, methane is represented as an isolated sphere, and tetrahydrofuran is represented as a chain of m tangentially bonded spherical segments. Dispersive interactions are modeled using the square-well intermolecular potential. In addition, two different molecular model mixtures are developed to take into account the subtle balance between water-tetrahydrofuran hydrogen-bonding interactions. The polar and quadrupolar interactions present in water, tetrahydrofuran, and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Giner et al. (Fluid Phase Equil. 2007, 255, 200), Galindo and Blas (J. Phys. Chem. B 2002, 106, 4503), Patel et al. (Ind. Eng. Chem. Res. 2003, 42, 3809), and Clark et al. (Mol. Phys. 2006, 104, 3561) for tetrahydrofuran, carbon dioxide, methane, and water, respectively. The phase diagrams of the binary mixtures exhibit different types of phase behavior according to the classification of van Konynenburg and Scott, ranging from types I, III, and VI phase behavior for the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) binary mixtures, respectively. This last type is characterized by the presence of a Bancroft point, positive azeotropy, and the so-called closed-loop curves that represent regions of liquid-liquid immiscibility in the phase diagram. The system exhibits lower critical solution temperatures (LCSTs), which denote the lower limit of immiscibility together with upper critical solution temperatures (UCSTs). This behavior is explained in terms of competition between the incompatibility with the alkyl parts of the tetrahydrofuran ring chain and the hydrogen bonding between water and the ether group. A minimum number of unlike interaction parameters are fitted to give the optimal representation of the most representative features of the binary phase diagrams. In the particular case of tetrahydrofuran(1) + water(2), two sets of intermolecular potential model parameters are proposed to describe accurately either the hypercritical point associated with the closed-loop liquid-liquid immiscibility region or the location of the mixture lower- and upper-critical end-points. The theory is not only able to predict the type of phase behavior of each mixture, but also provides a reasonably good description of the global phase behavior whenever experimental data are available.

We propose an extension of the improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 110, 6264-6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, r(c) = 2.5, 3, 4, and 5σ. In addition, we have also considered cutoff distances r(c) = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long-range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as the cutoff distance is larger. We have also checked the effect of the impulsive contribution to the pressure due to the discontinuity of the intermolecular interaction potential when it is cut. If this contribution is not accounted for in the calculation of the microscopic components of the pressure tensor, incorrect values of both components as well as a wrong structure along the vapour-liquid interface are obtained.

The aim of this work is to use a recently developed statistical model of dispersions with nonhydrodynamic interactions to describe the linear viscoelastic properties of emulsions of Newtonian liquids. None of the existing models can describe the rheological behavior of such systems, particularly the elastic properties, in the linear regime. We first present the results of numerical simulations of our model applied to emulsions. We show that taking nonhydrodynamic interactions into account allows to predict that emulsions of two purely viscous liquids have a complex viscoelastic behavior. We then compare the model to experimental results on oil/water emulsions, stabilized with ionic and nonionic surfactants. We find out that our statistical mechanical approach gives a much better description of the viscoelastic behavior of these samples than purely hydrodynamic models do. However, the elasticity observed is underestimated by our model. We indicate further theoretical developments which could improve the description of the viscoelastic properties of emulsions.

The gradient theory of fluid interfaces is for the first time applied, without any lumping, to complex mixtures of more than three components, here made up of hydrocarbons and of a high proportion of carbon dioxide, nitrogen, or methane. It is combined with the volume-corrected Peng-Robinson equation of state. No adjustable parameters are used in the influence parameters mixing rule, which allows use of the gradient theory in a predictive manner. It gives very good estimates of the surface tension of the complex mixtures studied. In any case, it is found to be much superior to the traditional parachor method. The gradient theory is also used to compute the density profiles of the mixture components in the interface; it confirms that the low interfacial tensions of the systems studied are principally induced by a local accumulation of carbon dioxide, nitrogen, or methane in the interface.

In this work the gradient theory of fluid interfaces is used to compute the surface tension of substances of industrial interest (hydrocarbons, gases and refrigerants) once an expression has been derived for their influence parameters. The vapour–liquid equilibria are first determined with a volume-corrected Peng–Robinson equation of state (PR-EOS). The volume corrections are accurately described by a correlation similar to the one suggested by Soreide, but with new parameters regressed on experimental data of the fluids considered here. The influence parameters are computed for each fluid outside the critical region. The results support the assumption that the density-dependence of the influence parameter can be neglected while a temperature-dependence needs to be conserved. A simple correlation is derived to account for this temperature-dependence. For hydrocarbons and gases, the parameters of the temperature-dependence are correlated with the acentric factor; for refrigerants, they are kept constant. When the gradient theory is applied with the expression presented here for the influence parameter and combined with the volume-corrected PR-EOS, the overall average absolute deviations of the calculated surface tensions is 2.2% for hydrocarbons and gases, 4% for refrigerants.

Micellar properties of four homogeneous polyoxyethyleneglycol n-dodecyl ethers C12H25(OCH2CH2)(i)OH (i = 3, 5, 7 and 9) were examined in the temperature range 15-80degreesC. For each surfactant, the variation in the critical micelle concentration (c.m.c.), deduced from surface tension measurements, exhibited a minimum as a function of temperature. The hydroxyl group contribution to the free energy of micellization was found to be higher than that of the ethylene oxide group, especially at the lowest temperatures. When temperature increased, the hydroxyl group contribution decreased as a result of a dehydration, while the ethylene oxide contribution remained practically constant. As an illustration of the possible uses of the contributions determined, enthalpies of micellization were calculated for surfactants of the same family but having different chain lengths. These enthalpies were in reasonable agreement with values directly derived from calorimetric measurements.

This study has investigated the influence of varying the ratio of paraffin, naphthene and aromatic (P/N/A) components in narrow, wide and real petroleum fractions on the parachors of the fractions. Surface tension and density measurements have been made on synthetic hydrocarbon mixtures simulating real SC8, SC10, SC13 groups, their mixtures and a kerosene sample covering the range SC4–SC14 in order to determine their experimental parachors. Two methods to compute the parachors of fractions are proposed based on the equation of Broseta, the correlations of Riazi and Al-Sahhaf and the pseudocompound approach of Daubert. The first, denoted method I, is given byPa(cut)=[0.85−0.19ω(cut)]Tc12/11(cut)Pc9/11(cut)and the second, denoted method II, byPa(cut)=zPPa(P)+zAPa(A)+zNPa(N)where Pa is the parachor of the cut, ω the acentric factor, P, N and A the P/N/A components, zP/N/A the mole fractions of the P/N/A components and the other terms have their usual meaning. Both of these methods were found to compute the parachors of mixtures representing the SC8, SC10 and SC13 groups, mixtures of these groups and the kerosene sample with an absolute deviation of 2%. Comparison of the experimental parachors with calculated ones show that the parachor of a petroleum fraction depends not only on its molecular weight but also on the ratio of the P/N/A components. It was also found that the parachor of each of the families of P, N and A components could be expressed as a linear function of molecular weight leading to the following expression for a mixture containing P, N and A componentsPa(cut)=(zPAP+zNAN+zAAA)MW+(zPBP+zNBN+zABA)where the A and B terms were those found in the linear regression fit for each family. The approach proposed gives quantitatively better results than methods such as that of Fawcett, where the P/N/A distribution is not taken into account in the computation of petroleum fraction parachors.

Experiments have been carried out to find the impact of the viscosity ratio p = eta (d)/eta (e), on the droplet size distributions of emulsions generated in a colloid mill. Under fixed experimental conditions, by increasing p, the droplet diameter according to Sauter (d(32)) goes through a pronounced maximum. This non-monotonous variation is observed whatever the volume fraction of dispersed phase smaller than 0.60.The analysis of the factors involved in the emulsion formation suggests that this behaviour could be due to the modifications of both the breakup process and the number of daughter droplets as p increases.

We have made a literature survey and performed a critical analysis of the available experimental surface tension data for the most volatile compounds in petroleum fluids: nitrogen, methane, ethane, propane, i-butane, n-butane, n-pentane, n-hexane, n-heptane and n-octane. Including the selected data with those for oxygen, xenon, krypton and those obtained recently for 16 partially halogenated hydrocarbons (refrigerants), we propose the following extended scaled equation to represent the surface tension of these substances:σ=kTcNAVc2/3(4.35+4.14ω)t1.26(1+0.19t0.5−0.25t)where t1−T/Tc is reduced temperature, k, NA, Vc, and ω are the Boltzmann constant, Avogadro number, the critical volume and the acentric factor, respectively. This equation, which only differs slightly from that proposed by Schmidt et al. [J.W. Schmidt, E. Carrillo-Nava, M.R. Moldover, Fluid Phase Equilibria 122 (1996) 187–206] for refrigerants, yields values for σ within 3.5% of the experimental values for all these compounds. Available data for other compounds (refrigerants) are in agreement with this relation; in the light of that we also examine some compounds (carbon dioxide and argon) for which there exist conflicting datasets.

The growth mechanism of droplets of hexadecane-in-water emulsions stabilized by heptaethylene glycol mono-n -dodecyl ether was studied by means of photon correlation spectroscopy. When the water-to-oil ratio (WOR) was varied from 4 to 10, a translucent oil in water emulsion (a so-called `miniemulsion') was obtained, while an opaque oil in water emulsion (O/W emulsion) was prepared when WOR was equal to 3. The z -average hydrodynamic radius of droplets, rz , was measured over the 24 days after preparation. Plotting the cube of the z -average radius as a function of time, we found that r3 z varies linearly with time in the system of the O/W emulsion (WOR = 3). This suggests that the process by which the droplets grow is that of Ostwald ripening. On the other hand, the same plot for the system of miniemulsions (4 < WOR < 10) shows two regimes in the process. In both regimes, r3 z varies linearly with time. The rate obtained for the earlier stage is smaller than that of the latter stage. The droplet size distribution became too broad compared with the prediction of Lifshitz-Slezov-Wagner theory for Ostwald ripening ~10 days after preparation. Then it approached the predicted distribution again ~20 days after preparation.

Recently phase formation mechanisms have been estimated by using various fluorescent probes. In this report, the mixing process between internal phases of oil-in-water miniemulsions is discussed for two-dimensional color graphics data (two-dimensional fluorescence images) based on the excimer formation of pyrene as a hydrophobic fluorescent probe. Just after miniemulsion solution B (water, oil, and nonionic surfactant) was gradually added to miniemulsion A (water, oil, surfactant, and trace amount of pyrene) with gentle and careful stirring, the fluorescence spectra and the two-dimensional image of pyrene were measured. The decreasing of the excimer peak of pyrene was observed as soon as miniemulsion solution B was added. The result showed that pyrene initially located in miniemulsion droplets was smoothly diluted by the addition of miniemulsion droplets which contain only oil in the internal phase. The internal phases of miniemulsion droplets are miscible without changing the droplet diameter, and it is declared that pyrene transfers smoothly to the interface between droplets stabilized by the nonionic surfactant because the droplet diameter showed no significant difference throughout this mixing process.

An improvement upon the single breakup/coalescence model is presented to account for the overemulsification generated by the turbulent stirring of surfactant-oil-water systems. The drop breakup process is revisited to produce small satellite droplets instead of just two equal daughter drops.The proposed multiple breakup/coalescence model has three adjustable parameters. With a single set of these parameters the droplet-size distribution can be predicted for a variety of emulsification conditions. The influence of important variables such as the surfactant concentration and the oil volume fraction is simulated on the model and the data are compared with experimental results.

The crystallization of n-Hexadecane dispersed within a suitable aqueous medium has been studied by the mean of Differential Scanning Calorimetry (DSC). The dispersion of the oil is found to be dependent on the mixing conditions: calorimetric curves exhibit one or two exothermic signals which represent different undercoolings. n-Hexadecane can be dispersed in microscopic droplets or in both microscopic and macroscopic phases. Furthermore, during an isothermal stabilization (in a particular temperature range) one can observe an oil transfer from the microscopic droplets to the macroscopic organic phase. The same phenomenon can also be induced by thermal cycling. The effect of aging was found to be in perfect agreement with the predictions that can be drawn from the calorimetric analysis of freshly made samples.

We present a simulation of the formation of moderately concentrated oil-in-water emulsions generated by turbulent stirring using an ionic surfactant as emulsifier. The simulation is based on a stochastic model in which the mass transfer between the droplets is induced by breakups and coalescences until statistical equilibrium is established. Breakups and coalescences are controlled by probability functions in which the influence of the emulsifier is introduced through efficiency factors. These factors account for the competition between the main conflicting forces acting on the droplets during turbulent stirring.The model has only two adjustable parameters. With a single pair of values, the droplet distribution can be predicted for a variety of emulsification conditions. In this paper, it is shown that the minimum amount of emulsifier required to produce the finest droplet size distributions of various emulsions can also be successfully predicted.

We propose a stochastic model to forecast the droplet size distributions of oil in water emulsions generated in a colloid mill. The model lays on breakup sequences of the oil droplets induced by the shear field existing within the mill. One single set of the three fitting parameters is sufficient to account for the variations of the droplet size distributions in function of the surfactant concentration, the surfacant nature, the rotation speed of the rotor.

We have worked out a simplified model to forecast the droplet size distribution in emulsions generated by turbulent agitation in a closed vessel. This model is suited only for semidiluted oil/water emulsions stabilized by an ionic surfactant. — In this model, during one step of the calculus, each droplet is submitted to a random transition: it can break into two droplets of half volume, or coalesce with another droplet of same volume, or remain unaltered. — At the instant t, the droplet size distribution is represented by a line vector, the elements of which are the volume percentages of the N possible states for the droplets. During the interval of time dt following the instant t, the random transition is represented by a [N, N] matrix, the elements of which are the transition probabilities in each state. These elements are updated after each step to make allowances for the creation of the oil/water interface and the corresponding surfactant adsorption. The size distribution at the instant t+dt is obtained by multiplying the line vector and the transition matrix. - The transitions result from the competition between the forces driving, breaking and coalescence. The expressions of their probabilities rest essentially on the kinetic theory of gas, the isotropic turbulence theory, and the DLVO theory. — The model has two adjustment parameters: the former linked to the ratio of breaking and coalescence probabilities, the second to the kinetic energy of the droplets in the turbulent medium. A couple of values of these parameters is found to be sufficient to account for the variation of the droplet size distribution in isooctane/water emulsions as a function of the concentration of sodium dodecylbenzene sulfonate.

We study interbubble gas transfer in liquid foams by measuring the relative decrease of the bubble area from reflectometry. Foams are obtained by independently fixing foaming solution and gas flows through a coarse porous structure. Precise measurements of these flows instantaneously give the gas volume fractions of the foams; real time diffractometry gives their initial bubble size distributions, which we found to be lognormal. — We calculate interbubble gas transfer within such foams on the basis of a theory developed by Lemlich for other bubble size distributions. For a given bubble mean size, we find that the experimentally measured width of the bubble size distribution provides the fastest transfer; then the calculated transfer is close to the one which corresponds to the Lemlich distribution. — Comparison between theoretical and experimental relative decreases of the bubble total area allows to obtain the initial effective permeability of the interbubble medium to gas transfer. We show that this permeability can be drastically lowered by associating an anionic surfactant with an amphoteric one in the foaming solution .

A phase separation model describing both the composition of the interfacial pseudophase and the partitioning of surfactant molecules into the oil and aqueous phases is proposed. Model parameters include the Critical Micelle Concentrations (CMC) and the partition coefficients of the individual surfactant molecules. These are parameters characteristic of the individual surfactant molecules. A second set of parameters relates to surfactant interactions within the interfacial pseudophase. For the cases studied, including those comprised of ternary surfactant systems, it is found that the binary interaction parameters derived from mixture CMC data are adequate to describe all of the experimental results.