Interfacial profiles in fluid/liquid systems: a description based on the storing of elastic energy.

An analytical expression for the interfacial energy is found by solving a Poisson equation and assuming a Boltzmann distribution of volume elements forming the fluid/liquid system. Interfacial phenomena are treated as a result of the response of a liquid when it makes contact with other fluid phase, in order to reach thermal and mechanical equilibrium. This model gives a quantitative description of the interface, obtaining values for its molar, force and energy density profiles. Also, our model allows the determination of the proportion of the fluids present in the interfacial zone, the values of interfacial tension and thickness. In the case of water+n-alkanes systems, the tensions are in agreement with the behavior shown by the experimental data. Finally, the values for interfacial thickness predicted from molar density profiles are lower than the range of influence of the elastic energy and elastic field.

Influence of droplet deformability on the coalescence rate of emulsions.

In this article the influence of deformation on the coalescence rates of oil-in-water (O/W) emulsions is analyzed. Calculations for doublets and many-particles systems were performed based on a Brownian dynamics algorithm. Extensional and bending energies were included in order to quantify the effect of the changes in the surface geometry on the coalescence rates. Also, the hydrodynamic resistance due to the flat film was included through a correction to the diffusion coefficient in the lubrication limit. Results of two particles calculations were compared with previous analytical evaluations of the coalescence time in absence of highly repulsive barriers [Danov, Langmuir 9, 1731 (1993)]. Lifetime of doublets was calculated as a function of the particle radius from 100 nm to 100 microm. It was found that the doublets lifetime strongly depends on the interplay between the potential of interaction between the droplets and the hydrodynamic resistance. Depending on the repulsive barrier either a monotonous increase of the lifetime with the droplet size or a maximum value is observed. Finally, the evolution of O/W emulsions with a volume fraction of phi=0.10 was studied. For these many-particle systems, the results show a sensitive dependence of the aggregation behavior on the interfacial tension. The procedure reported here allows us to include Derjaguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO forces and the film drainage velocity of many different systems.

Lifetime of micrometer-sized drops of oil pressed by buoyancy against a planar interface.

Emulsion stability simulations are used to estimate the coalescence time of one drop of hexadecane pressed by buoyancy against a planar water/hexadecane interface. In the present simulations, the homophase is represented by a big drop of oil at least 500 times larger than the approaching drop (1-10 microm). Both deformable and nondeformable drops are considered along with six different diffusion tensors. In each case, van der Waals, electrostatic, steric, and buoyancy forces are taken into account. The coalescence times are estimated as the average of 1000 random walks. It is found that the repulsive potential barrier has a significant influence in the results. The experimental data can only be reproduced assuming negligible repulsive barriers, as well as nondeformable drops that move with a combination of Stokes and Taylor tensors as they approach the interface.

Lifetime of oil drops pressed by buoyancy against a planar interface: large drops.

In a previous report [C. Rojas, G. Urbina-Villalba, and M. García-Sucre, Phys. Rev. E 81, 016302 (2010)] it was shown that emulsion stability simulations are able to reproduce the lifetime of micrometer-size drops of hexadecane pressed by buoyancy against a planar water-hexadecane interface. It was confirmed that small drops (r(i)< 10 µm) stabilized with ß -casein behave as nondeformable particles, moving with a combination of Stokes and Taylor tensors as they approach the interface. Here, a similar methodology is used to parametrize the potential of interaction of drops of soybean oil stabilized with bovine serum albumin. The potential obtained is then employed to study the lifetime of deformable drops in the range 10 ≤ r(i) ≤ 1000 µm . It is established that the average lifetime of these drops can be adequately replicated using the model of truncated spheres. However, the results depend sensibly on the expressions of the initial distance of deformation and the maximum film radius used in the calculations. The set of equations adequate for large drops is not satisfactory for medium-size drops (10 ≤ r(i) ≤ 100 µm) , and vice versa. In the case of large particles, the increase in the interfacial area as a consequence of the deformation of the drops generates a very large repulsive barrier which opposes coalescence. Nevertheless, the buoyancy force prevails. As a consequence, it is the hydrodynamic tensor of the drops which determine the characteristic behavior of the lifetime as a function of the particle size. While the average values of the coalescence time of the drops can be justified by the mechanism of film thinning, the scattering of the experimental data of large drops cannot be rationalized using the methodology previously described. A possible explanation of this phenomenon required elaborate simulations which combine deformable drops, capillary waves, repulsive interaction forces, and a time-dependent surfactant adsorption.

A simple model to describe dimple dynamics / Un modelo sencillo para la descripción de la dinámica de un dimple / Um modelo simples para a descrição da dinâmica de um dimple

A model based on the hydrodynamics equations that allows to describe the dynamics of a dimple, once it has formed, is proposed. The Navier-Stokes equations are considered, and two fundamental approaches are used to simplify the mathematical treatment of the hydrodynamics equations. Certain conditions are considered that must be fulfilled at the interface, which serve to close the system of differential equations and lead to an evolution equation that describes the interfacial film dynamics. With the intention of solving this equation, the method of finite differences has been used.

Se propone un modelo que permite la descripción de la dinámica de una depresión superficial (dimple) una vez que se ha formado. Las ecuaciones de Navier-Stokes son consideradas, y dos enfoques fundamentales son utilizados para simplificar el tratamiento matemático de las ecuaciones hidrodinámicas. Se consideraron ciertas condiciones que deben cumplirse en la interfase, las cuales sirven para completar el sistema de ecuaciones diferenciales y llevan a una ecuación de evolución que describe la dinámica de la película interfacial. A fin de resolver la ecuación se utilizó el método de diferencias finitas.

Propõe-se um modelo que permite a descrição da dinâmica de uma depressão superficial (dimple) após ter se formado. As equações de Navier-Stokes são consideradas, e dois enfoques fundamentais são utilizados para simplificar o tratamento matemático das equações hidrodinâmicas. Consideraram-se certas condições que devem cumprir-se na interfase, as quais servem para completar o sistema de equações diferenciais e conduzem a uma equação de evolução que descreve a dinâmica da película interfacial. A fim de resolver a equação se utilizou o método de diferenças finitas.

Thermal lens measurement of the Soret coefficient in acetone/water mixtures.

The Soret coefficient of acetone/water mixtures has been experimentally determined by a recently developed thermal lens technique [Appl. Phys. Lett. 94, 051103 (2009)]. The behavior of the Soret coefficient was reproduced, including its sign change with composition. For concentrations around the equimolar ones, we have also confirmed the disagreement between the experimental and simulation data that had previously been reported by Ning and Wiegand [J. Chem. Phys. 125, 221102 (2006)] using a transient holographic grating technique of thermal diffusion forced Rayleigh scattering. Additionally, we compare our experimental results with the theoretical values predicted by a recently developed viscous energy model [J. Chem. Phys. 130, 064506 (2009)].

Film drainage between two drops: Vortex formation in thin liquid films / Drenaje de la película interfacial entre dos gotas: Formación de vórtices en películas líquidas delgadas / Drenagem da película interfacial entre duas gotas: Formação de vórtices em películas líquidas delgadas

In this study, a mathematical formalism that takes into account the surfactant effect on the drainage of the interfacial film between two drops is considered. The effects of thermal perturbations and van der Waals forces are neglected. In the mathematical formalism the Navier-Stokes equations within the lubrication approximation are coupled to a diffusion-convection equation leading to an evolution equation for the interfacial film. This last equation is solved by using the numerical method of lines coupled with an implicit Runge-Kutta method for the integration with respect to time. As a result of the inclusion of interfacial tension gradients a non oscillating dimple arises, even beginning with an initial condition corresponding to a plane interfacial film.

En este estudio se desarrolla un formalismo matemático que toma en consideración el papel del surfactante en el drenaje de la película interfacial entre dos gotas. No se consideran los efectos de perturbaciones térmicas y fuerzas de van der Waals. En el formalismo matemático se acoplan las ecuaciones de Navier-Stokes (dentro de la aproximación de lubricación) con la ecuación de difusión-convección, lo cual conduce a una ecuación de evolución para la película interfacial. Esta última ecuación es resuelta utilizando el método numérico de líneas junto con un método implícito de Runge-Kutta para la integración con respecto al tiempo. Como resultado de la inclusión de los gradientes de tensión interfacial surge una depresión superficial (dimple) no oscilatoria, inclusive comenzando con una condición inicial correspondiente a una película interfacial plana.

Neste estudo se considera um formalismo matemático que toma em consideração o efeito surfactante na drenagem da película interfacial entre duas gotas. Não se consideram os efeitos de perturbações térmicas e forças de van der Waals. No formalismo matemático as equações de Navier-Stokes dentro da aproximação de lubrificação se acoplam a uma equação de difusão-convecção, o qual leva a uma equação de evolução para a película interfacial. Esta última equação é resolvida utilizando o método numérico de linhas junto com um método implícito de Runge-Kutta para a integração relativa ao tempo. Como resultado da inclusão de gradientes de tensão interfacial surge uma depresão superficial (dimple) não oscilatoria, inclusive começando com uma condição inicial correspondente a uma película interfacial plana.

Correction to the interfacial tension by curvature radius: differences between droplets and bubbles.

In this work we analyze the behavior of the interfacial tension with the curvature radius of the disperse phase. Following the Young-Laplace deduction of the equation relating the internal pressure with the curvature radius for a fluid confined by a spherical interface, we restate the Tolman approach [J. Chem. Phys. 1949, 108, 333] to obtain an analytical expression relating the interfacial tension with the radius. We have found small differences between our results and those of Tolman for the liquid/gas (droplets) case. However, important differences between liquid/gas (droplets) and gas/liquid (bubbles) dispersions were found. In particular, the decrease in the interfacial tension of bubbles may be expected to occur for much larger curvature radii than for the case of droplets when the curvature radius decreases. A simple relation between the Tolman's delta parameter and the interfacial width is also discussed. In our calculations we have considered dispersions of droplet of water in methane and bubbles of methane in water at T = 273.15 K.

Interfacial energy and the law of corresponding states 2: associated fluids.

A mesoscopic model for the liquid/vapor interface previously developed for nonpolar fluids [J. Phys. Chem. A 2003, 107, 875; 2003, 107, 883] is extended to the case of polar associated compounds. The interfacial energy is factorized in two terms: one corresponding to association depending on the hydrogen bonds density, the other corresponding to the nonpolar contribution. This last term is treated in the framework of the corresponding states formalism similar to the one used in the case of nonpolar fluids [J. Phys. Chem. B 2004, 108, 5951]. The model yields a generalized behavior of the association factor as a function of the dielectric constant for the treated fluids. The calculated surface tension shows a mean error of about 1% for seven compounds having different multivalent H-bond characters.

Theoretical estimation of stability ratios for hexadecane-in-water (H/W) emulsions stabilized with nonylphenol ethoxylated surfactants.

The effect of steric interactions on the stability of oil-in-water emulsions is studied here by means of emulsion stability simulations (ESS). For this purpose, a new steric potential based on a modification of the one formerly proposed by Vincent et. al. is employed. The parameters of the calculation correspond to hexadecane in water emulsions stabilized with nonylphenol ethoxylated surfactants of different chain lengths (NPEm). Stability ratios (W) were calculated using the half life time of the number of drops per unit volume of these systems. A functional relationship between W and the repulsive potential barrier, (DeltaV), similar to the one previously found by Prieve and Ruckenstein for electrostatically stabilized suspensions was obtained. However, according to our simulations there exists a threshold for the stability of emulsions with respect to coalescence which is approximately located around 12.7 k(B)T.

Role of the secondary minimum on the flocculation rate of nondeformable droplets.

The kinetic stability of suspensions is usually associated with a decrease in the flux of flocculating particles due to the action of a repulsive potential. However, previous calculations on bitumen drops suggest the possible occurrence of relatively fast aggregation rates in systems with large electrostatic barriers for primary minimum flocculation. This indicates a strong effect of the secondary minimum in the process of aggregation. Here, emulsion stability simulations (ESS) are used to study the aggregation behavior of 11 systems showing different depths of the secondary minimum and three particle sizes. Micron size drops (as those of Bitumen emulsions) usually exhibit deep secondary minima, which rarely occur between nanometer size particles. At high surfactant concentrations, these drops do not coalesce but can still show fast aggregation rates caused by irreversible secondary-minimum flocculation. On the other hand, the extent of coalescence in nanometer-size systems markedly depends on the height of the repulsive barrier. Furthermore, the secondary minimum of these smaller particles is usually shallow, causing reversible aggregation or no aggregation at all. In this article, the consequences of the referred behaviors on the magnitude of the stability ratio are discussed.

Calculation of flocculation and coalescence rates for concentrated dispersions using emulsion stability simulations.

A simple procedure for the quantification of flocculation (k(f)) and coalescence (k(c)) rates from emulsion stability simulations (ESS) of concentrated systems is presented. It is based on a simple analytical equation, which results from the sum of well-known formulas for the separate processes of flocculation and coalescence. The expression contains k(f) and k(c) as fitting parameters and is found to reproduce the behavior predicted by ESS spanning a wide range of volume fractions (1 < phi < 30%) and surfactant concentrations (1.2 x10(-5) < C < 1.2 x 10(-4) M). This procedure allows interpretation of ESS data in terms of the referred kinetic rates. Furthermore, it could also provide an additional mean for the direct comparison of the simulation data with experimental results.

Steric interaction between spherical colloidal particles.

The reliability of the Derjaguin approximation for the calculation of the mixing term between sterically stabilized colloidal particles is studied. For this purpose, the steric potential obtained from the experiment of Doroszkowski and Lambourne [J. Polym. Sci., Part C: Polym. Symp. 34, 253 (1971)] is regarded as an exact result. Several analytical expressions corresponding to the mixing term of the steric potential are tested. Vincent et al. [Colloids Surf. 18, 261 (1986)] obtained four of them using the Derjaguin approximation along with different profiles for the volume fraction of segments in grafted polymer layers. As will be shown, the exact calculation of the volume of interaction between two spheres with adsorbed polymer layers already leads to a considerable improvement of the theoretical prediction for the simplest case of constant spatial distribution of polymer monomers. This equation is also better than the four additional expressions that result from using Bagchi's formalism [J. Colloid Interface Sci. 47, 86 (1974)] with similar segment profiles. The deviations of Bagchi's formalism can be substantially minimized using Flory-Krigbaum theory instead of the Flory-Huggins formalism for the calculation of the free energy of mixing. The equations derived here for the steric potentials were derived for particles of distinct radii.

Average hydrodynamic correction for the Brownian dynamics calculation of flocculation rates in concentrated dispersions.

In order to account for the hydrodynamic interaction (HI) between suspended particles in an average way, Honig et al. [J. Colloid Interface Sci. 36, 97 (1971)] and more recently Heyes [Mol. Phys. 87, 287 (1996)] proposed different analytical forms for the diffusion constant. While the formalism of Honig et al. strictly applies to a binary collision, the one from Heyes accounts for the dependence of the diffusion constant on the local concentration of particles. However, the analytical expression of the latter approach is more complex and depends on the particular characteristics of each system. Here we report a combined methodology, which incorporates the formula of Honig et al. at very short distances and a simple local volume-fraction correction at longer separations. As will be shown, the flocculation behavior calculated from Brownian dynamics simulations employing the present technique, is found to be similar to that of Batchelor's tensor [J. Fluid. Mech. 74, 1 (1976); 119, 379 (1982)]. However, it corrects the anomalous coalescence found in concentrated systems as a result of the overestimation of many-body HI.