By use of the analytic result for the Laplace transform of the radial distribution function for two large hard spheres dispersed in a fluid of the smaller hard spheres, simple equations for the film interaction energy and film disjoining pressure, due to the structural and depletion forces, are derived. The proposed equations satisfy some known exact results and explicitly express the energy and pressure as a function of the film thickness and volume fraction of the small hard spheres. The predicted results for the film energy and film disjoining pressure are compared with existing computer simulation data. The proposed simple analytical expressions can be applied to understand the stability of liquid films containing colloidal particles and the stability of suspensions, foams, and emulsions.
The effective pair interaction (potential of the mean force) between large hard spherical colloidal particles in a dispersion containing small hard sphere particles has been studied theoretically. We calculated the effective interaction from the total correlation function by solving the Ornstein-Zernike equation. For a simple binary mixture of particles, the calculated effective interaction between two large (colloidal) particles is found to be oscillatory in general, including both the Asakura-Oosawa type attractive depletion well and the repulsive energy barrier (which is caused by the formation of small particle layers between these two large particles). A systematic study was conducted to examine the relationship between the effective interaction potential and the controllable parameters like the particle concentration and the size ratio. The existence of the structural energy barrier is expected to have dual effects on the stability of the large particle dispersion in general: stabilizing in a short time scale and destabilizing in a long time scale. The effect of the polydispersity of small particles on both depletion and the structural force between large particles is also addressed in our study, and we found that polydispersity affects the structural energy barrier more than it does the attractive depletion well. In comparison with the depletion/structuring force measured from the force apparatus experiments, we found that our theoretical results are in good agreement with the experiment.
The mechanisms of stabilization of water-in-crude oil emulsions have been investigated by changing the solvent-solute interactions in crude oil. Diluting the original crude oil with varying amounts of heptane, which is a poor solvent for asphaltenes, changes the solvent-solute interactions, leading to flocculation of asphaltenes and thus changing the emulsion stability. The interactions between the water droplets in an emulsion system have been quantified by measuring the radial distribution function and thereby the pair potential using the digitized optical imaging technique. It has been observed that the force of interaction between water droplets is oscillatory. This shows that non-DLVO forces, such as attractive depletion and repulsive structural forces, exist between the droplets. The interaction between the water droplets has been modeled by studying the properties of a thin liquid film sandwiched between the water droplets. Because of the film confinement effect, asphaltene-resin particles form a layered structure inside the thin liquid film. Also, the role of hydrodynamic interactions has been studied by using the film rheometer to measure the dynamic film tension and film elasticity. It has been found that, because of the adsorption of asphaltene at the film interfaces, the film elasticity plays a significant role in stabilizing these emulsions.
The phenomenon of layering of like-charged particles (ionic surfactant micelles or other colloidal particles) between two plane-parallel film surfaces and the evolution of in-film particle structuring are studied using the canonical Monte Carlo method combined with a simulation cell containing both the bulk solution and the film region. The simulations are performed using an effective one-component fluid potential model that incorporates micelle hard-core repulsion and both the screened Coulomb electrostatic interaction and the entropic contribution due to the discrete nature of the solvent and finite size of electrolyte ions. The proposed potential model is applied to mimic the properties of surfactant micelle solutions in the bulk and under film confinement. The effects of surfactant concentration and film thickness on the in-film micellar structuring phenomenon are analyzed. The relation of obtained results to experiments on stratifying sodium dodecyl sulfate micellar films is discussed.
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