The foam film's stepwise thinning phenomenon and role of oscillatory forces.

As a foam film formed from complex fluids thins, the particles under the film confinement self-organize into layers. Reflected light was used to monitor the rate of layer-by-layer thinning and the layers' thickness. The microscopic and macroscopic films thin using the same stepwise manner (stratify), via layers or stripes with equal thicknesses. The roles of the film area (size) and film capillary pressure on the film stepwise thinning were studied. A micron-sized dot with a thickness one layer less than that of the surrounding film area is observed. The dot expands into a spot when the film reaches the critical area. The 2D dot-spot exhibits a threshold process. The spot expands and the film's stepwise thinning begins. When the film area is reduced, the spot stops expanding and begins to reduce in size. The film slowly recovers its original thickness in a stepwise manner, one layer at a time. It was demonstrated that the film area is the governing factor in the film stepwise thinning rather than the film capillary pressure. A particle dislocation-diffusion-osmotic pressure model is proposed to explain the mechanism of the film stepwise thinning phenomenon via dot-spot formation. The model explains all the features of the foam stepwise thinning phenomenon, including the reversibility of the film's stepwise thinning. For the first time for a film with a thickness less than three layers, a 2D in-layer hexagonal particle entropy structural transition was observed and theoretically predicted by the analysis of the Radial Distribution Function (RDF).

Two-phase displacement dynamics in capillaries-nanofluid reduces the frictional coefficient.

Surfactant solutions containing polymeric nanoparticles have been shown to have an improved wetting and spreading on solid surfaces. In this work, we explored the effect of the polymeric nanoparticles on the frictional coefficient at the three-phase contact region by studying polymeric nanofluids displacing oil in capillaries. Our results show polymeric nanoparticles can reduce the frictional coefficient by as much as four times by forming structured layers in the confined wedge film. We also demonstrate the role of the interfacial tension in affecting the frictional coefficient.

Prediction of the rate of the rise of an air bubble in nanofluids in a vertical tube.

Our recent experiments have demonstrated that when a bubble rises through a nanofluid (a liquid containing dispersed nanoparticles) in a vertical tube, a nanofluidic film with several particle layers is formed between the gas bubble and the glass tube wall, which significantly changes the bubble velocity due to the nanoparticle layering phenomenon in the film. We calculated the structural nanofilm viscosity as a function of the number of particle layers confined in it and found that the film viscosity increases rather steeply when the film contains only one or two particle layers. The nanofilm viscosity was found to be several times higher than the bulk viscosity of the fluid. Consequently, the Bretherton equation cannot accurately predict the rate of the rise of a slow-moving long bubble in a vertical tube in a nanofluid because it is valid only for very thick films and uses the bulk viscosity of the fluid. However, in this brief note, we demonstrate that the Bretherton equation can indeed be used for predicting the rate of the rise of a long single bubble through a vertical tube filled with a nanofluid by simply replacing the bulk viscosity with the proper structural nanofilm viscosity of the fluid.

Estimation of structural film viscosity based on the bubble rise method in a nanofluid.

When a single bubble moves at a very low capillary number (10-7) through a liquid with dispersed nanoparticles (nanofluid) inside a vertical tube/capillary, a film is formed between the bubble surface and the tube wall and the nanoparticles self-layer inside the confined film. We measured the film thickness using reflected light interferometry. We calculated the film structural energy isotherm vs. the film thickness from the film-meniscus contact angle measurements using the reflected light interferometric method. Based on the experimental measurement of the film thickness and the calculated values of the film structural energy barrier, we estimated the structural film viscosity vs. the film thickness using the Frenkel approach. Because of the nanoparticle film self-layering phenomenon, we observed a gradual increase in the film viscosity with the decreasing film thickness. However, we observed a significant increase in the film viscosity accompanied by a step-wise decrease in the bubble velocity when the film thickness decreased from 3 to 2 particle layers due to the structural transition in the film.

Capillary Rise: Validity of the Dynamic Contact Angle Models.

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Step-Wise Velocity of an Air Bubble Rising in a Vertical Tube Filled with a Liquid Dispersion of Nanoparticles.

The motion of air bubbles in tubes filled with aqueous suspensions of nanoparticles (nanofluids) is of practical interest for bubble jets, lab-on-a-chip, and transporting media. Therefore, the focus of this study is the dynamics of air bubbles rising in a tube in a nanofluid. Many authors experimentally and analytically proposed that the velocity of rising air bubbles is constant for long air bubbles suspended in a vertical tube in common liquids (e.g. an aqueous glycerol solution) when the capillary number is larger than 10-4. For the first time, we report here a systematic study of an air bubble rising in a vertical tube in a nanofluid (e.g. an aqueous silica dioxide nanoparticle suspension, nominal particle size, 19 nm). We varied the bubble length scaled by the diameter of the tubes (L/D), the concentration of the nanofluid (10 and 12.5 v %), and the tube diameter (0.45, 0.47, and 0.50 cm). The presence of the nanoparticles creates a significant change in the bubble velocity compared with the bubble rising in the common liquid with the same bulk viscosity. We observed a novel phenomenon of a step-wise increase in the air bubble rising velocity versus bubble length for small capillary numbers less than 10-7. This step-wise velocity increase versus the bubble length was not observed in a common fluid. The step-wise velocity increase is attributed to the nanoparticle self-layering phenomenon in the film adjacent to the tube wall. To elucidate the role of the nanoparticle film self-layering on the bubble rising velocity, the effect of the capillary number, the tube diameter (e.g. the capillary pressure), and nanofilm viscosity are investigated. We propose a model that takes into consideration the nanoparticle layering in the film confinement to explain the step-wise velocity phenomenon versus the length of the bubble. The oscillatory film interaction energy isotherm is calculated and the Frenkel approach is used to estimate the film viscosity.

Particles driven up the wall by bursting bubbles.

The phenomenon of particles being "driven up the wall" of a vessel by bursting bubbles at an air-water interface covered with hydrophobic nanoparticles is reported. Experiments have shown that the bubbles bursting at the interface give rise to the local surface pressure gradient, which pushes the particles to climb and coat the walls of the vessel. A theoretical model based on the lubrication approach to estimate the height and speed at which the particle layers climb up the walls yields values that are in fair agreement with the experimental measurements. The effects of the liquid viscosity, electrolyte strength, and particle wettability are also examined.

Sedimentation of concentrated monodisperse colloidal suspensions: role of collective particle interaction forces.

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle-particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle-particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle-particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.

Sedimentation in nano-colloidal dispersions: effects of collective interactions and particle charge.

This is a review paper summarizing the progress of the development of colloidal sedimentation models for monodisperse, bidisperse, and polydisperse nanoparticle dispersions. This topic is of considerable interest because the sedimentation behavior of nanoparticles plays an important role in many practical systems, such as industrial coatings, optical products, ceramics, paints, dyes, and cosmetics. The limitations of various models are discussed. Multi-particle systems are highlighted, with a focus on the collective thermodynamic interactions resulting in the attractive depletion and repulsive structural forces. The effects of the particle concentration, particle charge, polydispersity in size, and electrolyte concentration on the sedimentation process are briefly summarized. Our contributions to this subject are reviewed.

Computer simulation of macroion layering in a wedge film.

The layering of macroions confined to a wedge slit formed by two uncharged hard walls is studied using a canonical Monte Carlo method combined with a simulation cell that contains both wedge-shaped slit and bath regions. The macroion solution is modeled within a one-component fluid approach that in an effective way incorporates the double layer repulsion due to simple electrolyte ions as well as the discrete nature of an aqueous solvent. The layer formation under a wedge confinement is analyzed by carrying out separate simulation runs for a set of consecutive wedge segments designed to represent a single wedge slit. As the wedge thickness progressively increases, the sequence of regions along the wedge film with distinct features of macroion layering has been established. This sequence comprises (i) a wedge region of the thickness smaller than the macroion diameter that is free of macroions; (ii) a region with a one-dimensional macroion chain along the wedge corner at a wedge thickness of a one macroion diameter; (iii) a region comprising a low-ordered macroion monolayer that extends until the wedge thickness slightly above two macroion diameters; (iv) a region comprising a pair of well-defined two-dimensional configurations of macroions segregated on each of the wedge walls; and (v) a free-of-macroions wedge region between two surface monolayers that now originates from an electrostatic repulsion imposed by the surface macroions, which is followed by (vi) a well-defined macroion monolayer film between two surface monolayers, a less defined bilayer film, a three-layer film, and so on up to the bulk solution. Once formed, the macroion surface monolayers persist for all remaining wedge thicknesses up to the bulk, forming in such a way effective charged wedge boundaries. Such a formation of the macroion surface monolayers on the uncharged confining walls is related to the haloing mechanism for regulating the stability in colloidal suspensions [Tohver et al. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 8951] and is discussed as well. Finally, the estimated boundary of the free of macroion region between surface monolayers correlates well with the location of the boundary of the so-called "vacuum" phase that has been observed experimentally in an aqueous suspension of charged polystyrene spheres bounded by electrostatically repulsive glass walls [Pieransky et al. Phys. Rev. Lett. 1983, 50, 900].

Spreading of nanofluids driven by the structural disjoining pressure gradient.

This paper discusses the role of the structural disjoining pressure exerted by nanoparticles on the spreading of a liquid film containing these particles. The origin of the structural disjoining pressure in a confined geometry is due to the layering of the particles normal to the confining plane and has already been traced to the net increase in the entropy of the system in previous studies. In a recent paper, Wasan and Nikolov (Nature, 423 (2003) 156) pointed out that the structural component of the disjoining pressure is strong enough to move a liquid wedge; this casts a new light on many applications-most notably, detergency. While the concept of spreading driven by the disjoining pressure is not new, the importance of the structural disjoining pressure arises from its long-range nature (as compared to the van der Waals' force), making it an important component of the overall force balance near the contact line. In this paper, we report on a parametric study of the spreading phenomena by examining the effects of nanoparticle size, concentration and polydispersity on the displacement of an oil-aqueous interface with the aqueous bulk containing nanoparticles. The solution of the extended Laplace-Young equations for the profile of the meniscus yields the position of the nominal contact line under the action of the structural disjoining pressure. Simulations show that the displacement of the contact line is greater with a high nanoparticle volume fraction, small particles for the same volume fraction, monodispersed (in size) particles rather than polydispersed particles and when the resisting capillary pressure is small, i.e., when the interfacial tension is low and/or the radius of the dispersed phase drop/bubble is large.

Interaction between a macrosphere and a flat wall mediated by a hard-sphere colloidal suspension.

The interaction between the macrosphere and the flat wall immersed in a binary fluid comprising small and large (size ratio around 1:10) hard spheres has been investigated. We find that the presence of the highly size-asymmetric particles qualitatively modifies the induced excluded-volume interaction between the macrosphere and the flat wall compared to that observed in a single-component suspending fluid comprised of only large or only small species. The role in the interaction between a macrosphere and a flat wall played by species of the fine component that usually is approximated by a continuum medium (primitive description of a bidisperse fluid) is emphasized. Particularly, we show that taking into account the smaller component of a bidisperse suspending fluid modifies significantly the macrosphere-wall depletion attraction that is predicted when only large particles are taken into account. The depletion attraction force created by the presence of small fluid particles enhances the adsorption of large particles and their structuring on the wall.

Attraction-driven disorder in a hard-core colloidal monolayer.

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.

Spreading of nanofluids on solids.

Suspensions of nanometre-sized particles (nanofluids) are used in a variety of technological contexts. For example, their spreading and adhesion behaviour on solid surfaces can yield materials with desirable structural and optical properties. Similarly, the spreading behaviour of nanofluids containing surfactant micelles has implications for soil remediation, oily soil removal, lubrication and enhanced oil recovery. But the well-established concepts of spreading and adhesion of simple liquids do not apply to nanofluids. Theoretical investigations have suggested that a solid-like ordering of suspended spheres will occur in the confined three-phase contact region at the edge of the spreading fluid, becoming more disordered and fluid-like towards the bulk phase. Calculations have also suggested that the pressure arising from such colloidal ordering in the confined region will enhance the spreading behaviour of nanofluids. Here we use video microscopy to demonstrate both the two-dimensional crystal-like ordering of charged nanometre-sized polystyrene spheres in water, and the enhanced spreading dynamics of a micellar fluid, at the three-phase contact region. Our findings suggest a new mechanism for oily soil removal--detergency.

Stability of Liquid Films Containing Monodisperse Colloidal Particles.

Thin liquid films containing colloidal particles are considered to be the key structural elements of three-phase foams containing liquid, gas, and colloidal particles. This study is aimed at understanding the stability of such films in the absence of any surfactants. The particles form a layered structure in the film and produce a stepwise thinning in the thin liquid films. We report here for the first time the effects of particle concentration and size on film thickness transition of curved liquid films containing monodispersed colloidal particles. The rate of stepwise film thinning was observed to be high when particle concentration was low and both particle size and film size were large. The phenomenon of stepwise film thinning (i.e., stratification) is rationalized on the basis of diffusion of colloidal particles from the film to the meniscus, i.e., the diffusive osmotic mechanism. There exists a critical film size below which at least one layer of particles always stays in the film (i.e., black spot expansion does not occur). This critical size is dependent upon both particle size and concentration. Also, Monte Carlo simulations of the film show that, at a high particle concentration, better particle in-layer structure develops that increases the energy barrier, inhibiting particle diffusion from the film to the bulk meniscus. Copyright 2001 Academic Press.