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.

Nanofluids alter the surface wettability of solids.

We report the results of our studies on the changes in the contact angle and interfacial tension using a nanofluid composed of silica nanoparticles dispersed in water on three different solid substrates: gold (partially hydrophobic), glass (hydrophilic), and a silicon wafer (hydrophilic). We used both the goniometric method and drop-shape analysis to make the measurements. On the basis of the results of the drop-shape analysis using the Laplace equation, we evaluated the contributions of the interfacial tension change to the equilibrium contact angle and the presence of nanoparticles near the solid substrate, thereby elucidating the change in the wettability of the solid substrate. We found that the nanoparticles decrease the contact angle of the substrate with the increase in the nanoparticle concentration. To rationalize our experimental observations on the decrease in the contact angle of the solid substrate in the presence of nanoparticles, we calculated the surface volume fraction of the nanoparticles in the layer near the solid substrate using the particle layering model (based on the nanoparticles' excluded volume effect). We found that the volume fraction of the nanoparticles in the layer close to the substrate increased with an increase in the nanoparticle volume fraction in the bulk and correlated qualitatively with the change in the substrate wettability. The extent of the wettability alteration depends on the volume fraction of the nanoparticles, their size, and the type of substrate. We found a strong correlation between the change in the substrate wettability and the nanoparticle volume fraction in the layer closer to the substrate surface.

Dynamic spreading of nanofluids on solids part II: modeling.

Recent studies on the spreading phenomena of liquid dispersions of nanoparticles (nanofluids) have revealed that the self-layering and two-dimensional structuring of nanoparticles in the three-phase contact region exert structural disjoining pressure, which drives the spreading of nanofluids by forming a continuous wedge film between the liquid (e.g., oil) and solid surface. Motivated by the practical applications of the phenomenon and experimental results reported in Part I of this two-part series, we thoroughly investigated the spreading dynamics of nanofluids against an oil drop on a solid surface. With the Laplace equation as a starting point, the spreading process is modeled by Navier-Stokes equations through the lubrication approach, which considers the structural disjoining pressure, gravity, and van der Waals force. The temporal interface profile and advancing inner contact line velocity of nanofluidic films are analyzed through varying the effective nanoparticle concentration, the outer contact angle, the effective nanoparticle size, and capillary pressure. It is found that a fast and spontaneous advance of the inner contact line movement can be obtained by increasing the nanoparticle concentration, decreasing the nanoparticle size, and/or decreasing the interfacial tension. Once the nanofluidic film is formed, the advancing inner contact line movement reaches a constant velocity, which is independent of the outer contact angle if the interfacial tension is held constant.

Dynamic spreading of nanofluids on solids. Part I: experimental.

Nanofluids have enhanced thermophysical properties compared to fluids without nanoparticles. Recent experiments have clearly shown that the presence of nanoparticles enhances the spreading of nanofluids. We report here the results of our experiments on the spreading of nanofluids comprising 5, 10, and 20 vol % silica suspensions of 19 nm particles displacing a sessile drop placed on a glass surface. The contact line position is observed from both the top and side views simultaneously using an advanced optical technique. It is found that the nanofluid spreads, forming a thin nanofluid film between the oil drop and the solid surface, which is seen as a bright inner contact line distinct from the conventional three-phase outer contact line. For the first time, the rate of the nanofluidic film spreading is experimentally observed as a function of the nanoparticle concentration and the oil drop volume. The speed of the inner contact line is seen to increase with an increase in the nanoparticle concentration and decrease with a decrease in the drop volume, that is, with an increase in the capillary pressure. Interestingly, the formation of the inner contact line is not seen in fluids without nanoparticles.

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.

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.

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.

Superspreading driven by Marangoni flow.

The spontaneous spreading (called superspreading) of aqueous trisiloxane ethoxylate surfactant solutions on hydrophobic solid surfaces is a fascinating phenomenon with several practical applications. For example, the ability of trisiloxane ethoxylate surfactants to enhance the spreading of spray solutions on waxy weed leaf surfaces, such as velvetleaf (Abutilion theophrasti), makes them excellent wetting agents for herbicide applications. The superspreading ability of silicone surfactants has been known for decades, but its mechanism is still not well understood. In this paper, we suggest that the spreading of trisiloxane ethoxylates is controlled by a surface tension gradient, which forms when a drop of surfactant solution is placed on a solid surface. The proposed model suggests that, as the spreading front stretches, the surface tension increases (the surfactant concentration becomes lower) at the front relative to the top of the droplet, thereby establishing a dynamic surface tension gradient. The driving force for spreading is due to the Marangoni effect, and our experiments showed that the higher the gradient, the faster the spreading. A simple model describing the phenomenon of superspreading is presented. We also suggest that the superspreading behavior of trisiloxane ethoxylates is a consequence of the molecular configuration at the air/water surface (i.e. small and compact hydrophobic part), as shown by molecular dynamics modeling. We also found that the aggregates and vesicles formed in trisiloxane solutions do not initiate the spreading process and therefore these structures are not a requirement for the superspreading process.

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.