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.

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.

Stratification of a Foam Film Formed from a Nonionic Micellar Solution: Experiments and Modeling.

Thin liquid films containing surfactant micelles or other nanocolloidal particles are considered to be the key structural elements of foams containing gas and liquid. We report here the experimental results and theoretical modeling for the phenomenon of the stratification (stepwise thinning) of a foam film formed from a nonionic micellar solution. The film stratification phenomenon was experimentally observed by reflected light microinterferometry. We observed that the stepwise layer-by-layer decrease of the film thickness is due to the appearance and growth of a dark spot of one layer less than the film thickness in the film. The dark spot expansion is driven by the diffusion of the dislocation (or vacancy) in the micellar lattice. The vacancies from the meniscus diffuse and condense into the dark spot, leading to its expansion inside the film. We experimentally observed the expansion of the dark spot at various film thicknesses (i.e., the number of micellar layers) and at different film sizes. We also measured the contact angle between the film and the meniscus; we used the data to estimate the structural film interaction energy barrier and the apparent diffusion coefficient. We used the two-dimensional diffusion model to model the dynamics of the dark spot expansion with consideration to the apparent diffusion coefficient and the film size. The model predictions are in good agreement with the experimental observations. On the basis of this model, we carried out a parametric study depicting the effects of the film thickness (or the number of micellar layers) and film area on the rate of the dark spot expansion. We also generalized the model previously proposed by Kralchevsky et al. [ Langmuir 1990 , 6 , 1180 - 1189 ], incorporating the effects of the film size, film thickness, and apparent diffusion coefficient to predict the dark spot expansion rate.

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.

Dewetting film dynamics inside a capillary using a micellar nanofluid.

An experimental study was performed in which hexadecane was displaced by a micellar nanofluid in a glass capillary. Experiments have shown that a thick film was formed on the capillary wall after hexadecane was displaced by the nanofluid. The thick hexadecane film is unstable, and over time it breaks and forms a thin film. Once the thick film ruptures, it retracts and forms an annular rim (liquid ridge) that collects liquid. As the volume of the annular rim increases over time, it forms a double-concave meniscus across the capillary and dewetting stops. The thin film on the right side of the double-concave meniscus then breaks and the contact angle increases. The process repeats until the droplets build up all along the capillary wall. Finally, the droplets are displaced from the capillary wall by the nanofluid and spherical droplets appear inside the capillary. This is a novel phenomenon because we did not observe any film formation when we used a solution without micelles. The theoretical model based on the lubrication approximation using the capillary pressure gradient was developed to estimate the annular rim dewetting velocity. The predicted dewetting velocity is found to be in fair agreement with the experimentally measured value.

DLVO surface forces in liquid films and statistical mechanics of colloidal oscillatory structural forces in dispersion stability.

This paper focuses on the theory of the dispersion stability considering two models. In the classical DLVO model of surface forces, the interactions between two particles consist of two terms: the London-van der Waals attractive interaction and the electrostatic repulsive interaction in the frame of the Debye-Hückel theory. The solvent, the aqueous solution of the electrolyte, was considered the continuous phase. The film stability criteria are Pγ > Π and dPγ/dh > 0. Henderson and Lozada-Cassou (HC) applied the statistical mechanics approach to calculate the film free energy to predict the dispersion stability by considering two large hard spheres as colloidal particles immersed in a fluid of dispersed small particles (the solvent). HC applied the radial distribution function g(r) to calculate the free oscillatory structural energy using W(r) = - kT ln g(r). HC's theoretical approach was also applied to the particle collective interactions in the film and explains the stability of film formed from complex fluids (e.g., micellar and colloidal dispersions). The differences between the solvation oscillatory layering forces and colloidal oscillatory structural forces are discussed. The application of the DLVO model to the dispersion stability is critically reviewed. The role of nanobubbles in the dispersion stability is discussed.

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.

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).

Wetting and spreading of nanofluids on solid surfaces driven by the structural disjoining pressure: statics analysis and experiments.

The wetting and spreading of nanofluids composed of liquid suspensions of nanoparticles have significant technological applications. Recent studies have revealed that, compared to the spreading of base liquids without nanoparticles, the spreading of wetting nanofluids on solid surfaces is enhanced by the structural disjoining pressure. Here, we present our experimental observations and the results of the statics analysis based on the augmented Laplace equation (which takes into account the contribution of the structural disjoining pressure) on the effects of the nanoparticle concentration, nanoparticle size, contact angle, and drop size (i.e., the capillary and hydrostatic pressure); we examined the effects on the displacement of the drop-meniscus profile and spontaneous spreading of a nanofluid as a film on a solid surface. Our analyses indicate that a suitable combination of the nanoparticle concentration, nanoparticle size, contact angle, and capillary pressure can result not only in the displacement of the three-phase contact line but also in the spontaneous spreading of the nanofluid as a film on a solid surface. We show here, for the first time, that the complete wetting and spontaneous spreading of the nanofluid as a film driven by the structural disjoining pressure gradient (arising due to the nanoparticle ordering in the confined wedge film) is possible by decreasing the nanoparticle size and the interfacial tension, even at a nonzero equilibrium contact angle. Experiments were conducted on the spreading of a nanofluid composed of 5, 10, 12.5, and 20 vol % silica suspensions of 20 nm (geometric diameter) particles. A drop of canola oil was placed underneath the glass surface surrounded by the nanofluid, and the spreading of the nanofluid was monitored using an advanced optical technique. The effect of an electrolyte, such as sodium chloride, on the nanofluid spreading phenomena was also explored. On the basis of the experimental results, we can conclude that a nanofluid with an effective particle size (including the electrical double layer) of about 40 nm, a low equilibrium contact angle (<3°), and a high effective volume concentration (>30 vol %) is desirable for the dynamic spreading of a nanofluid system with an interfacial tension of 0.5 mN/m. Our experimental observations also validate the major predications of our theoretical analysis.

Methods to monitor water-in-oil film thinning and stability: An application to bitumen demulsification.

Understanding what governs the water-in-oil emulsion film stability and demulsification is important for science and technology. The demulsification of the tar sands' water-in-bitumen emulsion and proposing methods for demulsification with an efficient demulsifier (emulsion breaker) are important but challenging tasks. Despite the long period of time researchers have been examining the factors governing bitumen emulsion stability and demulsification, these concepts are still not well understood and require more study. Due to the lack of suitable robust methods to reveal what governs bitumen emulsion thinning and stability, additional study is needed. The goal of this research is to provide an understanding of the role of the asphaltene-resin nanoparticles on the bitumen film and emulsion stability and to propose a possible solution to the challenges presented. The techniques were developed and applied to monitor the curved and flat bitumen emulsion films' thinning in transmitted and reflected light. The observed plane bitumen emulsion film stepwise thinning in reflected light interferometry reveals the role of the layered-lattice film structural stabilization. The role of the asphaltene-resin structure formation on film stability is discussed and a model is proposed. The data obtained by the techniques help to propose a methodology to optimize the performance of the demulsifier.

Nanoparticle self-structuring in a nanofluid film spreading on a solid surface.

Liquids containing nanoparticles (nanofluids) exhibit different spreading or thinning behaviors on solids than liquids without nanoparticles. Previous experiments and theoretical investigations have demonstrated that the spreading of nanofluids on solid surfaces is enhanced compared to the spreading of base fluids without nanoparticles. However, the mechanisms for the observed enhancement in the spreading of nanofluids on solid substrates are not well understood. The complex nature of the interactions between the particles in the nanofluid and with the solid substrate alters the spreading dynamics [Wasan, D. T.; Nikolov, A. D. Nature 2003, 423, 156]. Here, we report, for the first time, the results of an experimental observation of nanoparticles self-structuring in a nanofluid film formed between an oil drop and a solid surface. Using a silica-nanoparticle aqueous suspension (with a nominal diameter of 19 nm and 10 vol %) and reflected light interferometry, we show the nanoparticle layering (i.e., stratification) phenomenon during film thinning on a smooth hydrophilic glass surface. Our experiments revealed that the film thickness stability on a solid substrate depends on the film size (i.e., the drop size). A film formed from a small drop (with a high capillary pressure) is thicker and contains more particle layers than a film formed from a large drop (with a lower capillary pressure). The data for the film-meniscus contact angle verses film thickness (corresponding to the different number of particle layers) were obtained and used to calculate the film structural energy isotherm. These results may provide a better understanding of the complex phenomena involved in the enhanced spreading of nanofluids on solid surfaces.

How the capillarity and ink-air flow govern the performance of a fountain pen.

As kids, the authors enjoyed learning how to write by dipping nib pens into ink, and then later, using flex nib pens for calligraphy. They remember, less fondly, the troubles with ink leaks and spills over the paper's surface. Despite advances in fountain pen design, the performance of fountain pens is still not perfect. A robust fountain pen has to provide a sustainable ink flow-no leaks-for smooth and precise writing on paper. In the long history of the design and development of fountain pens, more attention has been focused on the ink flow than on the ink/air capillary flow balance. It is found that as ink flows out of the cartridge, the holding pressure in the ink cartridge builds up and the pressure drop across the capillary valve increases. Consequently, the air is sucked toward the ink cartridge. An air-ink meniscus is formed at the capillary valve and finally breaks into air bubbles due to Rayleigh instability. The air bubbles float into the ink cartridge under buoyancy force to reduce the holding pressure so that the ink can continuous flow out to the nib to keep the fountain pen in function. The unbalance between the air holding pressure in the ink cartridge and the pressure drop across the capillary valve is the key for the functionality of the fountain pen. A poor design of the feed/cartridge connection with a small orifice of the capillary valve leads to the malfunction of the fountain pen.

Air bubble bursting phenomenon at the air-water interface monitored by the piezoelectric-acoustic method.

When an air bubble arrives at the free interface, the bubble's lamella drains and ruptures. The bubble collapses, and gas vapor is released. The ruptured lamella retreats, and a rim at the edge of the retreating lamella forms. The rim becomes unstable and breaks into fine droplets, leading to the formation of a mist. As the collapsing bubble gas's vapor is released, the collapsing bubble oscillates and a vertical liquid jet erupts; this jet then breaks into a droplet(s). Here, we present a novel approach for monitoring the air bubble bursting frequency at the air-water interface by the piezoelectric-pressure-acoustic technique. The piezoelectric-acoustic technique monitors the lamella's rupture time, the frequency of the oscillation of the collapsing air bubble, and the frequency of the oscillation at the free air/water interface. The aqueous lamella rupture thickness was probed by reflected light interferometry, and the air bubble burst at the air/water interface was monitored with the high-speed photo imaging technique. The data obtained by the three techniques provided essential information for the stages of the air bubble collapse dynamics at the free interface without the presence of a surfactant. The simple model proposed by Rayleigh, Minnaert, and Lighthill (RML) for the oscillation resonance of a single air bubble was applied to calculate the air bubble collapsing frequency. The floating air bubble bursting frequency with an equatorial radius of 0.33 ±â€¯0.05 cm was well predicted using the air bubble resonance frequency model, and was estimated as 1.0 ±â€¯0.3 kHz. The velocity of the ruptured aqueous lamella covering the air bubble was estimated as 1 m/s. This research presents a comprehensive understanding of the phenomenon of the bare air bubble collapse at the free interface.

Novel approach for calculating the equilibrium foam nanofilm-meniscus contact angle and the film free energy.

The film meniscus is a capillary system that is part of everyday observed phenomena, such as in foams, emulsions, liquid suspensions of nanoparticles (nanofluids), and liquid-wetting solids. The capillarity of a microscopic free foam lamella with a meniscus is important for a fundamental understanding of the role of the surface forces vs. thickness and stability of dispersed systems. The film-meniscus transition region, known as the Gibbs-Plateau border, and macroscopic contact angle, defined by the extrapolated meniscus Laplace surfaces, are the characteristics of capillary systems that reveal how the surface forces contribute to the stability of the dispersed systems. The foam nanofilm formed from a nanofluid due to nanoparticle self-layering under the film surface confinement thins in a multiple regular stepwise manner (not like soap films) above the CMC. The equilibrium thickness of the nanofilm is governed by the film area rather than the capillary pressure, as was reported for common and Newtonian films. Our video clip shows that the nanofilm thins layer by layer as the film area decreases. Our observation reveals that the nanofilm with a small film area remains at the equilibrium thickness with several layers. An iterative method is proposed to locate the film meniscus contact line. The film-meniscus profile of the transition region is examined using the reflected light interferometry and by applying the two radii of curvature. The micro- and macroscopic contact angles between nanofilm and meniscuses are calculated. The foam nanofilm's structural free energy is calculated vs. the number of layers. The knowledge gained from this research will help to improve the understanding of the dispersion stability of foams, emulsions, and liquid suspensions of nanoparticles.

Structure and stability of nanofluid films wetting solids: An overview.

When an air bubble or an oil droplet in a nanofluid (liquid containing dispersed nanoparticles) approaches a solid surface, a nanofluid film is formed between the bubble or drop and a solid substrate. The nanoparticles confined in the film surfaces tend to self-layer and the film thins in a stepwise manner. The wetting behavior and film stability criteria valid for the classical molecularly thin films cannot be applied to nanofilm. Here we present an overview of the structure and stability of multilayer nanofilms wetting solid surfaces. We first present a brief review of the classical concept of molecular films wetting solid, and then we discuss the nanofluid film structure evolution as determined by the in-layer radial distribution function versus nanofilm's number of layers. The role of the particle volume fraction, size and polydispersity on the layering phenomenon is highlighted. The stability of the nanofilm, that is its layer-by-layer thinning is elucidated by the presence of particle voids or dislocations. We calculated the free energy of the nanofilm on a solid surface based on nanofilm osmotic pressure. We independently verified it by the direct measurement of the nanofilm-meniscus contact angle using reflected light interferometry. Finally, we present some practical applications of a wetting aqueous film for oily soil removal from a solid surface and the nanofilm displacing an oil phase from a capillary as in an enhanced oil recovery operation.

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.

Tears of wine: The dance of the droplets.

For a long time, the phenomenon known as the "tears of wine" was believed to be due only to the surface tension gradient (e.g., the Thomson-Marangoni stress on the fluid/fluid surface's dynamics of wetting) and gravity. We experimentally demonstrated that the wine tear formation is not solely due to the surface tension gradient; instead, the ridge instability triggers the wine tears. Pouring wine into a glass causes a wine film to form on the glass. The film drains down under gravity and a ridge forms at its upper part. Over time, the ridge becomes unstable. Under gravity, a necklace of droplets (tears) appears and slides down. Here, we present experimental evidence that the Plateau-Rayleigh-Taylor theory for the stability criterion of a horizontal annulus fluid column under small, exponentially growing capillary disturbances and the surface tension breakdown into droplets can also be applied to the stability of a horizontal fluid's (wine) ridge on a wetted solid, where gravity causes the droplets (tears) to slide down, resulting in the formation of a necklace of droplets ("tears"). The wine droplets ("tears") move down and up ("dance") due to the effects of the surface tension gradient and gravity. The process repeats itself for a while. Over time, the wine components (e.g., organic acids and tannins) adhere on the glass. The glass surface becomes less hydrophilic and the wine wets the glass less. The wine film on the glass becomes unstable, the ridge does not form, and the tears stop appearing. The knowledge gained from the present study will enhance our understanding of the wetting and spreading dynamics of fluid mixtures on solids. It will also benefit our understanding of fundamental phenomena (such as wetting and spreading) and applied technologies (such as painting, printing, cooling, and cleaning), as well as aid in the development of robust devices (such as the lab on a chip).

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.

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.