Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.     

Axisymmetric motion of a pair of deformable heavy drops in an upward temperature gradient

The axisymmetric deformation and motion of interacting droplets under the combined influence of the gravitational force and a vertical temperature gradient is considered using boundary-integral techniques for creeping flow. The focus is on the case when the net thermocapillary and buoyancy forces acting on the drops are directed oppositely. When these forces are almost balanced our analysis shows that, though the deformations of the drops are apparently small, their influence on the motion is considerable. For highly deformable drops moving in a gravity field, even a small temperature gradient that almost does not effect the drops velocity may drastically change the deformation pattern and prevent the drops from breakup.     

高温高压下水与非极性流体间的界面张力

The pendent drop or standing bubble method is applied to measure the interfacial tensions between water and nonpolar fluids (n-hexane, n-heptane, nitrogen, oxygen and methane) up to 473K and 220MPa. The high pressure autoclave with t wo visual windows and the auxiliary equipment are described. The sizes(ca 2mm) and shapes of drops or bubbles are recorded with microscope and video camera. The use of digital image permits fast, precise determination of the contour parameters. The densit y values of the liquids or gases have been chosen from literature. A special program is proposed to calculate the interfacial tensions automatically from drop shape at given temperature and pressure. The interfacial tensions σ12 increase with pr essure for the two liquid-liquid systems, but decrease with pressure for the three gas-liquid systems.     

Coalescence in foams and emulsions: Similarities and differences

Coalescence in emulsions and foams is far from being understood, despite many years of investigations. The phenomenon is not easy to be characterized because it is extremely rapid and coupled to several others, gravity effects, leading to vertical motion of drops/bubbles and ripening, leading to their growth. Coalescence implies the rupture of films between drops/bubbles and involves contributions from hydrodynamics, surface rheology, surface forces, and thermal fluctuations. Different coalescence scenarios were identified and are described. There are close similarities between emulsion and foam behavior, as remarked earlier by several researchers. Ivan Ivanov, to whom this article is dedicated, was one of them. He and his group pioneered parallel studies in both emulsions and foams, aiming to clarify coalescence mechanisms. As discussed in this review, such an approach proved very successful and deserves to be continued in the future.     

The thermocapillary migrations of two bubbles in microgravity environment

The thermocapillary motion of two bubbles along their line of centers in a uniform temperature gradient is investigated theoretically. The bubbles are moving in the direction of the temperature gradient. And the interaction between the leading bubble and the trailing one becomes significant as the separation distance between them is decreased greatly so that the bubble interaction is considered in this case. The appropriate equations of momentum and energy are solved using the method of reflections. In order to proceed analytically, sets of transformations between two coordinates are obtained. By using these transformations and the reflection process, accurate migration velocities of these two bubbles in the microgravity environment are derived for the limit of small Marangoni and Reynolds numbers. These results are employed to describe the thermocapillary motion of two bubbles and to estimate the effects of bubble size and the thermal gradient on the interaction between two bubbles. All of our results for the migration of the two bubbles demonstrate that the approach of the second bubble to the first one intensifies the mutual interaction between these two bubbles and yields some interesting thermocapillary motions.     

Buoyancy-driven coalescence of spherical drops covered with incompressible surfactant at arbitrary Péclet number

Collision efficiencies are determined for two surfactant-covered spherical drops in the limits of nearly uniform surface coverage and bulk insolubility for Brownian and/or gravitational motion as a function of drop-size ratio, drop-to-medium viscosity ratio, and retardation parameter. For two equal-sized drops in Brownian motion in the limit of small viscosity ratio, the calculated collision efficiencies agree well with earlier results for bubbles. While the two-sphere relative mobility functions for motion parallel to the drops' line of centers tend to the same values in the limits of infinite viscosity ratio and infinite retardation parameter, the asymmetric mobility functions do not, because the coefficients for the rotational term in Lamb's singular solution are independent of the presence of surfactant. The complex dependence of the transverse mobility functions on the viscosity ratio and retardation parameter makes it possible for the gravitational collision efficiency to increase slightly with viscosity ratio at fixed size ratio and retardation parameter of O(10(3)) or larger. Typical hydrosols are also studied in gravitational motion at arbitrary Péclet number, showing the combined influence of Brownian and gravitational motion.     

Thermocapillary Alignment of Gas Bubbles Induced by Convective Transport

The effect of a weak convective heat transfer on the thermocapillary interaction of two bubbles with an arbitrary orientation relative to an externally imposed temperature gradient is examined. Asymptotic analysis of the case of large separation distances, Z, suggests that the corrections to the bubbles' velocities are of (Pe/Z²), rather than (Pe²) previously found for an isolated bubble. Equal-sized bubbles are known to move with the same velocities, as if they were isolated, when heat conduction is the only transport mechanism. However, the convective transport results in a relative motion of the bubbles. The tendency of equal bubbles to line up in a plane perpendicular to the applied thermal gradient is shown analytically in the weakly nonlinear limit of small Pe numbers, and an interesting interaction behavior in the case of unequal bubbles is discussed.     

Rolled‐Up Monolayer Graphene Tubular Micromotors: Enhanced Performance and Antibacterial Property

The motion of catalytic tubular micromotors are driven by the oxygen bubbles generated from chemical reaction and is influenced by the resistance from the liquid environment. Herein, we fabricated a rolled‐up graphene tubular micromotor, in which the graphene layer was adopted as the outmost surface. Due to the hydrophobic property of the graphene layer, the fabricated micromotor performed a motion pattern that could escape from the attraction from the bubbles. In addition, Escherichia coli and Staphylococcus culture experiments proved that the graphene outer surface displays antibacterial property. Considering the bubble‐avoiding and antibacterial properties, the rolled‐up graphene tubular micromotor holds great potential for various applications such as in vivo drug delivery and biosensors.     

Breakup of a Multiple Emulsion Drop in a Uniform Electric Field

The steady deformation and breakup of emulsion drops in a uniform electric field are considered experimentally. Due to the low volume fraction of inner drops, the emulsions can be effectively assumed as Newtonian fluids with spatial nonuniformity. The measurements of the electrical properties show that the oil-in-water (o/w) emulsion drop behaves like a conducting drop. On the other hand, the water-in-oil (w/o) emulsion drops can be regarded as inhomogeneous leaky dielectric drops. It is found that the viscosity ratio is not an important parameter within the small deformation limit and breakup mode of the o/w emulsion drops. In the case of w/o emulsion drops, however, the breakup mode depends on the viscosity ratio. Inherent nonuniformity of the emulsion drops makes drop more deformable and unstable. The tip-streaming is the dominant breakup mode of o/w emulsion drops when the nonuniformity of drop phase is appreciable. Copyright 1999 Academic Press.     

Synthetic-based aphrons: Correlation between properties and filtrate reduction performance

Aphrons fluids, because of their “noninvasive” characteristic, are indicated for drilling zones that have multiple intercalations of depleted formations adjacent to formations that require high-density fluids. Aphrons are colloidal dispersions containing microbubbles, with cores of gas, liquid or emulsion ranging from 10 to 100 μm in diameter, that are highly stable due to their high interfacial area and multiple surrounding surfactant layers. This paper presents results of physical–chemical properties, bubble size distribution and filtration of systems containing microbubbles. The aphrons were generated by applying a pressure differential under a high-pressure high-temperature (HPHT) filtration cell. Tests were also run with different types of surfactants, specific for generation of bubbles in an organic medium (ester). The surfactants were analyzed for their surface tension and the dispersions produced were photographed under an optical microscope at 60× magnification. The images obtained were digitized to enable determination of the bubble size distribution using an ImageJ program. The filtrate reduction performance of these fluids was determined by static filtration in synthetic porous media. There was a correlation between the filtration characteristics of the fluids, the bubble size distribution and number of bubbles produced in each base and for each surfactant tested. The results obtained served as a reference to formulate a light, non-water-based drilling fluid containing microbubbles with “noninvasive” characteristics.     

Chemically Powered Micro‐ and Nanomotors

Chemically powered micro‐ and nanomotors are small devices that are self‐propelled by catalytic reactions in fluids. Taking inspiration from biomotors, scientists are aiming to find the best architecture for self‐propulsion, understand the mechanisms of motion, and develop accurate control over the motion. Remotely guided nanomotors can transport cargo to desired targets, drill into biomaterials, sense their environment, mix or pump fluids, and clean polluted water. This Review summarizes the major advances in the growing field of catalytic nanomotors, which started ten years ago.     

Integrating ultrafast and stochastic dynamics studies of Brownian motion in molecular systems and colloidal particles

Ultrafast spectroscopy and stochastic dynamics studies of chemical dynamics in solution with high resolution in both space and time have been undertaken for many years, but it is still challenging to connect fundamental knowledge obtained from stroboscopic approaches at ultrashort timescales and small length scales with that obtained by directly measuring individual particle motion at longer timescales. Therefore, it is interesting, conceptually and experimentally, to understand the similarities and differences between these two approaches to the study of chemical dynamics in condensed phase systems. We discuss recent advances in the understanding of the transition from ballistic to diffusive motion and chemical reaction rate theories and describe the significance of the findings in relation to the study of thermally activated processes at multiple time and length scales.     

Self-propulsion on liquid surfaces

Surface tension gradients are at the origin of the self-motion and deformation of millimeter-sized floating objects. For (quasi-)non-deformable systems, like solids and gels, the motion-mode is mainly controlled by the shape of the object and by the way the surface active propellant is released on the surrounding surface. Two situations are reviewed. In the first one, the propellant container is the propelled object itself, while in the second case the propellant is placed in a reservoir embarked on a manufactured float. The properties and efficiency of these solid systems are examined and compared for different geometries. They are also compared with the intriguing properties of self-motile liquid lenses/drops which present several additional abilities (spontaneous deformation to adapt their shape to the selected motion-mode, presence of complex fluid flows outside and inside the drops, partial break-ups…). Three mechanisms leading to spontaneous motility have been identified in the literature. Among them two are more largely exemplified in the following as they involve a contribution of the “Marangoni driven spreading” effect, leading to velocities on the cm/s scale. The main theoretical tools usually used for describing the motion and deformation of such self-propelled systems are also reviewed.     

Mixing enhancement for high viscous fluids in a microfluidic chamber

Due to small channel dimensions and laminar flows, mixing in microfluidic systems is always a challenging task, especially for high viscous fluids. Here we report a method of enhancing microfluidic mixing for high viscous fluids using acoustically induced bubbles. The bubbles can be generated in an acoustically profiled microfluidic structure by using a piezoelectric disk activated at a working frequency range between 1.5 kHz and 2 kHz. The mixing enhancement is achieved through interactions between the oscillating bubbles and fluids. Both experimental studies and numerical simulations are conducted. In the experiments, DI water-glycerol mixture solutions with various viscosities were used. The results, based on the mixing efficiency calculated from experimentally acquired fluorescent images, showed that good mixing can occur in the DI water-glycerol solutions with their maximum viscosity up to 44.75 mPa s, which to our best knowledge is the highest viscosity of fluids in microfluidic mixing experiments. To explain the mechanisms of bubble generation, the numerical simulation results show that, corresponding to the actuations at the working frequency range used in the experiment, there exists a low pressure region where the pressure is lower than the water vapor pressure in the DI water-glycerol solutions, resulting in the generation of bubbles.     

Spectral Properties of Foams and Emulsions

The optical and spectral properties of foams and emulsions provide information about their micro-/nanostructures, chemical and time stability and molecular data of their components. Foams and emulsions are collections of different kinds of bubbles or drops with particular properties. A summary of various surfactant and emulsifier types is performed here, as well as an overview of methods for producing foams and emulsions. Absorption, reflectance, and vibrational spectroscopy (Fourier Transform Infrared spectroscopy-FTIR, Raman spectroscopy) studies are detailed in connection with the spectral characterization techniques of colloidal systems. Diffusing Wave Spectroscopy (DWS) data for foams and emulsions are likewise introduced. The utility of spectroscopic approaches has grown as processing power and analysis capabilities have improved. In addition, lasers offer advantages due to the specific properties of the emitted beams which allow focusing on very small volumes and enable accurate, fast, and high spatial resolution sample characterization. Emulsions and foams provide exceptional sensitive bases for measuring low concentrations of molecules down to the level of traces using spectroscopy techniques, thus opening new horizons in microfluidics.     

Effect of Surfactants on the Film Drainage

Drainage of a partially mobile thin liquid film between two deformed and nondeformed gas bubbles with different radii is studied. The lubrication approximation is used to obtain the influence of soluble and insoluble surfactants on the velocity of film thinning in the case of quasi-steady state approach. The material properties of the interfaces (surface viscosity, Gibbs elasticity, surface diffusivity, and/or bulk diffusivity) are taken into account. In the case of deformed bubbles the influence of the meniscus is illustrated assuming simple approximated shape for the local film thickness. Simple analytical solutions for large and small values of the interfacial viscosity, and for deformed and nondeformed bubbles, are derived. The correctness of the boundary conditions used in the literature is discussed. The numerical analysis of the governing equation shows the region of transition from partially mobile to immobile interfaces. Quantitative explanation of the following effects is proposed: (i) increase of the mobility due to increasing bulk and surface diffusivities; (ii) role of the surface viscosity, comparable to that of the Gibbs elasticity; and (iii) significant influence of the meniscus on the film drainage due to the increased hydrodynamic resistance. Copyright 1999 Academic Press.     

Evaluation of translational friction coefficients of macroscopic probes in nematic liquid crystals

We present a study of the translational friction coefficients of spherical and ellipsoidal probes in nematic liquid crystalline fluids, based on the numerical treatment of Leslie-Ericksen equations [Q. J. Mech. Appl. Math. 19, 357 (1966); Adv. Liq. Cryst. 4, (1979); Trans. Soc. Rheol. 5, 23 (1961); Adv. Liq. Cryst. 2, 233 (1976)] for incompressible nematic fluids. Simulations of director dynamics in a local environment surrounding the moving probe are presented, and the dependence of translational diffusion on liquid crystal viscoelastic parameters is discussed. The time evolution of the director field is studied in the presence of an orienting magnetic field in two characteristic situations: Directors of motion parallel and perpendicular with respect to the field. In the particular case under investigation, a detailed analysis is given for the case of spherical, prolate, and oblate ellipsoidal probes in rectilinear motion in nematic (4-methoxibenzylidene-4'-n-butylaniline), together with a comparison with other nematogens, namely, 4,4'-dimethoxuazoxy benzene and (4'-n-pentyl-4-cyanobiphenil). A discussion of the general methodology presented in this work is given for the case of colloidal dispersions in nematic liquid crystals, which are considered as model systems of dispersions of particles in host media with anisotropic physical properties.     

Bubble entrainment with drops

The study reported here was undertaken because recent research on nucleate boiling has implicated vapor entrainment by drops as a mechanism for vapor bubble nucleation. The mechanism has been called secondary nucleation. The purpose of this research was to determine the behavior of entrained air bubbles when a drop of liquid strikes a liquid surface. A liquid drop striking the surface of a pool of the same liquid was found usually to entrain large numbers of small air bubbles. Some of these bubbles are frequently carried rapidly deep into the pool by a vortex ring but many can be deposited in a trail or left floating on the surface. Air bubble entrainment was observed with water and several organic liquids and some differences were noted. Drops with diameters from 200 μm to 4 mm were studied. Sometimes hundreds of bubbles were entrained some with diameters up to 100 μm. These results lend support to the secondary nucleation hypothesis and indicate further research on vapor bubble entrainment under conditions more typical of boiling would be appropriate.     

Motion and dissolution of drops of sparingly soluble alcohols on water

The dissolution of liquids with low mutual solubility is typically slow. However, drops of sparingly soluble, low-density, low-surface-tension liquids often dissolve rapidly on water due to surface tension instabilities and gradients. We report observations of the motion and dissolution of drops of aliphatic alcohols of a wide range of alkyl chain lengths as they dissolve in water. The alcohol drops are rendered visible by adding small amounts of iodine or other dyes. These drops display dewetting instabilities, fragmentation, fingering, and oscillation. As the length of the alcohol carbon chain increases from n = 4 to n = 9, dissolution slows dramatically. The roles of alcohol solubility and water surface area in promoting rapid dissolution are discussed.     

Spreading kinetics of water drops on self-assembled monolayers of thiols: significance of inertial effects

Spreading of 5-15 microL water drops on self-assembled monolayers of 1-hexadecanethiol and 11-mercapto-1-undecanol, both homogeneous and mixed compositions, formed on gold-coated silicon wafers or glass slides was recorded with a high-speed video camera. The time (t) evolution of the drop base diameter (D) during spreading was analyzed by a power law-correlation: D approximately t(n). The n value was found to increase from n = 0.3-0.5 for water drops on hydrophobic surfaces characterized by the advancing water contact angle of thetaA = 94-104 degrees to n = 0.5-0.8 on less hydrophobic surfaces (thetaA = 45-66 degrees ). These experimental values were found to be of similar magnitude as the literature values reported for small drops and bubbles, which spread over a variety of different substrates including water and water-ethanol drops on self-assembled monolayers of alkylsilanes, air bubbles in water on glass, molten metals on solid metals and ceramics, hydrocarbon drops on water, and others. Inertial effects, which are often not accounted for in the analysis of spreading results, appear to have an impact on the spreading kinetics of small drops in at least the first few milliseconds of the spreading phenomenon.