Direct measurement of hydrophobic particle–bubble interactions in aqueous solutions by atomic force microscopy: Effect of particle hydrophobicity

Direct measurements of the interaction forces between a spherical silica particle and a small air bubble have been conducted in aqueous electrolyte solutions by using an atomic force microscope (AFM). The silica particle was hydrophobized with a silanating reagent, and the interaction forces were measured by using several particles with different surface hydrophobicities. In the measured force curves, a repulsive force was observed at large separation distances as the particle moved towards the bubble. The origin of the repulsive force was attributed to an electrostatic double-layer force because both the particle and bubble were negatively charged. After the repulsive force, an extremely long-range attractive force acted between the surfaces. These results indicate that the intervening thin water film between the particle and bubble rapidly collapsed, resulting in the particle penetrating the bubble.

The instability of the thin water film between the surfaces suggests the existence of an additional attractive force. By comparing the repulsive forces of the obtained force curves with the DLVO theory, the rupture thickness was estimated. The hydrophobicity of the particle did not significantly change the rupture thickness, whereas the pH of the solution is considered to be a critical factor.     

Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

We describe here a new procedure for the simultaneous investigation of sedimentation and diffusion of a colloidal particle in close proximity to a solid, planar wall. The measurements were made using the optical technique of total internal reflection microscopy, coupled with optical radiation pressure, for dimensionless separation distances (gap width/radius of particle) ranging from 0.01 to 0.05. In this region, the hydrodynamic mobility and diffusion coefficient are substantially reduced below bulk values. The procedure involved measuring the mean and the variance of vertical displacements of a Brownian particle settling under gravity toward the plate. The spatially varying diffusion coefficient was calculated from the displacements at small times (where diffusive motion was dominant). The mobility relationship for motion normal to a flat plate was tested by measuring the average distance of travel versus time as the particle settled under the constant force of gravity. For the simple Newtonian fluid used here (aqueous salt solution), the magnitude of the diffusion coefficient and mobility, plus their dependence on separation distance, showed excellent agreement with predictions. This new technique could be of great value in measuring the mobility and diffusion coefficient for near-contact motion in more complex fluids for which the hydrodynamic correction factors are not known a priori, such as shear-thinning fluids.     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

Sedimentation of spheres at small Reynolds number

The effect of fluid inertia on the settling of spheres in a viscous incompressible fluid is studied in the limit of small Reynolds number. The kinetic energy of flow depends on the positions of the spheres, and gives rise to forces on the spheres. In the dilute limit it suffices to study the corresponding pair interaction. The interaction is calculated from the Stokes flow for two spheres settling between plane walls in the point particle limit. The dissipative interaction between a pair of spheres is calculated from the Proudman-Pearson [I. Proudman and J. R. A. Pearson, J. Fluid Mech. 2, 237 (1957)] solution of the Navier-Stokes equations for flow about a sphere in unbounded geometry. The combination of kinetic and dissipative interaction gives rise to a repulsive force of range of the order of the sphere diameter divided by the Reynolds number.     

Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of B-particles. This "depletion bubble" mechanism explains and predicts a brazil-nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetuous mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.     

Direct measurement of interactions between stimulation-responsive drug delivery vehicles and artificial mucin layers by colloid probe atomic force microscopy

A novel thermo- and pH-sensitive nanogel particle, which is a core-shell structured particle with a poly(N-isopropylacrylamide) (p(NIPAAm)) hydrogel core and a poly(ethylene glycol) monomethacrylate grafted poly(methacrylic acid) (p(MMA-g-EG)) shell, is of interest as a vehicle for the controlled release of peptide drugs. The interactions between such nanogel particles and artificial mucin layers during both approach and separation were successfully measured by using colloid probe atomic force microscopy (AFM) under various compression forces, scan velocities, and pH values. While the magnitudes of the compression forces and scan velocities did not affect the interactions during the approach process, the adhesive force during the separation process increased with these parameters. The pH values significantly influenced the interactions between the nanogel particles and a mucin layer. A large steric repulsive force and a long-range adhesive force were measured at neutral pH due to the swollen p(MMA-g-EG) shell. On the other hand, at low pH values, the steric repulsive force disappeared and a short-range adhesive force was detected, which resulted from the collapse of the shell layer. The nanogel particles possessed a pH response that was sufficient to protect the incorporated peptide drug under the harsh acidic conditions in the stomach and to effectively adhere to the mucin layer of the small intestine, where the pH is neutral. The relationships among the nanogel particle-mucin layer interactions, pH conditions, scan velocities, and compression forces were systemically investigated and discussed.     

Synergistic effects of polymers and surfactants on depletion forces

This work investigates the synergistic effects of a neutral polymer and an anionic surfactant on depletion forces as a function of bulk polymer and bulk surfactant concentration. In this work, we measure the force between a silica particle and a silica plate in aqueous solutions of the polymer and the surfactant using atomic force microscopy. The polymer is the triblock copolymer poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) (Pluronic F108), and the surfactant is sodium dodecyl sulfate (SDS). In F108-only solutions, the force between the silica particle and the silica plate is primarily repulsive for polymer concentrations ranging from 200 to 10 000 ppm. In SDS-only solutions, the net force between the silica surfaces is repulsive at all separations for concentrations below 16 mM SDS and is attractive with a structural force character above 16 mM SDS. When both F108 and SDS are present in the solution, a net attractive force is observed at SDS concentrations as low as 4 mM, a factor of 2 below the critical micelle concentration (cmc). We attribute this synergistic effect to the complexation of F108 with SDS in bulk solution at a critical aggregation concentration (cac) that is less than the cmc, producing a relatively large, charged complex that creates a significant depletion force between the particle and plate.     

Surfactant-induced forces between carbon nanotubes

Dissipative particle dynamics simulations are employed to study surfactant-mediated forces between a pair of perpendicular carbon nanotubes (CNTs) coated by surfactants which form spherical micelles in bulk solution and on the tubes. Two force regimes are observed: at small tube/tube distances the force is attractive, whereas it is repulsive at larger distances. The attractive regime is dominated by a central micelle binding the tubes, while in the repulsive regime the contact region is depleted. The two regimes are separated by a discontinuous transition. The repulsive regime is critical for stabilizing CNT suspensions. Viewing rebundling as a thermally activated process, a connection between the repulsive force and the rebundling rate is established. We find that a larger hydrophilic surfactant headgroup creates a stronger and longer ranged tube/tube force, which reduces the rebundling rate significantly. The longer range originates directly from the further reaching head corona of the adsorbed surfactant layer. The larger magnitude of the force appears to be related to the axial compression force the adsorbed phase can sustain. This compression force appears to be the most critical factor for suspension design.     

On the effect of induced electro-osmosis on a cylindrical particle next to a surface

The effect of induced electro-osmosis on a cylindrical particle positioned next to a planar surface (wall) is studied theoretically both under the thin double layer approximation utilizing the Smoluchowski slip velocity approximation and under thick electric double layer conditions by solving the Poisson-Nernst-Planck (PNP) equations. The imposed, undisturbed electric field is parallel to the planar surface. The induced hydrodynamic and electrostatic forces are calculated as functions of the particle's and the medium's dielectric constants and the distance between the particle and the surface. The resultant force acting on the particle is directed normal to and away from the wall. The presence of such a repulsive force may adversely affect the interactions between macromolecules suspended in solution and wall-immobilized molecules and may be significant to near-wall particle imaging velocimetry (PIV) in electrokinetic flows.     

重力对溶液悬浮粒子聚集过程影响的布朗动力学模拟

采用布朗动力学的计算机模拟方法, 研究重力因素对于稀溶液中悬浮粒子聚集过程的影响. 通过在计算机模拟程序中加入和排除重力因素的影响, 对不同重力条件下的粒子团数量随时间的变化曲线进行对比研究, 得到了重力对溶液中的粒子团总数和不同大小的粒子团数量随时间变化的影响规律,可以总结为: 在聚集阶段初期,重力不影响粒子的聚集; 而在聚集阶段后期, 重力加快了粒子的聚集. 同时, 从动力学分析的角度出发, 对重力如何影响悬浮溶液中粒子聚集过程的机制也进行了更加深入的探讨.     

Size segregation in a fluid-like or gel-like suspension settling under gravity or in a centrifuge

We investigate size segregation effects in a bidisperse concentrated suspension when slowly settling under gravity or when submitted to a centrifugal field. Experiments are carried out with PMMA spheres of two different mean diameters (190 and 25 microm) suspended in a hydrophobic index-matched fluid. Spatial repartitions of both small and large spheres and velocity fluctuations of particles are measured using fluorescently labeled PMMA spheres and a particle-image-velocimetry method. Large particles behave as hard spheres in purely hydrodynamic interactions, while small spheres interact through weakly attractive forces. For a small amount of small spheres among large ones, the suspension remains fluid during settling and the organization of the velocity field of particles into finite-sized structures also called "blobs" promotes size segregation. A larger proportion of weakly attractive small spheres in the bidisperse suspension causes a considerable slowdown of the settling process under gravity and the occurrence of a large-scale collective behavior together with a loss of size segregation. When centrifuging the gel-like bidisperse suspension, a shear-induced melting of the particle network induces a spectacular segregation of species. As a consequence, aging tests of soft yielding materials using centrifugation methods are not representative of the shelf-life stability of the products. A tentative model based on the competition between viscous stresses acting upon particles and adhesive stresses gives a correct estimate of the critical stationary acceleration for the destabilization of the particle network and the onset of size segregation in a gel-like suspension.     

Electrostatic Interaction and Partitioning of Ion-Penetrable Spheres

Electrostatic interaction between two ion-penetrable spheres near a horizontal plate or in a slit pore is investigated theoretically. The orientation of the line connecting the two particle centers can be arbitrary relative to the plate(s). The electrostatic interaction energy and force on each particle are obtained analytically by the method of images. Emphasis is placed on the effect of the presence of the second particle, compared to the case of a single particle or the case without any plate(s). It is found that the horizontal electrical force on each particle is always repulsive. This repulsive force is enhanced by the plate(s) of constant surface charge density, while it is reduced by the plate(s) of constant surface potential. The electrostatic interaction together with the steric effect is used to determine the partition coefficient for the case of a slit pore, correct to O(C(infinity)), where C(infinity) is the volume fraction of particles in the bulk solution. The positive correction coefficient is larger for conducting plates than for insulating plates. Copyright 2001 Academic Press.     

Experimental observations of the hydrodynamic behavior of solvent systems in high-speed counter-current chromatography. III. Effects of physical properties of the solvent systems and operating temperature on the distribution of two-phase solvent systems

Statistical studies were made to correlate the hydrodynamic behavior of two-phase solvent system in counter-current chromatography (CCC) to their physical properties including interfacial tension, viscosity, and the difference in density of the two phases. Settling time measured under unit gravity provided a reliable numerical index for the hydrodynamic behavior of the solvent systems in a centrifugal force field. Viscosity and settling time were strongly correlated (correlation coefficient, r = +0.88) while interfacial tension (r = -0.65) and phase density difference (r = -0.45) showed moderate and weak correlation, respectively. Studies of the effect of temperature on settling time as well as a preliminary apparatus operated at higher temperature show that raising the temperature will improve the performance of high-speed CCC.     

Influence of DNA adsorption and DNA/cationic surfactant coadsorption on the interaction forces between hydrophobic surfaces

The forces between hydrophobic surfaces with physisorbed DNA are markedly and irreversibly altered by exposure to DNA/cetyltrimethylammonium bromide (CTAB) mixtures. In this colloidal probe atomic force microscopy study of the interactions between a hydrophobic polystyrene particle and an octadecyltrimethylethoxysilane-modified mica surface in sodium bromide solutions, we measure distinct changes in colloidal forces depending on the existence and state of an adsorbed layer of DNA or CTAB-DNA complexes. For bare hydrophobic surfaces, a monotonically attractive approach curve and very large adhesion are observed. When DNA is adsorbed at low bulk concentrations, a long-range repulsive force dominates the approach, but on retraction some adhesion persists and DNA bridging is clearly observed. When the DNA solution is replaced with a CTAB-DNA mixture at relative low CTAB concentration, the length scale of the repulsive force decreases, the adhesion due to hydrophobic interactions greatly decreases, and bridging events disappear. Finally, when the surface is rinsed with NaBr solution, the length scale of the repulsive interaction increases modestly, and only a very tiny adhesion remains. These pronounced changes in the force behavior are consistent with CTAB-induced DNA compaction accompanied by increased DNA adsorption, both of which are partially irreversible.     

Stimulant sensitive flocculation and consolidation for improved solid/liquid separation

A novel method of flocculation resulting in both rapid sedimentation and low sediment moisture is described. It relies on changing the inter-particle forces from repulsive to attractive (aggregation and fast settling results) and then back to repulsive (densification of sediment then occurs). The change in inter-particle force is controlled by a stimulus such as pH or temperature. The technique is demonstrated without polymer using the isoelectric point and pH as the stimulus. The polyelectrolyte chitosan produces faster sedimentation and clearer supernatants as a pH sensitive flocculant. Methylcellulose is an effective temperature sensitive flocculant. The sediment bed volumes can be reduced by between 10 and 45% depending upon the conditions which, as yet, have not been fully optimized.     

Effect of pH and hydration on the normal and lateral interaction forces between alumina surfaces

Interaction forces between alumina surfaces were measured using an AFM-colloid probe method at different pHs. For an alpha-alumina-sapphire system at acidic pH, the force curve exhibited a well-defined repulsive barrier and an attractive minimum. At basic pH, the interactive force was repulsive at all separations with no primary minimum. Lateral force measurements under the same conditions showed that frictional forces were nearly an order of magnitude smaller at basic pH than those observed at acidic pH. This behavior was attributed to the hydration of the alumina surface. Normal and lateral force measurements with the strongly hydrated rho-alumina surfaces supported these findings.     

The utility of Bacillus subtilis as a bioflocculant for fine coal

The application of Bacillus subtilis as a flocculant for fine coal has been reported here. Zeta-potential measurements showed that both the coal and bacteria had similar surface charge as a function of pH. Surface free energy calculations showed that the coal was hydrophobic while the bacterium was hydrophilic. The adhesion of the bacteria to coal and subsequent settling was studied in detail. Adhesion of bacteria to coal surface and subsequent settling of coal was found to be quick. Both adhesion and settling were found to be independent of pH, which makes the process very attractive for field applications. The presence of an electrolyte along with the bacterium was found to not only enhance adhesion of bacteria, but also produce a clear supernatant. Further, the settled fraction was more compact than with bacteria alone. Interaction energy calculations using the extended DLVO theory showed that the electrical forces along with the acid–base interaction energy play a dominant role in the lower pH range. Above pH 7, the acid–base interaction energy is the predominant attractive force and is sufficient enough to overcome the repulsive forces due to electrical charges to bring about adhesion and thus settling of fine coal. With increase in electrolyte concentration, the change in total interaction energy with pH is minimal which probably leads to better adhesion and hence settling.     

Dynamic and static interactions between bitumen droplets in water

In the commercial bitumen extraction operation, dynamic and static interaction forces between bitumen drops in water determine the likelihood of desirable bitumen coalescence at different process stages. These dynamic and static forces were measured using colloidal particle scattering and hydrodynamic force balance techniques, respectively. In the former technique, dynamic interactions are studied through droplet-droplet collision trajectory measurement. In the latter technique, the static attractive forces between droplets are determined when a doublet is separated with a known and adjustable hydrodynamic force. The dynamic force measurement implies the presence of rigid chains on bitumen surfaces. The mean chain lengths for deasphalted bitumen at pH 7, whole bitumen at pH 7, and whole bitumen at pH 8.5 are 50, 78, and 41 nm, respectively. However, the static force measurement indicates much shorter mean chain lengths (<9 nm) in these three bitumen systems. Shorter chain length indicates weaker repulsive force. This finding of a much weaker repulsion between bitumen droplets under static conditions has important implications on the commercial bitumen extraction operation.     

Dielectrophoretic levitation in the presence of shear flow: implications for colloidal fouling of filtration membranes

The ability of dielectrophoretic (DEP) forces created using a microelectrode array to levitate particles in a colloidal suspension is studied experimentally and theoretically. The experimental system employs microfabricated electrode arrays on a glass substrate to apply repulsive DEP forces on polystyrene latex particles suspended in an aqueous medium. A numerical model based on the convection-diffusion-migration equation is presented to calculate the concentration distribution of colloidal particles in shear flow under the influence of a repulsive DEP force field. The results obtained from the numerical simulations are compared against trajectory analysis results and experimental data. The results indicate that by incorporating ac electric field-induced DEP forces in a shear flow, particle accumulation and deposition on the flow channel surfaces can be significantly reduced or even completely averted. The mathematical model is then used to indicate how the deposition behavior is modified in the presence of a permeable substrate, representative of tangential flow membrane filtration operations. The results indicate that the repulsive dielectrophoretic (DEP) forces imparted to the particles suspended in the feed can be employed to mitigate membrane fouling in a cross-flow filtration process.     

Mechanism of hydrodynamic separation of biological objects in microchannel devices

In this study, the separation mechanism employed in hydrodynamic chromatography in microchannel devices is analyzed. The main purpose of this work is to provide a methodology to develop a predictive model for hydrodynamic chromatography for biological macromolecules in microchannels and to assess the importance of various phenomenological coefficients. A theoretical model for the hydrodynamic chromatography of particles in a microchannel is investigated herein. A fully developed concentration profile for non-reactive particles in a microchannel was obtained to elucidate the hydrodynamic chromatography of these particles. The external forces acting on the particles considered in this model include the van der Waals attractive force, double-layer force as well as the gravitational force. The surface forces, such as van der Waals attractive force as well as the double-layer repulsive force, can either enhance or hinder the average velocity of the macromolecular particles. The average velocity of the particles decreases with the molecular radius because the van der Waals attractive force increases the concentration of the particles near the channel surface, which is the low-velocity region. The transport velocity of the particles is dominated by the gravity and the higher density enlarges the effect caused by gravity.