Measurement and analysis of forces in bubble and droplet systems using AFM

The use of atomic force microscopy to measure and understand the interactions between deformable colloids - particularly bubbles and drops - has grown to prominence over the last decade. Insight into surface and structural forces, hydrodynamic drainage and coalescence events has been obtained, aiding in the understanding of emulsions, foams and other soft matter systems. This article provides information on experimental techniques and considerations unique to performing such measurements. The theoretical modelling frameworks which have proven crucial to quantitative analysis are presented briefly, along with a summary of the most significant results from drop and bubble AFM measurements. The advantages and limitations of such measurements are noted in the context of other experimental force measurement techniques.     

Elastic deformation during dynamic force measurements in viscous fluids

Understanding and harnessing the coupling between lubrication pressure and elasticity provides materials design strategies for applications such as adhesives, coatings, microsensors, and biomaterials. Elastic deformation of compliant solids caused by viscous forces can also occur during dynamic force measurements in instruments such as the surface forces apparatus (SFA) or the atomic force microscope (AFM). We briefly review hydrodynamic interactions in the presence of soft, deformable interfaces in the lubrication limit. More specifically, we consider the scenario of two surfaces approaching each other in a viscous fluid where one or both surfaces is deformable, which is also relevant to many force measurement systems. In this article the basic theoretical background of the elastohydrodynamic problem is detailed, followed by a discussion of experimental validation and considerations, especially for the role of elastic deformation on surface forces measurements. Finally, current challenges to our understanding of soft hydrodynamic interactions, such as the consideration of substrate layering, poroelasticity, viscoelasticity, surface heterogeneity, as well as their implications are discussed.     

Measurement and modeling on hydrodynamic forces and deformation of an air bubble approaching a solid sphere in liquids

The interaction between bubbles and solid surfaces is central to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. A main challenge is to accurately and reliably control the relative motion over a wide range of hydrodynamic conditions and at the same time to determine the interaction forces, bubble–solid separation and bubble deformation. Existing experimental methods are able to focus only on one of the aspects of this problem, mostly for bubbles and particles with characteristic dimensions either below 100 μm or above 1 cm. As a result, either the interfacial deformations are measured directly with the forces being inferred from a model, or the forces are measured directly with the deformations to be deduced from the theory. The recently developed integrated thin film drainage apparatus (ITFDA) filled the gap of intermediate bubble/particle size ranges that are commonly encountered in mineral and oil recovery applications. Equipped with side-view digital cameras along with a bimorph cantilever as force sensor and speaker diaphragm as the driver for bubble to approach a solid sphere, the ITFDA has the capacity to measure simultaneously and independently the forces and interfacial deformations as a bubble approaches a solid sphere in a liquid. Coupled with the thin liquid film drainage modeling, the ITFDA measurement allows the critical role of surface tension, fluid viscosity and bubble approach speed in determining bubble deformation (profile) and hydrodynamic forces to be elucidated. Here we compare the available methods of studying bubble–solid interactions and demonstrate unique features and advantages of the ITFDA for measuring both forces and bubble deformations in systems of Reynolds numbers as high as 10. The consistency and accuracy of such measurement are tested against the well established Stokes–Reynolds–Young–Laplace model. The potential to use the design principles of the ITFDA for fundamental and developmental research is demonstrated.     

Measurement of dynamical forces between deformable drops using the atomic force microscope. I. Theory

Recent experimental developments have enabled the measurement of dynamical forces between two moving liquid drops in solution using an atomic force microscope (AFM). The drop sizes, interfacial tension, and approach velocities used in the experiments are in a regime where surface forces, hydrodynamics, and drop deformation are all significant. A detailed theoretical model of the experimental setup which accounts for surface forces, hydrodynamic interactions, droplet deformation, and AFM cantilever deflection has been developed. In agreement with experimental observations, the calculated force curves show pseudo-constant compliance regions due to drop flattening, as well as attractive pull-off forces due mainly to hydrodynamic lubrication forces.     

In situ hydrodynamic lateral force calibration of AFM colloidal probes

Lateral force microscopy (LFM) is an application of atomic force microscopy (AFM) to sense lateral forces applied to the AFM probe tip. Recent advances in tissue engineering and functional biomaterials have shown a need for the surface characterization of their material and biochemical properties under the application of lateral forces. LFM equipped with colloidal probes of well-defined tip geometries has been a natural fit to address these needs but has remained limited to provide primarily qualitative results. For quantitative measurements, LFM requires the successful determination of the lateral force or torque conversion factor of the probe. Usually, force calibration results obtained in air are used for force measurements in liquids, but refractive index differences between air and liquids induce changes in the conversion factor. Furthermore, in the case of biochemically functionalized tips, damage can occur during calibration because tip-surface contact is inevitable in most calibration methods. Therefore, a nondestructive in situ lateral force calibration is desirable for LFM applications in liquids. Here we present an in situ hydrodynamic lateral force calibration method for AFM colloidal probes. In this method, the laterally scanned substrate surface generated a creeping Couette flow, which deformed the probe under torsion. The spherical geometry of the tip enabled the calculation of tip drag forces, and the lateral torque conversion factor was calibrated from the lateral voltage change and estimated torque. Comparisons with lateral force calibrations performed in air show that the hydrodynamic lateral force calibration method enables quantitative lateral force measurements in liquid using colloidal probes.     

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.     

Analysis of Contact Interactions between a Rough Deformable Colloid and a Smooth Substrate

A model was developed for the effect of van der Waals interactions between a rough, deformable, spherical colloid and a flat, smooth, hard surface in contact. The model demonstrates the significant effect of colloid roughness on removal force. Small changes in colloid roughness produce large changes in the predicted removal force. Several authors attribute discrepancies in the observed interaction force between particles and surfaces to colloid roughness, and our model supports their hypotheses. Experimental data documenting the force required to remove colloids of polystyrene latex from silica substrates in aqueous solution were collected during AFM studies of this system. When colloid roughness exists, as is the case in this work, our model bounds the observed removal force. The predicted range of removal forces is in better quantitative agreement with our removal force data than are forces predicted by classical DLVO theory. Copyright 2000 Academic Press.     

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.     

Interaction forces in bitumen extraction from oil sands

Water-based extraction process (WBEP) has been successfully applied to bitumen recovery from Athabasca oil sand ore deposits in Alberta. In this process, two essential steps are involved. The bitumen first needs to be "liberated" from sand grains, followed by "aeration" with air bubbles. Bitumen "liberation" from the sand grains is controlled by the interaction between the bitumen and sand grains. Bitumen "aeration" is dependent, among other mechanical and hydrodynamic variables, on the hydrophobicity of the bitumen surface, which is controlled by water chemistry and interactions between bitumen and fine solids. In this paper, the interaction force measured with an atomic force microscope (AFM) between bitumen-bitumen, bitumen-silica, bitumen-clays and bitumen-fines is summarized. The measured interaction force barrier coupled with the contacted adhesion force allows us to predict the coagulative state of colloidal systems. Zeta potential distribution measurements, in terms of heterocoagulation, confirmed the prediction of the measured force profiles using AFM. The results show that solution pH and calcium addition can significantly affect the colloidal interactions of various components in oil sand extraction systems. The strong attachment of fines from a poor processing ore on bitumen is responsible for the corresponding low bitumen flotation recovery. The identification of the dominant non-contact forces by fitting with the classical DLVO or extended DLVO theory provides guidance for controlling the interaction behavior of the oil sand components through monitoring the factors that could affect the non-contact forces. The findings provide insights into megascale industrial operations of oil sand extraction.     

Dynamics of interactions involving deformable drops: hydrodynamic dimpling under attractive and repulsive electrical double layer interactions

A model developed previously to analyze force measurements between two deformable droplets in the atomic force microscope [Langmuir 2005, 21, 2912-2922] is used to model the drainage of an aqueous film between a mica plate and a deformable mercury drop for both repulsive and attractive electrical double-layer interactions between the mica and the mercury. The predictions of the model are compared with previously published data [Faraday Discuss. 2003, 123, 193-206] on the evolution of the aqueous film whose thickness has been measured with subnanometer precision. Excellent agreement is found between theoretical results and experimental data. This supports the assumptions made in the model which include no-slip boundary conditions at both interfaces. Furthermore, the successful fit attests to the utility of the model as a tool to explore details of the drainage mechanisms of nanometer-thick films in which fluid flow, surface deformations, and colloidal forces are all involved. One interesting result is that the model can predict the time at which the aqueous film collapses when attractive mica-mercury forces are present without the need to invoke capillary waves or other local instabilities of the mercury/electrolyte interface.     

Molecular Basis of the Dynamic Strength of the Sialyl Lewis X—Selectin Interaction

The selectins are Ca²⁺‐dependent cell adhesion molecules that facilitate the initial attachment of leukocytes to the vascular endothelium by binding to a carbohydrate moiety as exemplified by the tetrasaccharide, sialyl Lewis X (sLeX). An important property of the selectin‐sLeX interaction is its ability to withstand the hydrodynamic force of the blood flow. Herein, we used single‐molecule dynamic force spectroscopy (DFS) to identify the molecular determinants within sLeX that give rise to the dynamic properties of the selectin/sLeX interaction. Our atomic force microscopy (AFM) measurements revealed that the unbinding of the selectin/sLeX complexes involves overcoming at least two activation barriers. The inner barrier, which determines the dynamic response of the complex at high forces, is governed by the interaction between the Fuc residue of sLeX and a Ca²⁺ ion chelated to the lectin domain of the selectin molecule, whereas the outer activation barrier can be attributed to interactions involving the sialic acid residue of sLeX. Due to their steep inner activation barriers, the selectin‐sLeX complexes are less sensitive to high pulling forces. Hence, besides its contribution to the bond energy, the Ca²⁺ ion also grants the selectin–sLeX complexes a tensile strength that is crucial for the selectin‐mediated rolling of leukocytes.     

Bubble colloidal AFM probes formed from ultrasonically generated bubbles

Here we introduce a simple and effective experimental approach to measuring the interaction forces between two small bubbles (approximately 80-140 microm) in aqueous solution during controlled collisions on the scale of micrometers to nanometers. The colloidal probe technique using atomic force microscopy (AFM) was extended to measure interaction forces between a cantilever-attached bubble and surface-attached bubbles of various sizes. By using an ultrasonic source, we generated numerous small bubbles on a mildly hydrophobic surface of a glass slide. A single bubble picked up with a strongly hydrophobized V-shaped cantilever was used as the colloidal probe. Sample force measurements were used to evaluate the pure water bubble cleanliness and the general consistency of the measurements.     

Numerical simulation of bubble dynamics in a micro-channel under a nonuniform electric field

A numerical method is used to simulate the motion and coalescence of air bubbles in a micro-channel under a nonuniform electric field. The channel is equipped with arrays of electrodes embedded in its wall and voltages are applied on the electrodes to generate a specified electric field gradient in the longitudinal direction. In the study, the Navier-Stokes equations are solved by using the level set method handling the deformable/moving interfaces between the bubbles and the ambient liquid. Both the polarization Coulomb force and the dielectrophoresis force are considered as the force source of the Navier-Stokes equations by solving the Maxwell's equations. The flow field equations and the electric field equations are coupled and solved by using the finite element method. The electric field characteristics and the dynamic behavior of a bubble are analyzed by studying the distributions of the electric field and the force, the deformation and the moving velocity of the air bubble. The result suggests that the model of dispersed drops suspended in the immiscible dielectric liquid and driven by a nonuniform electric field is an effective method for the transportation and coalescence of micro-drops.     

Effect of solution concentration, surface bias and protonation on the dynamic response of amplitude-modulated atomic force microscopy in water

The dynamic response of amplitude-modulated atomic force microscopy (AM-AFM) is studied at the solid/water interface with respect to changes in ionic concentration, applied surface potential, and surface protonation. Each affects the electric double layer in the solution, charge on the tip and the sample surface, and thus the forces affecting the dynamic response. A theoretical model is developed to relate the effective stiffness and hydrodynamic damping of the AFM cantilever that is due to the tip/surface interaction with the phase and amplitude signals measured in the AM-AFM experiments. The phase and amplitude of an oscillating cantilever are measured as a function of tip-sample distance in three experiments: mica surface in potassium nitrate solutions with different concentrations, biased gold surface in potassium nitrate solution, and carboxylic acid-terminated self-assembled monolayers (SAMs) on gold in potassium nitrate pH buffers. Results show that, over the range where the higher harmonic modes of the oscillation are negligible, the effective stiffness of the AFM cantilever increases to a maximum as the tip approaches the surface before declining again as a result of the repulsive electrical double layer interaction. For attractive electrical double-layer interactions, the effective stiffness declines monotonically as the tip approaches the surface. Similarly, the hydrodynamic damping of the tip increases and then decreases as the tip approaches the solid/water interface, with the magnitude depending on the species present in the solution.     

Measurement of polyamide and polystyrene adhesion with coated-tip atomic force microscopy

This work presents atomic force microscopy (AFM) measurements of adhesion forces between polyamides, polystyrene and AFM tips coated with the same materials. The polymers employed were polyamide 6 (PA6), PA66, PA12 and polystyrene (PS). All adhesion forces between the various unmodified or modified AFM tips and the polymer surfaces were in the range -1.5 to -8 nN. The weakest force was observed for an unmodified AFM tip with a PS surface and the strongest was between a PS-coated tip and PS surface. The results point to both the benefits and drawbacks of coated-tip AFM force-distance measurements. Adhesion forces between the two most dissimilar (PA6-PS and PA66-PS) materials were significantly asymmetric, e.g., the forces were different depending on the relative placement of each polymer on the AFM tip or substrate. Materials with similar chemistry and intermolecular interactions yielded forces in close agreement regardless of placement on tip or substrate. Using experimental forces, we calculated the contact radii via four models: Derjaguin, Muller, and Toporov; Johnson, Kendall, and Roberts; parametric tip-force-distance relation; and a square pyramid-flat surface (SPFS) model developed herein. The SPFS model gave the most reasonable contact tip radius estimate. Hamaker constants calculated from the SPFS model using this radius agreed in both magnitude and trends with experiment and Lifshitz theory.     

Wet foams: Formation,properties and mechanism of stability

Overall picture of phenomena occuring during formation and existence of the wet foams is presented. Properties and mechanism of stability are discussed on the example of the wet foams obtained from solutions of two homologous series of surface active substances; the fatty acids and n-alkanols. In general three physical processes which contribute to foam stability can be distinguished: drainage of liquid out of the foam, coalescence and/or rupture of bubbles, and disproportionation (which may be called Ostwald ripening or gas diffusion from one bubble to another). Dynamic and non-equilibrium character of the wet foams is stressed.Motion of a bubble through the solution causes disequilibration of the surface concentration alongside the bubble surface. The surface concentration on the upstream part of the bubble is much smaller than the equilibrium concentration. Thus, the bubbles arrive at the solution surface with non-equilibrium surface concentration, and these actual non-equilibrium surface coverages determine possibility of formation and properties of the foams.Solution content ϕ in the volume of wet foam is high (of an order 307.), while in top foam layer it is much smaller (ϕ≅5%) . It shows that rupture of the wet foam takes place practically only in the top layer of bubbles and durability of these top foam films determine stability and volume of the whole foam column. On the basis of measurements of liquid content ϕ and lifetimes of bubbles in the top foam layer it was estimated that thicknesses of rupture of these top films were of an order of a few micrometers. At such thicknesses the force of disjoining pressure do not attain yet any meaningful value.Influence of kinetics of adsorption, frequency of external disturbances, surface activity of the solute and lifetime of the foam films on magnitude of the surface elasticity forces induced in the systems studied is discussed. It is shown that stability of the wet foams can be explained in terms of the effective elasticity farces, i.e. the surface elasticity forces which are induced at an actual non-equilibrium surface coverage. There is agreement between the courses of the dependences of the foamability parameter (retention time, rt) and the effective elasticity forces as a function of the number n of carbon atoms in the fatty acid and n-alkanol molecule. This shows that the effective elasticity forces are decisive parameter in formation and stability of the wet foams. It also explains why the foamability of a substance with a stronger surface activity can be lower than that of a substance with a weaker surface activity. The foamability, especially under dynamic conditions, cannot simply be correlated with the surface activity.     

Forces between two oil drops in aqueous solution measured by AFM

The surface and hydrodynamic forces between individual oil droplets in solution can provide insight into both emulsion stability and processes such as drop coalescence in liquid-liquid extraction. We present the first measurements of the interaction forces between alkane droplets in aqueous solution using atomic force microscopy. The radii of the droplets were well below the capillary lengths for the system, thus gravity effects are negligible, and interfacial tension and interaction forces governed the system behavior. The effects of modulating electrostatic double-layer interactions and interfacial tension through the presence of an anionic surfactant are demonstrated. Challenges in interpretation of the force data due to drop deformation are also discussed. A range of drop approach and retract speeds was used to determine the regime where hydrodynamic drainage effects had significant impact on the measurement.     

Chemical and physical aspects of organic fouling of forward osmosis membranes

The growing attention to forward osmosis (FO) membrane processes from various disciplines raises the demand for systematic research on FO membrane fouling. This study investigates the role of various physical and chemical interactions, such as intermolecular adhesion forces, calcium binding, initial permeate flux, and membrane orientation, in organic fouling of forward osmosis membranes. Alginate, bovine serum albumin (BSA), and Aldrich humic acid (AHA) were chosen as model organic foulants. Atomic force microscopy (AFM) was used to quantify the intermolecular adhesion forces between the foulant and the clean or fouled membrane in order to better understand the fouling mechanisms. A strong correlation between organic fouling and intermolecular adhesion was observed, indicating that foulant–foulant interaction plays an important role in determining the rate and extent of organic fouling. The fouling data showed that FO fouling is governed by the coupled influence of chemical and hydrodynamic interactions. Calcium binding, permeation drag, and hydrodynamic shear force are the major factors governing the development of a fouling layer on the membrane surface. However, the dominating factors controlling membrane fouling vary from foulant to foulant. With stronger intermolecular adhesion forces, hydrodynamic conditions for favorable foulant deposition leading to cake formation are more readily attained. Before a compact cake layer is formed, the fouling rate is affected by both the intermolecular adhesion forces and hydrodynamic conditions. However, once the cake layer forms, all three foulants have very similar flux decline rates, and further changes in hydrodynamic conditions do not influence fouling behavior.     

Single biomolecule imaging with frequency and force modulation in tapping-mode atomic force microscopy

A new intermittent-contact atomic force microscopy (AFM) mode (frequency and force modulation AFM, FFM-AFM) has been recently proposed to characterize soft samples. This method uses excitation force frequency and amplitude modulation to eliminate bistability and reduce the tip-sample forces. This letter describes theoretical modeling of FFM-AFM applied to a single bacteriorhodopsin molecule on a substrate, showing that its cross section can be measured without damage, in contrast to conventional tapping-mode AFM. Speculations are made regarding nonideal conditions and the ability of FFM-AFM to perform quantitative nanoelasticity measurements.     

Relationship between interfacial forces measured by colloid-probe atomic force microscopy and protein resistance of poly(ethylene glycol)-grafted poly(L-lysine) adlayers on niobia surfaces

Adsorbed layers of "comb-type" copolymers consisting of PEG chains grafted onto a poly(l-lysine) (PLL) backbone on niobium oxide substrates were studied by colloid-probe AFM in order to characterize the interfacial forces associated with coatings of varying architectures (PEG/PLL ratios and PEG chain lengths) and their relevance to protein resistance. The steric and electrostatic forces measured varied substantially with the architecture of the PLL-g-PEG copolymers. Varying the ionic strength of the buffer solutions enabled discrimination between electrostatic and steric-entropic contributions to the net interfacial force. For high PEG grafting densities the steric component was most prominent, but at low ionic strengths and high grafting densities, a repulsive electrostatic surface force was also observed; its origin was assigned to the niobia charges beneath the copolymer, as insufficient protonated amine groups in the PLL backbone were available for compensation of the oxide surface charges. For lower grafting densities and lower ionic strengths there was a substantial attractive electrostatic contribution arising from interaction of the electrical double layer arising from the protonated amine groups, with that of the silica probe surface (as under low ionic strength conditions, the electrical double layer was thicker than the PEG layer). For these PLL-g-PEG coatings the net interfacial force can thus be a markedly varying superposition of electrostatic and steric-entropic contributions, depending on various factors. The force curves correlate with protein adsorption data, demonstrating the utility of AFM colloid-probe force measurements for quantitative analysis of surface forces and how they determine interfacial interactions with proteins. Such characterization of the net interfacial forces is essential to elucidate the multiple types of interfacial forces relevant to the interactions between PLL-g-PEG coatings and proteins and to advance interpretation of protein adsorption or repellence beyond the oversimplified steric barrier model; in particular, our data demonstrate the importance of an ionic-strength-dependent minimum PEG layer thickness to screen the electrostatic interactions of charged interfaces.