Electrostatic Double-layer Forces Research Articles

Elevated temperature effects (T > 100 °C) on the interfacial water and microstructure swelling of Na-montmorillonite

Montmorillonite-based barriers are key elements of the engineered barrier systems (EBS) in geological disposal facilities (GDF). Their performance at temperatures above 100 °C is not sufficiently understood to assess the possibility of raising the temperature limits in GDF designs that could reduce construction costs and CO2 footprint. The present work provides new fundamental insights through molecular dynamics (MD) simulations of Na-montmorillonite's water-clay interactions and swelling pressure at temperatures 298–500 K and basal spacings of 1.5–3.5 nm. At temperatures above 100 °C, the swelling behaviour is governed by the attractive van der Waals force and the repulsive hydration force instead of the repulsive electrostatic (double layer) force. The swelling pressure reduction with increasing temperature is related to the weakened hydration repulsion and electric double layer repulsion, which result from the deterioration of the interlayer water layer structure and the shrinkage of the electric double layer. The applicability and breakdown of the classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory at elevated temperatures are examined. By excluding the osmotic contribution in the DLVO theory, the summation of the van der Waals interaction in DLVO and an additional non-DLVO hydration interaction can predict our MD system's swelling under high temperatures. The findings of this study provide a fundamental understanding of the swelling behaviour and the underlying molecular-level mechanisms of the clay microstructure under extreme conditions.

Ion correlation-driven like-charge attraction in multivalent salt solutions.

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations.

Programmable Interactions of Cellulose Acetate with Octadecyltrichlorosilane-Functionalized SiO2 Nanoparticles

It is significant to understand the interfacial interactions involved between the cellulose acetate (CA) and dispersed nanomaterials, in which the enhanced interaction improves the mechanical behavior of CA. In this work, the amendments of CA with SiO2 nanoparticles have been found to be endowed by grafting varying concentrations (0, 3, 5, and 6%) of octadecyltrichlorosilane (OTS). Aided by SiO2 colloid probe atomic force microscopy (AFM with a probe diameter of 20 μm), the adhesion force between CA and SiO2 is found to be programmable by tuning OTS concentrations functionalized onto SiO2 surfaces. The adhesion forces of 5% OTS-functionalized SiO2 with CA are the strongest, followed by the ones of 0, 3, and 6% OTS, resulting in a smoother and denser morphology on the film with 5% OTS. The AFM-measured approaching force-distance curves have been further compared to predictions by the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory, in which the XDLVO force is summed as the Liftshitz-van der Waals force (FLW), the electrostatic double-layer force (FEL), and the acid-base interaction force (FAB). FLW and FEL do not change significantly with OTS concentrations functionalized onto SiO2. However, FAB is sensitive to the functionalized OTS concentration onto SiO2 and significantly contributes to the interaction force of the composite films with 5% OTS, promoting the formation of a smooth and dense surface feature with a considerable mechanical performance demonstrated by load-displacement curves from a nanoindenter. This is highly encouraging and suggests that nanomaterials can be incorporated into CA to effectively improve their mechanical compatibility by programming the interaction between the CA matrix and nanomaterials.

Effect of decoration route on the nanomechanical, adhesive, and force response of nanocelluloses-An in situ force spectroscopy study.

Although cellulose derivatives are widely applied in high-tech materials, the relation between their force responses and their surface chemical properties in a biological environment as a function of pH is unknown. Here, interaction forces of surface modified cellulose nanocrystals (CNCs), lignin residual cellulose nanocrystals (LCNCs), and 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO)-oxidized cellulose nanofibres (TCNFs) with OSO3-, COO- and lignin chemical groups were measured using in situ peak force quantitative nanomechanical mapping and force spectroscopy in salt solution at two pH values. We found that the forces acting between the tip and CNC or LCNC are steric dominated showing long range and slow decay as a result of their low surface charge density. High Mw lignin contributed to the increased repulsion range for LCNCs compared to CNCs. The repulsion measured for TCNFs at the very short range was electrostatic force dominating showing a steep decay attributed to its high surface charge density. In the case of TCNFs, electrostatic double layer force was also evidenced by the attraction measured at secondary minima. In all the three cases the electro steric interactions are pH dependent. Dissipation maps verified that the force behavior for each material was related to structural conformation restriction of the groups at compression. The slow decayed repulsion of CNCs or LCNCs is related to a weak restriction of conformational change due to small surface groups or high molecular weight bound polymers forming flat layers, whereas the steep repulsion of TCNFs is attributed to a strong conformation restriction of carboxylic groups occurred by forming extended structure. Our results suggest that the force responses of the materials were dominated by surface charges and structural differences. TCNFs showed superior nanomechanical and repulsion properties over CNCs or LCNCs at neutral pH.

Mechanical–electrochemical coupling theory of bacterial cells

The environmental adaption, growth, motion, and other dynamic behaviors of bacteria are closely associated with the coupled mechanical–electrochemical properties of their subcellular structures, but the underlying regulatory mechanisms remain unclear. The mechanical responses of bacteria are difficult to elucidate by traditional models without considering the mechanical, chemical, and electric coupling effects. In this paper, a mechanical–electrochemical theory is constructed to investigate the deformation behavior of bacterial cells. A bacterium is treated as a bilayer structure consisting of a negatively charged polysaccharide capsule and an elastic envelope subjected to turgor pressure. This model is used to reveal the regulating roles of the electrostatic double-layer force and osmosis under different electrolyte conditions. Good agreement is found between the theoretical predictions and the experimentally observed three-stage nanoindentation responses of Klebsiella pneumoniae (K. pneumoniae) bacterial cells. Furthermore, we investigate the mechanical–electrochemical coupling mechanisms in the compression resistance of the bacterial capsule. The results reveal that the osmosis induced by ionic imbalance and polysaccharide–solvent aggregates plays a significant role in the compression resistance of the capsule. The present model not only deepens our understanding of the mechanical–electrochemical coupling mechanisms of bacterial cells at the subcellular scale, but also holds promise for applications in characterizing their mechanical properties.

Relation of EDL Forces between Clay Particles Calculated by Different Methods

Calculation of the electrostatic double layer force (EDL force) between clay particles is relevant as it is closely related to important macroscopic mechanical behaviors of clays. The popular method to calculate the EDL force is to integrate the electric potential and Maxwell stress along the boundary enclosing a simply connected domain within which a clay particle resides. The EDL force has also been calculated by the integration of the electrostatic force density over the preceding domain. However, the subtle relation of the EDL forces calculated by the different existing methods has not yet been investigated. By means of theoretical analysis and finite element simulation, it was shown that the force calculated by the integration of Maxwell stress along the complete boundary enclosing a multiply connected domain in which the clay particle is excluded, and that along the partial boundary enclosing the preceding simply connected domain represents the electrical attractive force and osmotic repulsive force, respectively, while the integration of the potential along both the same complete and partial boundary denotes the osmotic force. Numerical results showed that the calculated EDL force deviates from its actual value significantly with the decrease in distance between the chosen integral boundary and particle surface, and the deviation varies with surface potential and angle between particles. Moreover, the recommended minimum distance was proposed to be 10 times the thickness of the particle based on the present simulation results.

Numerical modeling of red blood cell interaction mechanics

In this work, a numerical analysis of the mechanics of the interaction of the red blood cell with the vessel wall was carried out. The deformation process is described using an adhesive dissipative elastic model. The influence of the electrostatic double layer and drag force on erythrocyte is investigated. The discrete element method is used to model erythrocyte dynamics. The focus is on the analysis of the effect of different acting forces on the erythrocyte. The results reflect force, displacement, time dependencies. The results indicate the process of erythrocyte deformation before contact, at certain distance from the interacting vessel surface.

Pore-scale simulation of nanoparticle transport and deposition in a microchannel using a Lagrangian approach

The application of nanoparticles to a fluid improves heat transfer and hydrodynamics, especially in porous media. To analyze the flow of nanoparticles and heat transfer in porous media at the pore scale, simulation in micro-scale channels of porous media is necessary. One concern is the deposition of nanoparticles to solid surfaces, which reduces the amount of material available in the bulk fluid. Also, in porous media, the nanoparticle deposition increases the surface roughness of pore surfaces, affecting the volumetric flow rate of nanofluid. Nanoparticle transport and deposition in a microchannel (as a representation of pore) are investigated numerically. The open-source library of OpenFOAM is used, and the Eulerian-Lagrangian (EL) approach is employed to simulate nanoparticles interacting with the base fluid and the surfaces of the microchannel. Integration of all forces exerted on nanoparticles, from base fluid and also microchannel’s surfaces are considered simultaneously. Brownian motion, drag, buoyancy, gravity, and Saffman lift forces are considered between nanoparticles and the base fluid. Van der Waals and electrostatic double-layer forces based on DLVO theory are considered between nanoparticles and microchannel surfaces. The deposition ratio of nanoparticles (the fraction of nanoparticles that deposit on the solid surface) is analyzed by the variation of nanoparticle diameter, fluid velocity, temperature, surface potentials, and double-layer thickness. It is assumed that the nanofluid is dilute, and the collisions between the nanoparticles are neglected.The results of nanoparticle deposition ratio are validated through comparison with available data in the literature. It has been shown that the nanoparticle deposition ratio decreases from 0.98 to 0.4 when the nanoparticle diameter increases from 30 to 150 nm. The effect of Van der Waals force on the enhancement of nanoparticle deposition ratio is about 1.6 %. Next, the deposition of nanoparticles is studied for different Reynolds number values, surface potential, nanoparticle radius, and double-layer thickness. Brownian motion dominates the behavior; increasing temperature and decreasing nanoparticle diameter will increase nanoparticle deposition. The magnitude of the nanoparticle and surface potentials and the double layer thickness are the two essential parameters that control the electrostatic double-layer force; its effect on deposition is also investigated. It has been concluded that the rise of the surface potential value decreases the deposition ratio.

Microstructure and Time-Dependent Behavior of STx-1b Calcium Montmorillonite Suspensions

CaMnt is much less important than NaMnt due to its limited commercial applications. The time-dependent property of NaMnt gel has been studied extensively as it is exploited in many applications such as drilling mud and viscosity-modifier applications. In contrast, the time-dependent property of CaMnt suspension and the factors affecting it are largely unknown. The speciation of Ca2+ ions is one such factor to be evaluated. In the current study, pH and solids concentration were examined and then used to validate a recent theory on clay gel time dependency. The results supported the theory that a strong electrostatic double layer (EDL) repulsion in the 3-D network is needed to reorganize the structure and drive it toward the state of minimum free energy. The 12 wt.% CaMnt (STx-1b) gel displayed time-dependent behavior at pH 5 but not at its natural pH of 8.4. At pH 5, the interlayer Ca2+ ions became fully hydrated and desorbed from the platelet surface. This enhanced the EDL repulsion between the platelets. At pH >6.5, the positively charged hydrolysis product Ca(OH)+ began to form and was adsorbed, partially neutralizing the permanent layer charge and weakening the repulsion. However, at 19.4 wt.% solids, the gel displayed pronounced time-dependent behavior despite the high natural pH of 8. The platelets were much closer together, allowing the EDL force to operate and effect structural reorganization. The microstructure of these CaMnt gels showed high platelet concentrations interacting to form a relatively open structure. The microstructure of a kaolin (KGa-2) suspension which showed no time-dependent behavior even after 1 day of ageing revealed the importance of particle morphology and layer charge on time dependency. Its 3-D structure was formed by relatively thick, layered platelets with a low layer charge.

Peridynamic modelling of coupled hydro-chemical processes in clay erosion

Hydro-chemical interactions at the interface between host rock and clay buffer in geological disposal facility for nuclear waste can lead to buffer erosion. The erosion of clay buffer can induce loss of a critical component of the engineered barrier system and migration of highly hazardous radionuclides into the environment. Classical local formulations for modelling the hydro-mechanical behavior of soils are not suitable for analysis of this discontinuous physical phenomenon, while non-local formulations offered by Peridynamics (PD) provide clear advantages. A bond-based PD formulation of coupled clay extrusion and sol transport in a fracture is presented. The PD model, named Pyramid, of clay extrusion accounts for the van der Waals forces, repulsive electrostatic double layer forces and friction forces between the particles. A 2D case study of clay extrusion and erosion under water flow in a fracture is presented. The case study is compared with experimental results of erosion of compacted MX-80 bentonite reported in the literature to demonstrate the accuracy of formulations and the Pyramid model. This validation shows the potential applications and prediction capability of the Pyramid model for evaluating the erosion of clay buffer under geological disposal conditions.

A diffusion model for the swelling of compacted Na–montmorillonite in water

A diffusion model, which considers the hydration force, is presented to predict Na–montmorillonite swelling in water. The swelling originates from the growth of the layer–to–layer distance in the montmorillonite layered structure. The hydration force controls the swelling when the montmorillonite has a layer–to–layer distance less than 100 Å. The layer separation increases because of the diffusion motion of the layers in water. The motion is controlled by a viscous drag force of liquids and four interaction forces between the layers, including hydration, van der Waals, repulsive electrostatic double–layer, and repulsive entropic forces. Based on the model, a diffusivity is defined for the compacted Na–montmorillonite over a wide concentration range of montmorillonite. The model predicted the volume fraction of the montmorillonite in the swelling process and agreed with the published experimental results from 60% to 0.001% volume fraction. Besides that, the result revealed that hydration force, repulsive electrostatic double–layer force, and repulsive entropic force, dominate crystalline swelling, osmotic swelling, and Brownian swelling respectively. The result explained the coexistence phenomenon of dense dispersion, concentrated dispersion, and dilute dispersion in the swelling process.

Stability of a Rolled-Up Conformation State for Two-Dimensional Materials in Aqueous Solutions.

Two-dimensional (2D) materials can roll up, forming stable scrolls under suitable conditions. However, the great diversity of materials and fabrication techniques has resulted in a huge parameter space significantly complicating the theoretical description of scrolls. In this Letter, we describe a universal binding energy of scrolls determined solely by their material parameters, the bending stiffness, and the Hamaker coefficient. Aiming to predict the stability of functionalized scrolls in water solutions, we consider the electrostatic double-layer repulsion force that may overcome the binding energy and flatten the scrolls. Our predictions are represented as comprehensive maps indicating the stable and unstable regions of a rolled-up conformation state in the space of material and external parameters. While focusing mostly on functionalized graphene in this work, our approach is applicable to the whole range of 2D materials able to form scrolls.

Contribution of friction to the heterocoagulation between coal surface and quartz particles studied by the particle vision and measurement (PVM)

The heterocoagulation between coal and micron-sized gangue particles is detrimental to the flotation separation of clean coal. Mineral heterocoagulation is usually inhibited by the adjustment of solution chemistry. But it is not explicit whether solution chemistry adjustment is universally suitable to inhibit heterocoagulation of gangue particles of different sizes, as the heterocoagulation mechanism may vary with the increase of particle size. In this work, the heterocoagulation between coal surface and quartz particles of different particle size was observed in turbulent flow field at acid and neutral pH by the in-situ particle vision and measurement (PVM) probe and was quantified via image processing. The observations indicated that the heterocoagulation between coal surface and fine quartz particles (D3,2 = 11 and 21 µm) was mitigated as pH varied from 3 to 7, however, the heterocoagulation between coal surface and coarse quartz particles (D3,2 = 31 µm) unexpectedly did not change with pH. The dependence of heterocoagulation on pH was different for fine and coarse quartz particles, indicating the variation of heterocoagulation mechanism. The heterocoagulation of fine quartz particles was regulated by the electrostatic double layer force in the framework of the DLVO theory, whereas the heterocoagulation of coarse quartz particles was mainly attributed to the non-DLVO force such as friction.

Numerical simulation of the mechanics of oblique interaction of a bacterium with a flat surface

Looking from the mechanical point of view the suspension containing the bacteria may be considered as a system of living active ultrafine particles. Here a model is developed for the interaction of the bacterium in an oblique direction during contact. The model considers an adhesive bacterium moving through a fluid, acting with appropriate specific forces, such as steric, electrostatic double layer and hydrodynamic forces. To understand the influence of the latter hydrodynamic forces on the bacterium, numerical experiments using DEM are carried out with this force and without it. A comparison of these two cases shows the difference in movement.

Interactions between CO2-Responsive Switchable Emulsion Droplets Determined by Using Optical Tweezers.

CO2-responsive switchable emulsions have been of great interest in some industrial processes where the stability of the emulsion is only required temporarily, such as oil transport, drug delivery, and fossil fuel production. The good understanding of the stability and instability mechanism is vital to the switchable behavior between emulsification and demulsification. Herein, a novel approach was developed to determine the interactions between two switchable emulsion droplets directly by a dual-laser optical tweezers instrument. The repulsive force between a couple of tetradecane droplets occurs to increase progressively with the increasing concentration of switchable surfactant in solutions. However, the repulsive force appears to decrease progressively in turn when the switchable surfactant concentration is far higher than the critical micelle concentration (CMC). Moreover, the depletion effect starts to emerge in the higher surfactant concentration which is attributed to the switchable surfactant micelles generated in solutions. In addition, according to the measurements of interaction forces, a mechanism of the switchable behavior is well proposed, which is established by the principle of self-assembly/detachment of the switchable surfactant, resulting in the weakening and re-enhancing of the electrostatic double-layer (EDL) repulsive forces between tetradecane droplets, upon selective introduction and removal of CO2. Based on this work, a novel perspective was provided to study the switchable emulsion, which can contribute instructive messages for the understanding of stability and instability mechanisms of switchable emulsions.

Interactions between colliding oil drops coated with non-ionic surfactant determined using optical tweezers

Non-ionic surfactants are widely used in many industrial applications such as detergents, oil recovery, and mineral flotation techniques. Non-ionic surfactants readily adsorb onto the oil-water interface, although they cannot dissociate in solutions like ionic surfactants can. Nonetheless, the electrostatic double-layer (EDL) repulsive force between oil drops coated with the non-ionic surfactant can still provide stability against coalescence. In this work, the interaction forces between two tetradecane drops with diameter of 6.5 µm were measured in the presence of the non-ionic fluorocarbon-based surfactant FS-30 in various salt solutions using optical tweezers. The measured force curves were consistent with the presence of a surface charge, even though the surfactant was non-ionic in nature. The results clearly show that the EDL repulsive force is gradually screened with increasing salt concentration. It was also found that the EDL repulsive force was significantly screened in the divalent cation salt solutions (Ca2+, Ba2+) in comparison to in the monovalent cation salt solutions (Na+). In addition, the absolute value of the measured zeta potential (−ξ) of emulsified tetradecane drops gradually decreased with increasing FS-30 concentration. In all experimental processes, the emulsified tetradecane drops coated with FS-30 were stable against coalescence. These findings have significant implications for the stability of emulsions used in the food, cosmetic, and detergent industries.

Interactions between micro-scale oil droplets in aqueous surfactant solution determined using optical tweezers

HypothesisThe stability of the emulsions is crucial, which relies on a well-developed understanding of dynamic interaction forces between single dispersed droplets. In the previous studies, many interests focus on the oil droplets of size range of 20–200 µm. However, emulsion droplets with diameter below 10 µm are rarely mentioned, which is the size scale of real emulsion droplets in various applications, such as toners, spacers for liquid crystal displays, and materials in biomedical and biochemical analysis. The micro-scale droplets have many differences on the deformation, internal pressure and hydrodynamic effects. It is necessary to understand the interaction mechanisms between two real size scales of oil droplets for guiding practical production and application. ExperimentsIn this work, tetradecane was chosen as the model oil phase in all experiments. The interaction forces of two tetradecane droplets with the diameter of 5.0 µm in water in the presence of surfactant and salt solution were directly measured using optical tweezers. The force-distance curves were established, and the zeta potential of tetradecane droplets was studied using Zetasizer Nano ZSP. FindingsThe absolute value of zeta potential of tetradecane droplets was found to decrease with the increase of salt concentration and increase with the increase of surfactant concentration. The repulsive force between two tetradecane droplets was found to decrease with the increase of salt concentration because the electrostatic double-layer force was suppressed gradually with the increase of salt concentration. The “hydrodynamic suction” effect during the process of retraction becomes more pronounced due to the corresponding increase in the hydrodynamic force with the increase of the approaching velocity between the tetradecane droplets. Furthermore, we found the existing model for the measurement of large droplets by atomic force microscope (AFM) is invalid for the measurement of micro-scale droplets by optical tweezers. The deformation of colliding micro-scale droplets can be safely ignored, which is quite different from the large droplets. Our results provide a useful method to study the interaction forces between micro-scale emulsion droplets with pN force resolution, and gives a deep insight of the stabilization mechanism of real size scale of O/W emulsions. These findings have significant implications on the stability of emulsions in many food, cosmetics, medicine, and advanced materials.

Influence of bubble approach velocity on liquid film drainage between a bubble and a spherical particle

The flotation process strongly depends on drainage of liquid film between a bubble and a particle which might be influenced by hydrodynamic conditions in a flotation cell. This technical note investigates the influence of bubble approach velocity on the liquid drainage process between a bubble and a particle under constant conditions. It was found that the increase in bubble approach velocity results in a higher critical thickness of the wetting liquid film. The results also showed that the rupture of the films was affected more strongly by electrostatic double layer forces than hydrophobic forces. Hydrophobic forces were more pronounced at high bubble approach velocities. This work shows that hydrodynamic conditions should not be neglected when investigating liquid film drainage process.

Role of Collectors and Depressants in Mineral Flotation: A Theoretical Analysis Based on Extended DLVO Theory

A theoretical analysis was conducted to study the role of collectors and depressants in flotation, based on the extended Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, where the hydrophobic force is considered. The collector-coated hydrophilic particle and the depressant-coated hydrophobic particle are simplified to a sphere uniformly covered with respectively hydrophobic and hydrophilic nanometer-sized hemispherical asperities of identical radius. Results show that the role of a collector in bubble–particle attachment is to create an attractive hydrophobic force and thus overcome the repulsive van der Waals and electrostatic forces. Moreover, increasing the length of the hydrophobic part of the collector molecule is a more effective way to enhance flotation recovery, compared to increasing the collector concentration. For a depressant, however, its function mechanism is to create a strong electrostatic double-layer force, while the suppression of the hydrophobic force plays a secondary role in decreasing the bubble–particle attachment barrier. The depressant molecule length is also a dominant parameter in designing a powerful depressant.

Enhancement of oxidized coal flotation by preconditioning with positive-charged microbubbles

ABSTRACT An oxidized coal surface is more negatively charged and hydrophilic than that of fresh coal because of the introduction of polar oxygen functional groups. During flotation, the decreased attractive hydrophobic force between bubbles and coal particles and the increased repulsive electrostatic force result in a low recovery for oxidized coal. In the present study, preconditioning with positive-charged microbubbles (PCMs), generated using a microbubbles generator and a cationic surfactant hexadecyl trimethyl ammonium bromide (CTAB), was proposed to enhance oxidized coal flotation. Conventional column flotation tests were also carried out for comparison. The results show that many oxygen functional groups (-OH and C-O) existed on the oxidized coal surface as indicated by X-ray photoelectron spectroscopy (XPS). A flotation recovery of 84.33% with an ash recovery of 82.97% was obtained when PCM was used, much higher than that of conventional flotation (a recovery of 17.82% with an ash recovery of 9.64%). PCM preferably adsorbed at the negative-charged hydrophilic sites on oxidized coal in the preconditioning stage. An additional attractive electrostatic double-layer force between oxidized coal and negative flotation bubbles was introduced, enhancing PCM preconditioning. However, the worst flotation selectivity was observed using PCM compared with that of conventional flotation based on Fuerstenau upgrading curves analysis.