Double Layer Interaction Research Articles

Alignment, Rising, Sticking, and Phototaxis: Modulating the Behavior of Hematite Micropeanuts

AbstractArtificial active colloids are an active area of research in the field of active matter and microrobotic systems. In particular, light‐driven semiconductor particles are shown to display interesting behaviors ranging from phototaxis (movement toward or away from a light source), rising from the substrate, interparticle attraction, attraction to the substrate, or other phenomena. However, these observations involve using multiple different designs of particles in varying conditions, making it unclear how the experimental parameters, such as pH, peroxide concentration, and light intensity, affect the outcomes. In this work, a peanut‐shaped hematite semiconductor particle is shown to exhibit a rich range of behavior as a function of the experimental conditions. The particles show rising, sticking, phototaxis, and in‐plane alignment of their long axes perpendicular to a magnetic field. A theoretical model accounting for gravity, van der Waals forces, electric double layer interactions with the glass surface, and self‐diffusiophoresis is formulated to describe the system. Using experimental data on the dependence of particle behavior on pH and ionic concentrations, the model captures the interplay of competing effects and explains many of the observed behaviors, providing insight into the relevant physical phenomena and how different environmental conditions can lead to such a rich diversity of behavior.

Clays as Micro-Electrodes in Environmental Detoxification

AbstractIn-situ reduction of contamination in soil and groundwater is an ongoing challenge that often requires a multi-pronged approach for effective and efficient clean-up. Spontaneous or assisted electrochemical reactions that break down certain pollutants held on clay surfaces can render natural clays a unique and powerful ally in environmental mitigation of contaminated soils. Application of a low-level DC electric field (mV/cm) has been shown to facilitate transformation of some compounds and ionic species through redox reactions in addition to transporting them through the pores in wet clay soils. Results from previous tests suggest that the natural electrochemical processes that promote pollutant sloughing or chemical breakdown can be enhanced for targeted treatment by applying low-level electric field to the contaminated soil with clay content. The central idea of this hypothesis is that clay, due to its surface charge and electrostatic interaction with adjacent pore fluid, acts as a “micro-electrode” through the diffused double layer (DDL) interactions when subjected to an external electric field. This hypothesis, proven viable, may unlock potential ability of natural clays to generate beneficial reactions for detoxification of contaminated sub-surfaces. Evidence from past laboratory experiments accompanied by a proposed electrical model of clay behaving as a micro-electrode are presented in this paper. The laboratory experiment results support the proposed electrical model.

Image charge effects under metal and dielectric boundary conditions.

Theimage charge(IC)effect is a fundamental problem in electrostatics. However, proper treatment at the continuum level for many-ion systems, such as electrolyte solutions or ionic liquids, remains an open theoretical question. Here, we demonstrate and systematically compare the IC effects under metal and dielectric boundary conditions (BCs), based on a renormalized Gaussian-fluctuation theory. Our calculations for a simple 1:1 symmetric electrolyte in the point-charge approximation show that the double-layer structure, capacitance, and interaction forces between like-charged plates depend strongly on the types of boundaries, even in the weak-coupling regime. Like-charge attraction is predicted for both metal and dielectric BCs. Finally, we comment on the effects of a dielectricallysaturated solvent layer on the metal surface. We provide these results to serve as a baseline for comparison with more realistic molecular dynamics simulations and experiments.

Impact of temperature and salinity on fines detachment: AFM measurements and XDLVO theory

Fine particle detachment and subsequent migration can lead to severe pore plugging and consequent permeability decline. Therefore, it is crucial to quantify the critical condition when fine particle detachment occurs. The frequently observed deviations or even contradictions between experimental results and theoretical predictions of fines detachment arise from an insufficient understanding of adhesion force that can be highly influenced by salinity and temperature. To clarify the intrinsic influence of salinity and temperature on fines detachment, adhesion forces between carboxyl microspheres and hydrophilic silica substrates in an aqueous medium were measured at various salinities and temperatures using atomic force microscopy (AFM). The AFM-measured adhesion force decreases with increasing salinity or temperature. Trends of mean measured adhesion forces with temperature and salinity were compared with the DLVO and XDLVO theories. DLVO theory captured the trend with temperature via the impact of temperature on electric double layer interactions, whereas XDLVO theory captured the observed trend with salinity via the impact of salinity on the repulsive hydration force. Our results highlight the significance of hydration force in accurately predicting the fate of fines in porous media.

Effects of chemical solution components on the contact angle of typical minerals in soil: quartz, orthoclase and plagioclase

Different chemical solutions can significantly change the contact angle (CA) of soil, but few studies have studied the change rule and action mechanism of the CA from the mineral composition of soil essence. In unsaturated soil mechanics, the CA is an important parameter to calculate the wet suction between soil particles in unsaturated soil. When the chemical composition of the soil pore liquid changes, the CA will also change, which will affect the wet suction and other parameters, thus changing the macroscopic mechanical properties of the soil. In this study, the CA of air-solution-mineral phases with different solution components (pH, type and concentration of salt solution) of different minerals (quartz, orthoclase and plagioclase) were measured. The results show that the CAs of quartz, orthoclase and plagioclase all rise first and then drop with the rise of pH. The peak CAs are pH = 5, pH = 4 and pH = 3, respectively. Quartz, orthoclase and plagioclase all have valley values in different concentrations of NaCl and KCl solutions. In CaCl2 solution, only quartz has valley value, while orthoclase and plagioclase increase monotonously. Quartz in soil plays a main role in the influence of soil CA, followed by orthoclase and plagioclase. The CA of different minerals in different chemical solutions is mainly controlled by electric double layer interaction and functional groups interaction. In different salt solution environment, in addition to the above two effects, the mineral CA is also affected by the surface tension.

Enhancing biofilm formation with powder carriers for efficient nitrogen and phosphorus removal

This study assesses the improvement in nitrogen and phosphorus removal from wastewater achieved through the integration of zeolite and attapulgite carrier materials into the activated sludge (AS) process. It was found that the addition of these materials significantly enhanced the processing performance of the reactor. Specifically, the use of zeolite and attapulgite powders increased sludge particle sizes to averages of 231.56 μm and 219.62 μm, respectively. This facilitated micro-granule formation, substantially improving the settling characteristics of the sludge and boosting the activity and proliferation of essential microbes. Illumina MiSeq sequencing demonstrated significant accumulations of DGAOs (Candidatus_Competibacter) and DPAOs (Candidatus_Accumulibacter). Furthermore, these carriers augmented the protein content in extracellular polymers, enhancing the hydrophobicity of the sludge and promoting aggregation. Comparative analysis based on the extended Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory indicated a preferential adhesion affinity of sludge for zeolite compared to attapulgite, attributed primarily to Lewis acid-base and electric double-layer interactions. These findings underscore zeolite's enhanced efficacy in biomass fixation and suggest significant potential for the technological advancement of wastewater treatment plants.

Mechanical and physicochemical characteristics of sub-millimeter and macrobubbles: Insights from AFM analysis, zeta potential measurements and rise velocity

This study presents the change in mechanical and physicochemical behaviour of macrobubbles and sub-millimeter bubbles with respect to pH. While macrobubbles conventionally range from 100 μm to 2 mm in diameter, this study focuses on the comparatively less-explored sub-millimeter bubble range, centered around a median diameter of 500 μm. The difference in sub-millimeter bubbles (500 μm) compared to their larger counterparts (1100 μm) within macrobubble size range were evidenced through atomic force microscopy (AFM) analysis, zeta potential measurements, and rise velocity experiments. The adhesion force and energy between bubbles and the silicon nitride cantilever tip showed a decreasing trend with increasing pH, notably diminishing by about 50% beyond pH 9. Although no significant differences were statistically revealed between the two bubble sizes at lower pH, the adhesion force and energy were consistently smaller for macrobubble compared to sub-millimeter bubble at higher pH beyond pH 9. This finding suggests that the electrical double layer (EDL) interactions are influenced by the specific surface area, particularly in the alkaline region. Zeta potential measurements exhibited a cubic trend, with an isoelectric point at pH 3.5 and a minimum zeta potential at pH 11. The study also depicted a similar trend in the rise velocity of bubbles, suggesting a direct relationship between bubble stiffness and its rise velocity. Therefore, changes in pH affected the bubbles' properties, while on the other hand, certain physicochemical properties are also influenced by bubble sizes.

Rheological Behavior of an Aqueous Suspension of Oxidized Carbon Nanohorn (CNHox).

Oxidized carbon nanohorn (CNHox) a carbon nanomaterial that has attracted attention due to its unique material properties. It is expected to be applied in various areas like cancer treatment, gene-expression technology, fluids with high thermal conductivity, lubricants, and so on. While the rheological measurements of suspensions provide information on the effective size and interactions of suspended particles, the rheological behaviors of aqueous suspensions of CNHox have never been systematically investigated. To clarify the rheological behaviors of aqueous suspensions of CNHox, their viscosity and dynamic viscoelasticity were measured with changing particle concentration and salt concentration. The viscosity of a CNHox suspension showed yield stress at low shear rates and showed shear-thinning behavior with increasing shear rates. The viscosity of 5 weight % CNHox suspensions was comparable to that of 60 weight % silica suspensions. This high viscosity at a low CNHox concentration is probably due to the porous structure and large effective volume of the CNHox particle. The estimated effective volume of CNHox calculated by the Krieger-Dougherty equation was 18.9 times larger than the actual volume calculated by the mass concentration and density. The dependence of rheological behavior of the CNHox suspension on salt concentration was weak compared to that of the colloidal silica suspension. This weak dependence on salt concentration may be due to the roughness of the particle surface, which would weaken the effect of electric double-layer interactions and/or van der Waals interactions between particles. These rheological behaviors of the aqueous suspension of CNHox shown in this research will be useful in efforts to improve the efficiency of its utilization for the various applications.

Ion- and surface-sensitive interactions during oxygen evolution reaction in alkaline media

Abstract Clean and sustainable energy has turned towards electrochemical water splitting as a viable solution in minimizing carbon emissions. Electrolysis of water converts electrical energy to chemical energy, through the production of hydrogen and oxygen gases, which can be harnessed for potential applications without contributing to greenhouse emissions. While this energy storage process shows great potential, its efficiency is hindered by the sluggish kinetics of the oxygen evolution reaction (OER). As a result, its widespread application in green electrolytic technologies is limited hence investigations on improving OER kinetics are of utmost importance. Recent research breakthroughs indicate that alkali metal cations are more than passive observers. They play complex roles in the electric double layer (EDL), which positively influences the OER kinetics. The presence of numerous ions and their combinations presents a challenge of complexity. This study aims to delve into the impact of alkali metal cations on OER activity due to the variance in their hydration energies. Specific investigations focusing on different alkali metal cations in solution, such as Li+, Na+, and K+, was conducted on RuO2 to gain a deeper understanding of how these ions interact with both reactants and intermediate species in the reaction kinetics. Traditional electrochemical tests, including cyclic voltammetry (CV), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS), and accelerated degradation test (ADT) measurements were employed to elucidate critical aspects such as surface activation, electric double layer interactions, catalytic activity and stability, ohmic resistance, and mass and charge transport.

Exploring the mechanisms of calcium carbonate deposition on various substrates with implications for effective anti-scaling material selection

The unexpected scaling phenomena have resulted in significant damages to the oil and gas industries, leading to issues such as heat exchanger failures and pipeline clogging. It is of practical and fundamental importance to understand the scaling mechanisms and develop efficient anti-scaling strategies. However, the underlying surface interaction mechanisms of scalants (e.g., calcite) with various substrates are still not fully understood. In this work, the colloidal probe atomic force microscopy (AFM) technique has been applied to directly quantify the surface forces between calcite particles and different metallic substrates, including carbon steel (CR1018), low alloy steel (4140), stainless steel (SS304) and tungsten carbide, under different water chemistries (i.e., salinity and pH). Measured force profiles revealed that the attractive van der Waals (VDW) interaction contributed to the attachment of the calcium carbonate particles on substrate surfaces, while the repulsive electric double layer (EDL) interactions could inhibit the attachment behaviors. High salinity and acidic pH conditions of aqueous solutions could weaken the EDL repulsion and promote the attachment behavior. The adhesion of calcite particles with CR1018 and 4140 substrates was much stronger than that with SS304 and tungsten carbide substrates. The bulk scaling tests in aqueous solutions from an industrial oil production process showed that much more severe scaling behaviors of calcite was detected on CR1018 and 4140 than those on SS304 and tungsten carbide, which agreed with surface force measurement results. Besides, high salinity and acidic pH can significantly enhance the scaling phenomena. This work provides fundamental insights into the scaling mechanisms of calcite at the nanoscale with practical implications for the selection of suitable anti-scaling materials in petroleum industries.

Clay micromechanics: Numerical modelling of electrical double-layer interactions to develop particle-based models for clay

Discrete element modelling of clays requires defining the interaction energy between two particles. The Derjaguin, Landau, Verwey and Overbeek (DLVO) theory combining the effect of the van der Waals forces and the Coulombic forces due to the double layer of counterions provides a widely accepted framework to characterise the pair potential energy. Solutions of the Poisson-Boltzmann (PB) equation to quantify the Coulombic forces are only available for the case of infinitely extended and uniformly charged facing plates (1D conditions). However, these assumptions are not representative of a clay particle system. Particles should be represented by platelets of finite size and finite thickness, with different charges between the edge and the basal planes. This paper addresses the problem of deriving the Coulombic interaction forces for plates of finite size and thickness in 3D configuration by solving the Poisson-Boltzmann equation numerically via the Finite Element Method (FEM). It is shown that 2D particles (plates of infinitesimal thickness) provide an adequate representation of Coulombic interaction as long as the particles are uniformly charged. The advantage of 2D particles is to reconcile numerical modelling with analytical solutions available in the literature. The use of 2D particles is questionable when considering different charges between basal planes and edges.

Algae–water–silica interactions in low and high ionic strength environments

The interaction between algae and solid surfaces is of direct interest for the optimization of biofuel production technologies. Silica is particularly relevant due the use of solgel matrices for enhanced growth and ease of processing, where ionic strength variation is an important consideration. Here, an inverted fluorescence experiment is used to perform measurements of the distance between a silica surface and algae in solution. At low ionic strength, the average algae–silica distance is approximately 90 nm but increases to roughly 130 nm at 1 M NaCl, contradicting the prediction based on simple electrical double layer interaction models. These findings illustrate the role of biochemical and electrostatic interactions at charged aqueous interfaces of relevance to biofuel production.

On the balance of hydrophilicity and electrostatic interactions during particle filtration and backwash at microfiltration pores

Colloidal fouling is a notoriously limiting factor in many membrane processes. Although intensely studied in mostly macroscopic filtration systems, the underlying phenomena leading to generally decreased fouling remain unknown. This study systematically investigates fouling and backwashing of anionic polystyrene particles in microfluidic structures with engineered surface charge and hydrophilicity. We interpret the observed phenomena with the extended Derjaguin–Landau–Verwey–Overbeek (xDLVO) theory for interaction potentials. Polyelectrolyte coatings of the membrane-mimicking structure allow us to investigate particle–membrane interactions in (1) hydrophobic structures with negative zeta potential, (2) hydrophilic structures with positive zeta potential, and (3) hydrophilic structures with negative zeta potential. We assess the qualitative changes in membrane–particle interaction potentials regarding their hydrophilic and electrostatic double-layer interactions on the basis of the extensive study of particle deposition and resuspension during filtration and backwash. The results generally confirm the known trend of decreased fouling with increased hydrophilicity. However, we also show that hydrophilicity alone is an insufficient measure to estimate a membrane’s particle deposition and removal behavior. More important to achieve a low-fouling membrane that can be cleaned with pure flow reversal during regular backwashing is the design of a hydrophilic membrane with an engineered surface charge.

Colloidal interactions for a polystyrene particle and a smooth silicon surface: Atomic force microscopy, XDLVO theory, and Surface Element Integration

In this study Liftshitz van der Waals, electrostatic and acid base interaction forces of a 4 µm polystyrene particle with flat silicon surfaces were experimentally determined using interfacial interaction energy measurements and atomic force microscopy (AFM). Interfacial forces computed using analytical expressions based on the Surface Element Integration (SEI) technique were compared with the standard Derjaguin Approximation (DA) and Continuum Mechanics Adhesion approaches, namely: Derjaguin, Muller and Toporov (DMT), Johnson, Kendall and Roberts (JKR) and Maugis and Pollock (MP) theories in order to assess the effect of curvature on a sphere-plate geometry. For acid base interactions, the SEI was found to deviate from the DA at small particles radii (less than 100 nm) and over a wide ratio of decay length, λ, to particle size, R. Accounting for curvature for acid base interaction requires geometric factors that are functions of λ/R. For van der Waals force of interaction, the SEI and DA showed large variation at large ratios of interparticle separation, D, to particle radius, R. For Double layer interaction force large variation between SEI and DA was observed for small κa values, and good agreement observed at large κa values. The AFM forces of adhesion of polystyrene in 0.01 mM and 100 mM KCl electrolyte solutions were found to be 2.38 ± 2.15 nN and 9.29 ± 6.89 nN, respectively. These results were found to be consistent with the SEI technique that gave adhesion forces of 4.8 and 10.2 nN at the low and high electrolyte concentrations, respectively. These data are also aligned with Maugis and Pollock (MP) theory that accounts for elasto-plastic deformation, Pe.

Connecting Colloidal Forces to the Equilibrium Thickness of Particulate Deposits on a Substrate in Contact with a Suspension Using Classical Density Functional Theory

We study contributions of colloidal forces, i.e., hydrophobic, van der Waals, and electrical double layer interactions, to the thickness of a colloidal deposit in equilibrium with an aqueous suspension by using classical density functional theory, which we expand to obtain a Ginzburg-Landau type energy functional. We regard colloidal particles as clusters of molecular segments-a reminiscent of polymer statistical physics and of the classic Hamaker treatment of van der Waals interactions between particles. This approach appropriately accounts for the integral interaction energy between colloidal particles, which may take magnitudes of many times the characteristic molecular thermal energy kBT (Boltzmann constant times temperature). The analysis highlights the well-known insight that entropy is mostly governed by the solvent molecules and gives physical values to the statistical coefficients in a Ginzburg-Landau type energy functional.

Distinct behaviors of KNO3 and NaNO3 in specific heat enhancement of molten salt nanofluid

This study aims to examine the effects of the solvent of molten salt nanofluids on the specific heat capacity (SHC) and furthermore to understand the mechanism for enhanced SHC of the nanofluids. Moreover, the effects of the electrical double layer (EDL) on the SHC enhancement were quantitatively analyzed for a single salt and binary salt-based nanofluids. Two different nanoparticles, SiO2 and graphite, were dispersed in sodium nitrate (NaNO3), potassium nitrate (KNO3) and NaNO3-KNO3 mixtures. The SHC of the nanofluids was experimentally measured by a differential scanning calorimetry. The SHC of the NaNO3-SiO2 nanofluids was increased up to 17.2 % in liquid phase, whereas the SHC enhancements of the binary salt-SiO2 nanofluids were varied between-1.2 and 8.2 % in liquid phase. Additionally, the SHC enhancement was unfavorably proportional to the mass ratio of NaNO3 in the binary salt-SiO2 nanofluids. In graphite nanofluids, the SHC was enhanced up to 20.1 % and 7.1 % in KNO3 and NaNO3, respectively. However, the enhancement in the SHC was <7.8 % in the binary salt-graphite nanofluids. The zeta potentials of the SiO2 nanoparticle in the aqueous salt solution were linearly increased with the composition of NaNO3 which can be correlated with the salt solvent dependent SHC in the binary salt nanofluid. Finally, the EDL analysis indicates that SiO2 nanoparticles have stronger attractive force in ionic solutions than graphite. Furthermore, the EDL interactive forces demonstrate that the potential energy in the EDL adjacent to the nanoparticles determines the SHC enhancement of the molten salt nanofluids. KeywordsNanofluidSpecific heatMolten saltZeta potentialElectric double layerInteraction potential energy

Enhanced and efficient removal of heavy metals by amino-decorated membranes in coordination with multi-function

A multi-functional MA/GMA@PVDF membrane with abundant amino groups was first prepared by grafting the intermediate with an epoxy group from glycidyl methacrylate (GMA) into a defluorinated polyvinylidene fluoride (PVDF) and subsequently conducting an ammonifying process with melamine. The highest pure water flux of the selected 0.2 %-MA/GMA@PVDF was up to 562 L/(m2·h), with a high flux recovery ratio of 97.7 %, indicating excellent antifouling performance. Cu(II) concentration in the treatment volume of 47.44 L/m2 met the discharge limitation of 0.5 mg/L, which was more than 5.3 times that of the PVDF membrane. The obvious enhancement was mainly attributed to the grafted amino groups, which could coordinate with Cu(II) with the lone-pair electrons. Moreover, inorganic salts and organic matter could improve 0.2 %-MA/GMA@PVDF rejection performance in mixed systems. Among them, NaNO3 could increase the effective treatment volume to 55.12 L/m2 by charge shielding and compression double layer interaction owing to the unique property of amino groups. The maximum removal of Cu(II) by citric acid was increased by 48.63 % by the complexation of NH2/NH groups. Thus, the multi-functional membrane decorated with amino groups shows great potential as a promising material to efficiently remove heavy metals from complex wastewater.

A Coarse-Grained Interaction Model for Sodium Dominant Montmorillonite.

Montmorillonite is the main crystalline mineral present in bentonite. It is an absorbent, swelling material; the physical chemistry underlying its ability to absorb water and swell occurs at the nanoscale, governed by electrical double-layer interactions. In turn, absorption and swelling lead to important changes in the macroscopic transport properties of the clay. Mesoscale models can help us establish a link between these nanoscale processes and macroscale properties, notably by providing a detailed description of its pore network. Models on the scale of hundreds to thousands of nanometers are required, which cannot realistically be handled using traditional all-atom molecular dynamics simulations. This work presents a coarse-grained (CG) mesoscale model of sodium montmorillonite. In our model, montmorillonite platelets are represented by two types of particles: central nonhydrogen-bonded particles and edge hydrogen-bonding particles. The particle interactions are described by two-body potentials, which were optimized based on all-atom molecular dynamics simulations. Specifically, several potential mean force calculations involving dry and hydrated montmorillonite were performed, using the ClayFF potential to calculate interatomic forces. The CG model was validated by testing the scalability of the model, testing its ability to reproduce potentials of mean force reported elsewhere in the literature, and by comparing the calculated elastic properties of a system containing 1000 Na montmorillonite platelets to experimentally measured elastic properties of bentonite. The simulated elastic properties obtained using our mesoscale model agree with these experimental values.

Modeling the Environment-Dependent Kinetics of Oxygen Reduction Reaction – Effect of Relative Humidity

For proton exchange membrane fuel cells (PEMFCs) to achieve broad commercialization, the kinetics of oxygen reduction reaction (ORR) need to be better understood to improve the efficiency with minimized use of expensive Pt-based electrocatalyst(1). The increasing demands of PEMFC-powered heavy-duty vehicles make this issue critical, especially to meet the efficiency target (ultimately 72%)(2). Previous first principle-based theoretical analyses reasonably explained catalyst-dependent activity in ideal conditions (on single crystal catalysts in HClO4 solution under room temperature)(3). To design a practical catalyst, further analysis is required to bridge the gap between the ideal and actual PEMFC conditions (typically, covered with perfluorosulfonic acids under 60 to 90 °C, and 30 to 100% RH). In this talk, we examine the effect of relative humidity (RH) on ORR activity on a platinum surface. The effect of RH on ORR activity has been a controversial topic: an experimental study suggested lower RH increases the ORR activity(4), while another study showed the opposite trend(5). By using a multiscale continuum model, we validate our hypothesis that the controversial experimental results stem from the difference in the properties of the electrode/electrolyte interface. In the mathematical calculation, we assume that the polycrystalline platinum catalysts consist of multiple single crystalline surfaces(6) and that their activity is described by the summation of the activities on the single crystalline surfaces. Based on transition state theory, the reaction rate of each elementary step is calculated from the reaction free energy, reactant concentration, and activation energy with explicit accounting of the double-layer structure and interactions. In the presentation, the calculation results will be compared with experimental solid-state data using microelectrodes, and the mechanism of RH-dependent ORR activity will be discussed. Reference I. E. L. Stephens, A. S. Bondarenko, U. Grønbjerg, J. Rossmeisl and I. Chorkendorff, Energy & Environmental Science, 5 (2012).D. A. Cullen, K. C. Neyerlin, R. K. Ahluwalia, R. Mukundan, K. L. More, R. L. Borup, A. Z. Weber, D. J. Myers and A. Kusoglu, Nature Energy, 6, 462 (2021).H. A. Hansen, V. Viswanathan and J. K. Nørskov, The Journal of Physical Chemistry C, 118, 6706 (2014).M. Shibata, M. Inaba, K. Shinozaki, K. Kodama and R. Jinnouchi, Journal of The Electrochemical Society, 169, 044507 (2022).H. Xu, Y. Song, H. R. Kunz and J. M. Fenton, Journal of The Electrochemical Society, 152 (2005).G. A. Tritsaris, J. Greeley, J. Rossmeisl and J. K. Nørskov, Catalysis Letters, 141, 909 (2011).

Proposition of a bubble-particle attachment model based on DLVO van der Waals and electric double layer interactions for froth flotation modelling

Proposition of a bubble-particle attachment model based on DLVO van der Waals and electric double layer interactions for froth flotation modelling