Interparticle Repulsion Research Articles

Effect of surfactant and PAM on the settlement of kaolinite particles and its mechanism analysis

High concentrations of fine-grained clay minerals in tailings water are highly detrimental to environmental protection and water recycling. Using kaolinite as the study subject, this research investigates the effects of various cationic surfactants (DDA, DTAB, TTAB, CTAB) and flocculants (APAM, NPAM, CPAM) on the sedimentation of kaolinite particles. The study explores the impact of single agents, combined agents, and the sequence of their addition on kaolinite particle sedimentation. The results indicate that when using individual agents at low concentrations, CTAB outperforms TTAB, DTAB, and DDA, while APAM is more effective than NPAM and CPAM. The optimal performance is achieved with a CTAB concentration of 2×10<sup>-4</sup> mol/L and an APAM dosage of 20 mg/L. When combining agents, the best results are observed when CTAB is added before APAM. By fixing the APAM dosage at 20 mg/L and varying the CTAB concentration, the highest sedimentation rate and lowest turbidity are obtained at a CTAB concentration of 1.5×10<sup>-4</sup> mol/L. Mechanistic insights were obtained through aggregate imaging, area measurement, zeta potential testing, and contact angle testing. Cationic surfactants alter the surface properties of particles, reducing surface electronegativity and increasing hydrophobicity, which diminishes inter-particle repulsion and promotes aggregation, thereby reducing turbidity. Flocculants form larger flocs through adsorption and bridging, accelerating the sedimentation process. When flocculants and cationic surfactants are used together, the resulting flocs are more stable and larger, with an average floc area reaching 5017.6079 µm<sup>2</sup>, indicating a significant reduction in fine particles within the solution.

Effect of Bulk Nanobubbles on the Flocculation and Filtration Characteristics of Kaolin Using Cationic Polyacrylamide

This study investigated the influence of bulk nanobubbles (NBs) on the flocculation and filtration behavior of kaolin suspensions treated with cationic polyacrylamide (CPAM). Traditionally, flocculation relies on bridging mechanisms by polymers like CPAM. The present work examines the possibility of combining NBs with CPAM to achieve more efficient kaolin separation. The settling behavior of kaolin suspensions with and without bulk nanobubbles was compared. The results with 2 mL CPAM and 300 s settling time revealed that bulk NBs significantly enhanced flocculation efficiency, with supernatant zone height reductions exceeding 50% compared to CPAM alone, indicating a faster settling rate resulting from bulk NBs. This improvement in the settling rate is attributed to NBs’ ability to reduce inter-particle repulsion (as evidenced by a shift in zeta potential from −20 mV to −10 mV) and bridge kaolin particles, complementing the action of CPAM. Additionally, the study demonstrated that bulk NBs improved dewatering characteristics by lowering the medium resistance and specific cake resistance during filtration. These findings pave the way for the utilization of bulk NBs as a novel and efficient strategy for kaolin separation in mineral processing, potentially leading to reduced processing times and lower operational costs.

Hyperreflective photonic crystals created by shearing colloidal dispersions at ultrahigh volume fraction

Colloidal crystallization serves as one of the most economic and scalable production methods for photonic crystals. However, insufficient optical performance, nonuniformity and low reproducibility remain challenges for advanced high-value applications. In this study, we optimally formulate a photocurable dispersion of silica particles and apply shear flow to unify the orientation of the colloidal crystals, ensuring high optical performance and uniformity. The silica particles experience strong repulsion at ultrahigh volume fractions of 50% but demonstrate low mobility, leading to polycrystalline structures. Applying shear flow to the dispersions allows the silica particles to rearrange into larger crystalline domains with a unidirectional orientation along the flow. This shear-induced structural change produces absolute reflectivity at the stopband as high as 90% and a high transparency of 90% at off-resonant wavelengths with minimal diffusive scattering. Furthermore, the strong interparticle repulsion ensures a uniform volume fraction of particles throughout the dispersion, reducing deviations in the optical properties. We intricately micropattern the photocurable dispersions using photolithography. Additionally, the photonic films and patterns can be stacked to form multiple layers, displaying mixed structural colors and multiple reflectance peaks without sacrificing reflectivity. These superior photonic materials hold promise for various optical applications, including optical components and anticounterfeiting patches.

Energy is not a convex function of particle number for r-k interparticle potentials with k > log34.

The energy of a many-particle system is not convex with respect to particle number for r-k interparticle repulsion potentials if k > log34 ≈ 1.262. With such potentials, some finite electronic systems have ionization potentials that are less than the electron affinity: they have negative band gap (chemical hardness). Although the energy may be a convex function of the number of electrons (for which k = 1), it suggests that finding an analytic proof of convexity will be very difficult. The bound on k is postulated to be tight. An apparent signature of non-convex behavior is that the Dyson orbital corresponding to the lowest-energy mode of electron attachment has a vanishingly small amplitude.

Low-frequency hybridized excess vibrations of two-dimensional glasses

One hallmark of glasses is the existence of excess vibrational modes at low frequencies ω beyond Debye’s prediction. Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses. However, there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations. In particular, excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow D exc(ω) ∼ ω 2 in 2D glasses with an inverse power law potential. Yet, the universality of the quadratic scaling remains unknown, since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum. Here, we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion. Moreover, we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion, which is accompanied by a suppression of the strength of the sound attenuation. Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

Effect of Precursor Solution on Sedimentation of Alkaline-earth Phosphates at Different Temperatures

Kinetic study of sedimentation of alkaline-earth phosphates-magnesium phosphate (MP), calcium phosphate (CP), strontium phosphate (SP) and barium phosphate (BP) precipitates was carried out by varying reactant concentration approach involving turn-wise variation of precursor metal ions (Mg2+, Ca2+, Sr2+ and Ba2+) and phosphate ion (PO43-) concentrations, and monitoring the settling of the precipitate formed in a precipitate sedimentation measurement apparatus. A pseudo-rate order equation, associated with the approach of varying reactant concentration, was linearized, and the dependence of precipitate sedimentation on precursor concentration, established therewith. Whereas MP precipitate gave positive order-sedimentation increased with increase in concentrations of precursor solutions, orders of CP, SP and BP precipitates were negative-sedimentation decreased with increase in concentrations of precursor solutions. Inter-particle attraction and repulsion associated with high solid concentration, volume of precipitate particles formed as well as chemical interactions of precipitate with the mother solution might have caused these effects.

Hydrogel-Encased Photonic Microspheres with Enhanced Color Saturation and High Suspension Stability.

Regular arrays of colloidal particles can produce striking structural colors without the need for any chemical pigments. Regular arrays of colloidal particles can be processed into microparticles via emulsion templates for use as structural colorants. Photonic microparticles, however, suffer from intense incoherent scattering and lack of suspension stability. We propose a microfluidic technique to generate hydrogel-shelled photonic microspheres that display enhanced color saturation and suspension stability. We created these microspheres using oil-in-water-in-oil (O/W/O) double-emulsion droplets with well-defined dimensions with a capillary microfluidic device. The inner oil droplet contains silica particles in a photocurable monomer, while the middle water droplet carries the hydrogel precursor. Within the inner oil droplet, silica particles arrange into crystalline arrays due to solvation-layer-induced interparticle repulsion. UV irradiation solidifies the inner photonic core and the outer hydrogel shell. The hydrogel shell reduces white scattering and enhances the suspension stability in water. Notably, the hydrogel precursor in the water droplet aids in maintaining the solvation layer, resulting in enhanced crystallinity and richer colors compared with microspheres from O/W single-emulsion droplets. These hydrogel-encased photonic microspheres show promise as structural colorants in water-based inks and polymer composites.

Assisting and eliminating memory effects of paste by adding polysaccharides.

A densely packed colloidal suspension, called a paste, is known to remember the direction of its motion because of its plasticity. Because the memory in the paste determines the preferential direction for crack propagation, the desiccation crack pattern morphology depends on memory of its motions (memory effect of paste). Two types of memory effects are memory of vibration and memory of flow. When a paste is dried, it usually shows an "isotropic and random cellular" desiccation crack pattern. However, when a paste is vibrated before drying and it remembers the direction of its vibrational motion, primary desiccation cracks propagate in a direction perpendicular to its vibrational motion before drying (memory of vibration). Once it flows and remembers the direction of its flow motion, primary desiccation cracks propagate in the direction parallel to its flow motion (memory of flow). Anisotropic network formation via interparticle attraction among colloidal particles in a suspension is the dominant factor affecting a paste's memory of its motion. Calcium carbonate (CaCO_{3}) paste remembers the direction of its vibrational motion, but not its own flow direction because Coulombic repulsion among charged CaCO_{3} colloidal particles prevents the formation of a network structure in a flow. For this study, we strove to assist and eliminate CaCO_{3} paste memory effects by adding polysaccharides. First, to characterize memory in paste, we propose a method of image analysis to quantify the strength and the direction of the anisotropy of desiccation crack patterns using Shannon's information entropy. Next, we conduct experiments to add polysaccharide to CaCO_{3} paste, revealing that the addition of a small amount of polysaccharide to CaCO_{3} paste assists the paste in remembering its own flow motion. Findings also indicate that the addition of a large amount of polysaccharide prevents the formation of both memories of its flow and vibrational motion and eliminates the memory effects of paste. We then perform "flocculation and sedimentation" experiments to investigate the interaction among CaCO_{3} colloidal particles in a solution. Results show that, in an aqueous solution with low polysaccharide concentration, CaCO_{3} colloidal particles flocculate each other and quickly form a sediment in a short time, whereas, in an aqueous solution with high polysaccharide concentration, a longer time is necessary for flocculation and sedimentation. Because the addition of small amounts of polysaccharides to CaCO_{3} paste induces polymer bridging between colloidal particles as interparticle attraction, it helps to produce a macroscopic network structure which retains memory of its flow motion and thereby assists the formation of memory of flow, whereas the addition of large amounts of polysaccharides induces interparticle repulsion, which prevents the formation of memory effects of all types.

Effect of silica fume on rheology of slag-fly ash-silica fume-based geopolymer pastes with different activators

This study examined the effect of silica fume contents on the rheological behavior of slag-fly ash-silica fume-based geopolymer pastes by packing density measurement, low-field NMR, zeta potential, dynamic light scattering and FTIR analyses. Incorporating silica fume into sodium hydroxide (SH)-activated geopolymer pastes resulted in the decrease of packing density and the increases of yield stress, plastic viscosity and hysteresis loop curve area. The contrary results were found in the pastes activated by sodium silicate (SS). The water states of geopolymer pastes were influenced by SiO2/Na2O ratio of activator and silica fume dosage. The mobile water content in the sample increased as the silica fume dosage increased, regardless of the SiO2/Na2O ratio of activator. The particle size of the silica species in the activator and interstitial fluids is close to that of silica fume. The incorporation of silica fume resulted in the variation in the silicate structural characteristics of the interstitial fluids. The influence of silica fume on the rheological behaviors of geopolymer systems is strongly governed by the interparticle repulsion or attractiveness and activator nature, opposed to the filler effect and dissolution of silica fume. In SS-activated systems, the repulsion between the silanol groups on the silica fume surface and silicate species adsorbed on the surface of precursors particles contributed to the particle separations, thereby enhancing rheological behaviors. In SH-activated system, the attractiveness between divalent metal cations and silanol groups on the surfaces of precursor and silica fume particles was increased and the particle space was restrained. This study would provide new insights into the role of silica fume in the particle interaction of fresh ultra-high performance geopolymer concrete.

A front-tracking method for simulating interfacial flows with particles and soluble surfactants

In this research, a three-dimensional model is proposed to simulate the behavior of particle-covered droplets that contain soluble surfactant. The model includes a full two-way coupling between surfactant transport and particle motion, with surfactant concentrations at the interface and in the bulk linked to the flow and motion of the interface by a convection-diffusion equation. A front-tracking method is used to track the interfacial flow, while a semi-resolved particle method is used to model the particles, accounting for various forces acting on them, such as the excluded volume force, the direct contact force and the hydrodynamic lubrication force. The model also includes a surfactant-dependent surface tension that can affect the particle-interface interactions. The model is validated against previous numerical data and a parametric study is performed to examine the delicate interplay between flow fields and interfaces associated with surfactant concentration and particle motion. The study then investigates the role of surfactants in the dynamics of a particle-covered droplet, focusing on their coupled influence on droplet deformation. In addition, it is observed that particles bridge colliding droplet interfaces and suppress fluid drainage from the gap, preventing droplet coalescence along with the interparticle repulsion force.

Phase transitions in the driven lattice gas (TASEP) with repulsive energies

We report on non-equilibrium phase transitions in the driven lattice gas model totally asymmetric exclusion processes caused by nearest-neighbor (NN) repulsions between particles, ɛ > 0, employing extensive Monte Carlo simulations and mean-field calculations. The diagra of phase regimes has five different regimes which are separated by distinct boundaries. We discuss the density of particles and the current which depend differently in the various regimes on the system’s entry and exit rates of particles, α and β, respectively. The steady state can be described by quasi-particles called ‘soft dimerons’, where each dimeron consists of a particle dragging an empty NN site on its left. The asymptotic state of dimerons at is equivalent to the state of hard dimers at ɛ = 0. Since the model is a uni-directional fluid, it has an internal hydrodynamic pressure which increases with increasing inter-particle repulsion ɛ. This leads to a collective effect which causes phase transitions between high and low densities of particles at certain critical points ɛ c .

The Mechanism of Viscosity-Enhancing Admixture in Backfill Slurry and the Evolution of Its Rheological Properties

Since filling slurry is a cement-based material, viscosity-enhancing admixture exerts a significant effect on its rheological performance and mechanical properties. Viscosity-enhancing admixture can improve pipeline transportation performance and reduce pipeline wear during the filling process of a kilometer-deep mine by changing the plastic viscosity and yield stress of high-concentration filling slurries. In order to reveal the influence mechanism of viscosity-enhancing admixture on rheological performance in slurry, the influence of viscosity-enhancing admixture on the rheological performance of slurry is explored by adjusting viscosity-enhancing admixture dosage and conducting bleeding test, liquidity test, and rheological performance test. The extended DLVO theory is employed to analyze the mechanism of HPMC on the stability of filling slurry. The results show that compared with ordinary slurry, after adding HPMC and XG, the particles of filling slurry are prone to link to form a mesh structure. Besides, the increasing frictional force between particles results in a significant decrease in the bleeding rate and liquidity of the slurry. Such an effect becomes more obvious with the increase of viscosity-enhancing admixture dosage. Meanwhile, the overall effect of HPMC molecules is better than that of XG molecules since HPMC can reduce inter-particle repulsion and facilitate particle aggregation. The optimal dosage is about 0.1%, at which time the yield stress of the filling slurry increases from 89.236 to 160.06 Pa, the plastic viscosity increases from 0.296 to 1.063 Pa·s, and the compressive strength increases from 2.58 to 3.59 MPa in 28 days. The study reveals the influence of viscosity-enhancing admixture on the rheological performance of filling slurry and its evolution characteristics, which provides theoretical support for the development of filling resistance and wear reduction technology.

Enhanced rheological and tribological properties of nanoenhanced greases by tuning interparticle contacts

HypothesisDespite the wide spectrum of available nanoparticles, their utilization in lubricant and grease formulations remains challenging. To enhance their performance, an improved link between the interparticle contacts, brittleness of the resulting particle network, time-dependent rheology and tribology is required. ExperimentsWe systematically changed interparticle contacts and examined their effect on the colloidal stability, microstructure, rheological and tribological behavior of model greases by investigating four types of nanoclays: montmorillonite (Cloisite Na+), oleic-acid functionalized Cloisite Na+ (OA-Cloisite Na+), organomodified montmorillonite (C20A) and oleic-acid functionalized C20A (C20A-OA). FindingsWe observed a range of behaviors, starting from the lack of colloidal stability in greases derived with Cloisite Na+ and OA-Cloisite Na+ to semi-solid type systems with C20A and C20A-OA. Consistent with previous studies, the rheological and tribological properties of C20A systems scale with nanoclay loadings. Surprisingly, the functionalized C20A-OA system exhibited a delayed transition towards hydrodynamic lubrication, and enhanced lubrication properties, both of which were largely independent of nanoclay loadings. Coupled microstructural investigation and time-dependent rheology reveal that this behavior is governed by increasing repulsive forces, decreasing inter-particle friction between C20A-OA nanoparticles, and faster reorganization of the C20A-OA nanoparticle network under shear. Increased interparticle repulsion enables C20A-OA nanoclays to pass each other under shear and align in direction of shear, which reduces the overall viscosity, while the presence of OA on nanoclays decreases inter-particle friction and particle-steel surface friction.

Finite-temperature equilibrium density profiles of integrable systems in confining potentials.

We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the interparticle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and we compare them with results from Monte Carlo simulations. In both cases we find good agreement between the field theory and simulations. We also consider the case of the Toda model in which interparticle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited and instead, in certain parameter regimes, we present an approximate Hessian theory to understand the density profile. Our work provides an analytical approach toward understanding the equilibrium properties for interacting integrable systems in confining traps.

Investigating Adsorption of Cellulose Nanocrystals at Air–Liquid and Substrate–Liquid Interfaces after pH Manipulation

AbstractCoatings of anisotropic nanoparticles such as cellulose nanocrystals (CNCs) can provide tuneable physicochemical surface properties to a substrate such as modifying wettability. These coatings are often formed using dip coating, with CNCs enriched at the air–water interface transferred to a substrate as a monolayer. This process is commonly facilitated by surfactants, which can remain present in the final product, affecting coating properties. In this work, an “additive free” method for creating CNC coatings by exploiting electrostatic interactions within the pH window between pH 2–4 is demonstrated. Within this pH window, the air–water interface is positively charged and CNCs are negatively charged, with surface pressure tensiometry, X‐ray reflectivity, and Brewster angle microscopy indicating that CNCs are driven to the air–water interface. The optimal condition for monolayer coverage was pH 3; at pH 2 charge screening causes localized flocculation at the air–water interface, and at pH 4 interparticle repulsion leads to incomplete, patchy coverage. These findings successfully translate to dip coated CNC monolayers as characterized by atomic force microscopy, showing that the manipulation of pH can facilitate the surfactant‐free dip coating of CNCs, with advantages over the surfactants that are more typically used.

Direct Measurement of Surfactant-Mediated Picoforces among Nanoparticles in a Quasi-Two-Dimensional Environment.

The lack of methodologies which enable us to measure forces acting between nanomaterials is one of the factors limiting the full comprehension of their behavior and their more effective exploitation in new devices. Here we exploit the irreversible adsorption of surfactant-decorated nanoparticles at the air/water interface to investigate interparticle forces and the effect of the surfactant structure on them. We measured the interparticle repulsive forces as a function of the modulation of the interparticle distance by simultaneously performing compression isotherms and the grazing incidence small-angle X-ray scattering (GISAXS) structural characterization of the monolayers at water–vapor interfaces. Our results demonstrate that the short-range interparticle forces are strongly affected by the presence of the organic ligands, which are shown to be able to influence the interparticle repulsions even when added in micromolar amounts. In particular, we demonstrate the predominant steric nature of short-range forces, which are accounted for in terms of the compression-induced stretched-to-coiled conformational transition of the ligand hydrophobic tail.

Preservation of a Dust Crystal as it Falls in an Afterglow Plasma

In an experiment, the power that sustains a plasma was extinguished, so that microspheres, which had been levitated, fell downward toward a lower electrode. At the beginning of their fall, the microspheres were self-organized with a crystalline structure. This structure was found to be preserved as the microspheres accelerated all the way to the lower electrode. Although microspheres had, in this afterglow plasma, large positive charges of 12,500 e, their interparticle repulsion was unable to significantly alter the crystalline arrangement of the microspheres, as they fell. After their impact on the lower electrode, the microspheres bounced upward, and only then was the crystalline structure lost.

Bioinspired Approaches to Self-Assembly of Virus-like Particles: From Molecules to Materials.

When viewed through the lens of materials science, nature provides a vast library of hierarchically organized structures that serve as inspiration and raw materials for new synthetic materials. The structural organization of complex bioarchitectures with advanced functions arises from the association of building blocks and is strongly supported by ubiquitous mechanisms of self-assembly, where interactions among components result in spontaneous assembly into defined structures. Viruses are exemplary, where a capsid structure, often formed from the self-assembly of many individual protein subunits, serves as a vehicle for the transport and protection of the viral genome. Higher-order assemblies of viral particles are also found in nature with unexpected collective behaviors. When the infectious aspect of viruses is removed, the self-assembly of viral particles and their potential for hierarchical assembly become an inspiration for the design and construction of a new class of functional materials at a range of different length scales.Salmonella typhimurium bacteriophage P22 is a well-studied model for understanding viral self-assembly and the construction of virus-like particle (VLP)-based materials. The formation of cage-like P22 VLP structures results from scaffold protein (SP)-directed self-assembly of coat protein (CP) subunits into icosahedral capsids with encapsulation of SP inside the capsid. Employing the CP-SP interaction during self-assembly, the encapsulation of guest protein cargos inside P22 VLPs can be achieved with control over the composition and the number of guest cargos. The morphology of cargo-loaded VLPs can be altered, along with changes in both the physical properties of the capsid and the cargo-capsid interactions, by mimicking aspects of the infectious P22 viral maturation. The structure of the capsid differentiates the inside cavity from the outside environment and serves as a protecting layer for the encapsulated cargos. Pores in the capsid shell regulate molecular exchange between inside and outside, where small molecules can traverse the capsid freely while the diffusion of larger molecules is limited by the pores. The interior cavity of the P22 capsid can be packed with hundreds of copies of cargo proteins (especially enzymes), enforcing intermolecular proximity, making this an ideal model system in which to study enzymatic catalysis in crowded and confined environments. These aspects highlight the development of functional nanomaterials from individual P22 VLPs, through biomimetic design and self-assembly, resulting in fabrication of nanoreactors with controlled catalytic behaviors.Individual P22 VLPs have been used as building blocks for the self-assembly of higher-order structures. This relies on a balance between the intrinsic interparticle repulsion and a tunable interparticle attraction. The ordering of VLPs within three-dimensional assemblies is dependent on the balance between repulsive and attractive interactions: too strong an attraction results in kinetically trapped disordered structures, while decreasing the attraction can lead to more ordered arrays. These higher-order assemblies display collective behavior of high charge density beyond those of the individual VLPs.The development of synthetic nanomaterials based on P22 VLPs demonstrates how the potential for hierarchical self-assembly can be applied to other self-assembling capsid structures across multiple length scales toward future bioinspired functional materials.

Average Size and Density of Clusters in Dusty Plasma

As is well known, metal and metal oxide dust particles either in combustion plasmas or in low-pressure gas-discharge plasmas are able to get a positive or negative charge. When the particles are identically charged, the Debye interparticle repulsion force arises. However, due to the additional interaction of grains with plasma electrons and ions, the resultant intergrain pair potential energy becomes non-Debye. As a result, it can cause local minima by certain plasma parameters. This case develops a quasimolecular structuralization, where two equally charged grains are spaced at a finite distance in equilibrium. The same principle of grain structuralization is valid for the multibody case where grains are associated in a crystal structure or clusters. The present work is devoted to the description of the dependence of the average size and the density of clusters on the interparticle potential. The general formula for the average cluster energy via the pair potential energy is derived.

Interparticle Repulsion of Microparticles Delivered to a Pendent Drop by an Electric Field.

We report an unusually large spacing observed between microparticles after delivery to the surface of a pendent water droplet using a DC nonuniform electrostatic field, primarily via dielectrophoresis. The influence of particle properties was investigated using core particles, which were either coated or surface-modified to alter their wettability and conductivity. Particles that exhibited this spacing were both hydrophobic and possessed some dielectric material exposed to the external field, such as a coating or exposed dielectric core. The origin of this behavior is proposed to be the induced dipole-dipole repulsion between particles, which increases with particle size and decreases when the magnitude of the electric field is reduced. When the particles were no longer subjected to an external field, this large interparticle repulsion ceased and the particles settled to the bottom of the droplet under the force of gravity. We derive a simple model to predict this spacing, with the dipole-dipole repulsion balanced against particle weight. The external electric field was calculated using the existing electric field models. The spacing was found to be dependent on particle density and the induced dipole moment as well as the number of particles present on the droplet interface. As the number of particles increased, a decrease in interparticle spacing was observed.