Critical Particle Concentration Research Articles

Modeling order–disorder boundaries of colloidal dispersions in organic solvents using interaction force measurements

HypothesisThe formation of soft colloidal crystals, which are nonclose-packed ordered arrays of colloidal particles suspended in a solvent, is dictated by a single physical factor that yields a fixed threshold at order–disorder boundaries for different experimental conditions such as ion concentration, solvent type, and particle size. Identifying the determinant factor and its threshold value should enable the prediction of the critical concentrations of colloidal particles to form soft colloidal crystals. ExperimentsSoft colloidal crystals were fabricated using a series of monohydric alcohols as dispersion media and reflectance spectra were measured to locate order–disorder boundaries. The interaction forces acting between particles were also measured by employing atomic force microscopy. FindingsThe interparticle forces at the order–disorder boundaries exhibited a universal threshold that was independent of the solvent types including alcohols and water. Therefore, the determinant factor for the formation of soft colloidal crystals was determined to be the force acting between the particles. Furthermore, a priori calculation of this critical force and consequently the critical particle concentration in colloidal systems was demonstrated by referring to the pressure at the liquid-to-solid transition in a hard sphere system (Alder transition).

Magnetic field dependent viscoelasticity of a highly stable magnetorheological fluid under oscillatory shear

In our previous works, a new kind of magnetorheological fluid (MRF) consisting of high viscosity linear polysiloxane (HVLP) as carrier and carbonyl iron particles (CIPs) as magnetoactive dispersions, i.e., HVLP MRF, was proposed. HVLP MRF is a promising candidate in the field of heavy equipment for its long-term suspension stability. In this study, we further investigate the viscoelastic properties of HVLP MRF under oscillatory shear in order to evaluate its work performance. HVLP MRFs with different CIP concentrations (0, 20, 40, 60, and 70 wt. %) were synthesized. SEM microstructure, visible MR effect, and magnetic properties were performed. The effects of magnetic flux density, CIP concentration, shear strain, and shear angular frequency on the viscoelastic moduli were examined by using a Physica MCR-301 rheometer. The results show that the viscoelastic moduli are magnetic field dependent. The storage modulus increases with increasing the magnetic flux density, while the loss modulus presents a tendency of rising up at the beginning and declining in late. A critical particle concentration threshold (∼70 wt. %) was found to maximize the magneto-storage modulus increment. Both the upper limit of linear viscoelastic region and the flow point increase as the magnetic flux density increases. It reveals that the field dependent viscoelasticity of HVLP MRF is the result of competition between the structure-enhancement of magneto-induced particle chains and structural deformation under oscillatory shear. Additionally, in the linear viscoelastic region, HVLP MRF shows little dependence on shear angular frequency, implying an excellent working stability in a complex environment.

Nonequilibrium Structure Diagram of Pendular Suspensions under Large-Amplitude Oscillatory Shear.

For pendular suspensions with particles in contact with immiscible secondary liquid bridges, the shear field significantly influences particle aggregates and networks. In this work, we study the structure of the pendular network and how the structure changes under large-amplitude-oscillatory shear. Using rheology and optical microscopy, we found unique network destruction followed by reconstruction with increasing strain. Two processes show different shear-field dependencies, strain-rate dependency for destruction and strain dependency for reconstruction. A nonequilibrium state diagram is constructed to show the phase behavior, where the critical particle concentration of sol-gel transition is dependent on the shear history and may depend on shear strain nonmonotonically. Two different mechanisms, shear-induced network breakdown at low strain and shear-induced agglomeration at high strain, are suggested to describe the nonmonotonic critical concentration under the upward strain sweep quantitatively.

Extraordinary optical transmission in nano-bridged plasmonic arrays mimicking a stable weakly-connected percolation threshold.

Ultrasensitive sensors of various physical properties can be based on percolation systems, e.g., insulating media filled with nearly touching conducting particles. Such a system at its percolation threshold featuring the critical particle concentration, changes drastically its response (electrical conduction, light transmission, etc.) when subjected to an external stimulus. Due to the critical nature of this threshold, a given state at the threshold is typically very unstable. However, stability can be restored without significantly sacrificing the structure sensitivity by forming weak connections between the conducting particles. In this work, we employed nano-bridged nanosphere lithography to produce such a weakly connected percolation system. It consists of two coupled quasi-Babinet complementary arrays, one with weakly connected, and the other with disconnected metallic islands. We demonstrate via experiment and simulation that the physics of this plasmonic system is non-trivial, and leads to the extraordinary optical transmission at narrowly defined peaks sensitive to system parameters, with surface plasmons mediating this process. Thus, our system is a potential candidate for percolation effect based sensor applications. Promising detection schemes could be based on these effects.

Surface chemistry driven dynamic rheology, microstructure of fumed and colloidal silica particles in nematic liquid crystals

We investigate the influence of surface chemistry of silica particles on the dynamic rheology and underlying microstructure of silica in nematic liquid crystal (NLC), 4-cyano-4-pentylbiphenyl (5CB) suspensions. The hydrophilic fumed silica (Aerosil 200), synthesized (uncoated) and N-methyl-3-aminopropyltrimethoxysilane (MAP) coated colloidal silica particles in 5CB suspensions form gels at a critical particle concentration of 1.5 wt% (φ = 0.007), 15 wt% (φ = 0.075) and 20 wt% (φ = 0.103) respectively. On the other hand hydrophobic fumed silica (Aerosil RX300) and Dimethyl octadecyl [3-(trimethoxysilyl) propyl] ammonium chloride (DMOAP) coated colloidal silica particles in 5CB suspensions form gels at relatively higher particle loading of 3.5 wt% (φ = 0.016) and 50 wt% (φ = 0.314) respectively. The storage modulus (G′) of the Aerosil 200/5CB, uncoated silica/5CB and MAP coated silica/5CB suspensions follow power-law scaling G′ ~ φm, where m is 4.74 ± 0.5 and 5.89 ± 0.3 and 6.28 ± 0.5 respectively. In contrast, Aerosil RX300/5CB suspensions have a higher value of m (6.53 ± 0.4). Dynamic rheology data of solid gel-like Aerosil 200/5CB, uncoated silica/5CB and MAP coated silica/5CB suspensions exhibit signatures of soft glassy materials, exemplified by (a) an almost frequency (ω) independent G′ and a minima in loss modulus (G″) and (b) strain overshoot in G″, whereas Aerosil RX300/5CB and DMOAP coated silica/5CB suspensions show signatures of flocculated gels with strong dependence of G′ on ω, an absence of minima in G″ and no strain overshoot in G″. Furthermore, G′ of gel-like Aerosil 200/5CB suspension is insensitive to the nematic-isotropic phase transition (TNI) of 5CB, while the Aerosil RX300/5CB suspension shows a liquid-like behavior (G″ > G′) at temperature (T) > TNI of 5CB. We believe that the observed differences in the dynamic rheology are dictated by the surface anchoring or interactions of 5CB molecules with the –OH groups of hydrophilic silica. The microscopy results show that at T < TNI, the 5CB in Aerosil 200/5CB suspensions gets restricted in the network of Aerosil 200 nanoparticles, whereas the flocs of Aerosil RX300 nanoparticles are expelled by the nucleating 5CB domains to form a particulate network in Aerosil RX300/5CB suspensions. Moreover, the uncoated, MAP and DMOAP coated colloidal silica/5CB suspensions do not exhibit the prominent effect of T on rheology except the discontinuity in G′ and G″ at TNI of 5CB.

Coupled CFD-DEM simulation of granular LCM bridging in a fracture

Developed fractures are important storage space and permeable channel in hydrocarbon reservoirs. However, they will lead to drill-in fluid loss and induce severe formation damage. Fracture plugging with granular lost circulation material (LCM) is most commonly used to control drill-in fluid loss. To our best knowledge, traditional research about LCM bridging mainly performed by the trial-and-error method. However, the behavior of granular LCM migration and bridging in a fracture on mesoscale is still unclear. In this paper, the coupled CFD-DEM approach is used to simulate the flow of granular LCM in a vertical fracture. The effects of particle size distribution (PSD) and concentration on the fracture plugging process are studied by a series of controlled numerical experiments. The research suggests that: (1) When Wf/D50<1.5, the critical particle concentration softly increases with particle size distribution (PSD), but the area with Wf/D50>1.5 the critical particle concentration sharply increases with PSD. (2) The plugging process can be divided into two distinct stages from pressure drop rate: particle bridging and particle accumulation. (3) The drill-in fluid loss rate is affected by the plugging process, the structure of plugging zone and PSD.

Experimental Measurement of the Solid Particle Concentration in Geophysical Turbulent Gas‐Particle Mixtures

AbstractDilute gas‐particle mixtures in which the particles are carried by the turbulent fluid are found in various geophysical contexts, from cold snow avalanches to hot pyroclastic density currents. Though previous studies suggest that such mixtures have maximum particle concentrations of a few volume percent, the dependence of this maximum concentration on the Reynolds number is unclear. We addressed this issue through laboratory experiments in a vertical pipe, where dilute gas‐particle mixtures were created by injecting a turbulent air flow from below. Nearly monodisperse mixtures of glass beads of different grain sizes (77 to 1,550 μm) were used with varying bulk concentrations from 0.025 to 8 vol. %. To create quasi‐static mixtures, the mean air velocity matched the terminal settling velocity for the grain sizes investigated. The maximum Reynolds numbers of the mixtures were ~104–106. The air pressure indicated full support of the particle weight at concentrations down to 0.025 vol. %. Above a critical particle concentration, at which all the particles were suspended, subsequent additional particles were not maintained in the mixture and led to the formation of clusters that settled downward in the pipe to form a dense fluidized bed. Maximum mean particle concentrations of the dilute mixtures increased from ~1 to ~2.8 vol. % and reached a plateau at increasing mixture Reynolds number. These results give insights into the maximum particle concentrations of geophysical turbulent gas‐particle mixtures and may serve to constrain observations as well as the input and output data of models.

An investigation of CFD simulations capability in treating non-spherical particle dynamics in a rotary drum

A systematic study upon the Eulerian approach capability in predicting irregular particle (non-spherical) dynamics inside an unbaffled rotary drum was carried out through the investigation of different particle-particle interaction models and wall boundary conditions. The drum length effect on particle dynamics was also analyzed. The frictional viscosity, the wall movement method, and the particle boundary condition at the wall were shown to be of fundamental importance for irregular particles modelling in rotary drums. The moving mesh method did not represent well the experimental observation, regardless of the solid boundary condition used at the drum wall. The moving wall method combined with a no-slip boundary condition for the solid phase at the drum wall, and the frictional viscosity model using a critical particle concentration (αsc) of 0.4, satisfactory agreed with experiments. For the end-caps analyses, the higher the ratio L/ds, the lower the bed material surface slope and the lower the particle velocity values in the active region. From L/ds of 40.7 no differences were observed in particle dynamics behavior anymore.

Phase behavior of binary and polydisperse suspensions of compressible microgels controlled by selective particle deswelling.

We investigate the phase behavior of suspensions of poly(N-isopropylacrylamide) (pNIPAM) microgels with either bimodal or polydisperse size distribution. We observe a shift of the fluid-crystal transition to higher concentrations depending on the polydispersity or the fraction of large particles in suspension. Crystallization is observed up to polydispersities as high as 18.5%, and up to a number fraction of large particles of 29% in bidisperse suspensions. The crystal structure is random hexagonal close-packed as in monodisperse pNIPAM microgel suspensions. We explain our experimental results by considering the effect of bound counterions. Above a critical particle concentration, these cause deswelling of the largest microgels, which are the softest, changing the size distribution of the suspension and enabling crystal formation in conditions where incompressible particles would not crystallize.

Coupled CFD-DEM simulation of hydrodynamic bridging at constrictions

This paper presents a coupled CFD-DEM approach to simulate the flow of particulate suspensions in the intermediate concentration regime where solid volume concentration is 1% < ϕ < 50%. In particular, hydrodynamic multi-particle bridging during flow through a single constriction in a rectangular channel is studied. It is shown that for neutrally buoyant, monodispersed particulate suspensions, the probability of jamming increases with the particle concentration. There also exists a critical particle concentration (ϕ*) for spontaneous bridging, which depends on the ratio of pore size to particle size, the flow velocity, the particle-fluid density contrast, and the flow geometry leading to the constriction. The ϕ* has a strong dependence on the outlet-to-particle relative size (Ro). For 1.5 ≤ Ro ≤ 2.5, a direct transition from a flowing state to a jammed state was observed. For Ro ≥ 3, the flowing state typically transitioned to a dense state characterized by the accumulation of particles near the constriction before jamming. Increasing the inlet-to-particle relative size (Rip) lowers ϕ* by increasing the number of particles arriving at the constriction simultaneously. The effect of changing Rip is more pronounced at high Ro when the probability of bridging is lower. A high fluid velocity increases particle interactions near the constriction and accelerates the onset of bridging. However, no distinct effect of velocity on ϕ* was observed in this study. A higher particle-to-fluid density ratio (ρp/ρf) increases the probability of bridging and leads to a lower ϕ* in a given constriction geometry. The effect saturates at higher ρp/ρfwhen gravitational forces completely dominate over viscous drag forces. ϕ* is also found to decrease with increasing angle of constriction convergence (θ) for θ < 30°, but increases beyond that at θ=60∘.

Numerical study on the effect of fine coal accumulation in a coal beneficiation fluidized bed

One important phenomenon in coal beneficiation fluidized bed (CBFB) is the accumulation of fine coal particles in beneficiation due to poor screening efficiency and attrition of coal samples. The effect of fine coal accumulation is numerically studied in this work using a TFM–DEM hybrid model. The gas phase and medium solid phase are modeled by a two-fluid model (TFM), while the fine coal particles are modeled by the discrete element method (DEM). Particles with a diameter of 0.9mm are used as the fine coal sample in the simulation. The gas–solid flow pattern and particle dynamics are investigated with different concentrations of fine coal particles accumulated in the bed. For model validation purpose, the mean bed density distributions are compared with the experimental reports from He et al. (2013). The results show that a critical particle concentration exists in the fine coal accumulation process in CBFB. When the fine coal particles are less than 11wt% in the bed, the flow pattern of medium phase is little affected and the coal particles are well mixed in the bed. However, when the particle concentration exceeds this threshold, the uniformity of bed density distribution is destroyed and particle stratification occurs along the bed height according to their density difference. Flow dynamics of the dense bed and main forces acting on the fine coal particles are analyzed to explain the underlying mechanism. With a large number of particles accumulated in the bed, the mixing effect of medium flow is suppressed. Motion of the fine coal particles is less dependent on the bed disturbance, instead, the particle gravity plays a decisive role in the particle distribution and results in the particle segregation in the fine coal accumulation process.

Interfacial Activity of Poly[oligo(ethylene oxide)–monomethyl ether methacrylate]-Grafted Silica Nanoparticles

The interfacial behavior of water-soluble poly[oligo(ethylene oxide) monomethyl ether methacrylate], grafted from 15-nm-diameter silica nanoparticles using a living atom-transfer radical polymerization technique, was examined for hexane and water interfaces. The polymer-grafted nanoparticles reduced the hexane–water interfacial tension from ∼50 to ∼20 mN/m at concentrations of silica in the range of 1–10 ppm. The hydrodynamic size of the dispersed hybrid nanoparticle, a function of the molecular weight of the polymer and grafting density, was the dominant variable in determining the critical particle concentration and efficacy of the hybrid nanoparticles in reducing the hexane–water interfacial tension. A simple phenomenological model is used to explain the strong dependence of the critical particle concentration on the effective hydrodynamic size of the nanoparticles. Water–hexane and water–squalene emulsions formed using 1000 ppm of hybrid nanoparticles were stable for more than 60 days.

Phase and steady shear behavior of dilute carbon black suspensions and carbon black stabilized emulsions.

We use para-amino benzoic acid terminated carbon black (CB) as a model particulate material to study the effect of salt-modulated attractive interactions on phase behavior and steady shear stresses in suspensions and particle-stabilized emulsions. Surprisingly, the suspension displayed a yield stress at a CB volume fraction of ϕCB = 0.008. The yield stress scaled with CB concentration with power law behavior; the power law exponent changed abruptly at a critical CB concentration, suggesting a substantial change in network structure. Cryogenic scanning electron microscopy revealed structural differences between the networks found in each scaling regime. Randomly oriented pores with thick CB boundaries were observed in the scaling region above the critical particle concentration, suggesting a strong gel network, and long, oriented pores were found in the scaling region below the critical particle concentration, suggesting a weak network influenced by an induced shear stress. These findings correlate with the existence of gels and transient networks. Transient networks break down under gravitational forces over time periods of 12-24 hours. The yield stresses of CB-gels containing oil emulsion droplets were found to scale with carbon black concentration similar to the CB-gels without oil. These results offer insight into salt-induced attractive colloidal networks and the difference in structure and yield-stress behavior between transient networks and gels. Furthermore, CB offers the ability to stabilize an oil phase in discrete droplets and contain them within a rigid network structure.

High interfacial activity of polymers "grafted through" functionalized iron oxide nanoparticle clusters.

The mechanism by which polymers, when grafted to inorganic nanoparticles, lower the interfacial tension at the oil-water interface is not well understood, despite the great interest in particle stabilized emulsions and foams. A simple and highly versatile free radical "grafting through" technique was used to bond high organic fractions (by weight) of poly(oligo(ethylene oxide) monomethyl ether methacrylate) onto iron oxide clusters, without the need for catalysts. In the resulting ∼1 μm hybrid particles, the inorganic cores and grafting architecture contribute to the high local concentration of grafted polymer chains to the dodecane/water interface to produce low interfacial tensions of only 0.003 w/v % (polymer and particle core). This "critical particle concentration" (CPC) for these hybrid inorganic/polymer amphiphilic particles to lower the interfacial tension by 36 mN/m was over 30-fold lower than the critical micelle concentration of the free polymer (without inorganic cores) to produce nearly the same interfacial tension. The low CPC is favored by the high adsorption energy (∼10(6) kBT) for the large ∼1 μm hybrid particles, the high local polymer concentration on the particles surfaces, and the ability of the deformable hybrid nanocluster cores as well as the polymer chains to conform to the interface. The nanocluster cores also increased the entanglement of the polymer chains in bulk DI water or synthetic seawater, producing a viscosity up to 35,000 cP at 0.01 s(-1), in contrast with only 600 cP for the free polymer. As a consequence of these interfacial and rheological properties, the hybrid particles stabilized oil-in-water emulsions at concentrations as low as 0.01 w/v %, with average drop sizes down to 30 μm. In contrast, the bulk viscosity was low for the free polymer, and it did not stabilize the emulsions. The ability to influence the interfacial activity and rheology of polymers upon grafting them to inorganic particles, including clusters, may be expected to be broadly applicable to stabilization of emulsions and foams.

Rheological properties and structural correlations in particle-in-oil gels

Solid, hydrophobic matrices are used to increase the viscoelasticity of pharmaceutical products, cosmetics and foods. We have developed a method for transforming low viscosity oils into highly elastic solids. The solid is derived from an oil-in-water emulsion template where silanised fumed silica nanoparticles are attached to the droplet surfaces. Removing the water by freeze drying drives the template into a three dimensional network of particles in oil. The gels have oil contents as high as 98% due to the low concentration of particles required. We show that the gel elasticity is a power law function of the particle concentration, consistent with theoretical predictions. A key finding is that the gels can show strain thickening, an increase in elasticity under large applied strains. This is due to a sharp increase in the characteristic size of the gel microstructure above a critical particle concentration.

Dissolution of coated microbubbles: The effect of nanoparticles and surfactant concentration

The ability of solid particles to stabilise emulsions is a well known phenomenon which has recently been demonstrated for the stabilisation of gas bubbles. In this paper, a new theoretical model is developed which describes how an adsorbed layer of solid nanoparticles modifies the interfacial tension and diffusivity of a gas bubble in a liquid and hence its stability. In agreement with experimental observations on microbubbles coated with 15nm diameter spherical gold particles, the results of simulations with the model indicate that the particles substantially decrease the rate at which bubble dissolution occurs and enables them to maintain a stable radius once a critical particle concentration has been reached.

Superhydrophobic polymer‐particle composite films produced using various particle sizes

Hydrophilic alumina (Al2O3) nanoparticles (25, 35, and 150 nm) are dispersed in different concentrations in solutions of a commercial hydrophobic poly(alkyl siloxane) (Silres BS‐290), and the suspensions are sprayed on glass surfaces. Static contact angles (θS), measured on surfaces of siloxane‐nanoparticle composite films that were prepared from dilute dispersions, increase rapidly with particle concentration. Composite films prepared from concentrated dispersions exhibit a maximum, constant θS (at saturation θS is 160°), which is not affected by the size of the particles. These films exhibit also very small contact angle hysteresis (5°), which is also independent of the particle size. Consequently, the same superhydrophobic character can be induced in siloxane films using nanoparticles, which can range from a few up to several tenths of nanometers. However, the particle size and more precisely the particle specific surface area affects dramatically the minimum critical particle concentration, which must be used in the dispersions to induce superhydrophobicity on the surface of the composite films, that is, to achieve θS = 150°. It is shown that critical particle concentration decreases exponentially with specific surface area. This result can be important for manufacturers of superhydrophobic surfaces who are interested in having a good control on the wettability of the composite films. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Formation and stability of nanoparticle-stabilised oil-in-water emulsions in a microfluidic chip

The formation and stability of drops in the presence of nanoparticles was studied in a microfluidic device to directly observe the early stages of Pickering emulsification (low interfacial coverage). We observed several key differences between oil droplet necking and rupture in aqueous phases of nanoparticles (methylated silica) and well-characterised surfactant systems. The presence of particles did not influence drop formation dynamics and thus the size of the drops generated. In addition, observations of in-channel drop stability shortly after formation (several milliseconds) indicated that particles in the aqueous phase slow film thinning processes, but do not prevent coalescence. In contrast, downstream collection and densification (at the microchannel outlet), showed that particle-stabilised drops do not coalesce for several weeks, above a critical particle concentration. The implications of our results for droplet microfluidics and our understanding of conventional emulsification systems are discussed.

UNDERSTANDING ELECTRIC INTERACTIONS IN SUSPENSIONS IN GRADIENT AC ELECTRIC FIELDS I: EXPERIMENTAL

When neutrally buoyant poly alpha olefin particles in corn oil were exposed to a gradient ac electric field generated by a spatially periodic electrode array, these particles experienced the negative dielectrophoresis and instability in all the suspensions of concentration range from 0.01% to 5% (v/v). One critical particle concentration was experimentally determined as 1% (v/v) below which the particles in corn oil were segregated to form island-like structures in the lower electric field regions; and above which, particles only formed straight stripes. The island-like structure was suspended in the lowest electric field area. Specially designed experiments with a suspension of 1.126% (v/v) confirmed that there exists particle instability. Anisotropic properties of electric interactions are responsible for particle instability in all the suspensions of different concentrations and island-like structures were formed only in the dilute suspensions in which the particle instability has enough space to be developed.

UNDERSTANDING ELECTRIC INTERACTIONS IN SUSPENSIONS IN GRADIENT AC ELECTRIC FIELDS II: SIMULATIONS AND APPLICATION EXPLORATION

We used numerical simulations of a continuous model and the molecular dynamics model to understand the particle instability, formation of island-like structures and existence of one critical particle concentration of 1% (v/v) for formation of island-like structures in the suspension in a gradient AC electric field reported in Paper I. The simulations of the continuous model show that the critical concentration of 1% (v/v) is the concentration of which the particles of a suspension are just fully filling the lower field region finally. According to the MD simulations, the particles instability does exist in the corn oil in a gradient AC electric field, anisotropic polarization interactions among the particles are responsible for the particle instability and have memory, and the memory is still kept even when the particles are transported by a dielectrophoresis force. The island-like structures can be regarded as signature of the memory. We explored possibilities to apply our findings in biomedical fields.