Range Of Volume Fractions Research Articles

Dynamic and phase transition studies of ionic surfactant-stabilized oil/water microemulsion: Effects of volume fraction, polymer grafting, and temperature

In this work, we study the dynamic/phase transition relationship of a system composed of spherical particles of oil/water microemulsion, stabilised by an ionic surfactant based on cetylpyridinium chloride (CpCl) and an octanol-based cosurfactant, and dispersed in salt water. We examine a large range of volume fractions Φ. To do this, we use molecular dynamics simulations with an appropriate interaction potential that accounts for Van der Waals and electrostatic interactions. We also graft different numbers of dodecyl-(polyethylene oxide)227-dodecyltriblock copolymers onto the microemulsion nanodroplets, which we denote (n(D−PEO227−D)), where n varies from 0 to 12. Specifically, we treat the dynamic properties, using the mean square displacement (MSD) and diffusion coefficients, and then use Arrhenius law to determine the activation energy. In our study, we vary three main parameters: the volume fraction, the number of polymer added to the n(D−PEO227−D) microemulsion, and the temperature. The result shows a transition from the sol to the gel state of the bare microemulsion as the volume fraction increases or as the temperature decreases. Also, it proves that when a D-PEO-D polymer is added to the microemulsion, the system rapidly changes its state either as the volume fraction Φ increases or as the temperature T decreases. We also calculate the activation energy of the bare particles in the microemulsion at different volume fractions (ϕ) using the Arrhenius equation.

Effect of the volume fraction of nanocrystals on the mechanical properties of (Fe0·9Ni0.1)86B14 amorphous/nanocrystalline alloy

The effect of the volume fraction of nanocrystals on the macroscopic mechanical properties and microscopic atomic structure of Fe-based nanocrystalline alloys, as well as the relationship between the two, is an urgent issue to be explored. Seven nanocrystalline alloys with different volume fractions of nanocrystals were formed by annealing treatment of (Fe0·9Ni0.1)86B14 amorphous precursor. Through hardness, flat plate bending, and nanoindentation experiments, it is found that when the volume fraction of nanocrystals reaches the range of 45–55 %, there is an abrupt change in the macroscopic mechanical properties. Specifically, when the volume fraction is less than this range, the properties inherit the amorphous matrix, however, larger than this range, the properties are dominated by precipitated nanocrystalline phases. Meanwhile, based on the molecular dynamics simulation method, seven Fe90Ni10 amorphous nanocrystalline models with different volume fractions of body-centered cubic nanocrystals are established, and the deformation mechanism of models and the evolution of their microstructures during the nanoindentation process are obtained intuitively. Moreover, it is further revealed that the significant changes in the Voronoi polyhedral index, which represents the microscopic atomic structure in this range of nanocrystal volume fractions, are the main reason for the abrupt changes in the mechanical properties at the macroscopic level.

Analysis of parabolic trough solar collector thermal efficiency with application of a graphene oxide nanosheet‐based nanofluid

AbstractNowadays, clean energy production and reconciliation with nature is one of the best solutions known to rectify the global warming issue. Solar energy, as a clean and green one, has recently been drawing scientists' attention to itself more than ever. Applying parabolic trough solar collectors (PTSCs) is one of the state‐of‐the‐art ways to extract energy from the sun. As one of the most interesting research topics, the thermal efficiency enhancement of PTSCs is studied. The current study demonstrates how the thermal efficiency of PTSCs is enhanced through the application of graphene oxide (GO) nanosheets, as an inexpensive nanomaterial with superb thermal conductivity and unique structure, in thermal oil, namely, Behran oil, as heat transfer fluid, within the effective volume fraction range of 0.05. The above‐mentioned analysis is based on the theoretical calculations performed through a mathematical model based on the Taylor series approximation. All the calculations are performed with respect to a PTSC unit of a solar–thermal power plant situated in Shiraz, Iran, as the research case study. In addition, the Nan et al. model is used to analytically predict how the increase in the volume fraction of GO nanosheets raises the thermal conductivity and consequently increases the convection heat transfer coefficient of the nanofluid, leading to the thermal efficiency enhancement of PTSCs. The results reveal a maximum thermal efficiency of 71.10% for the volume fraction of 0.05. In comparison to the thermal efficiency of the real‐world case‐study mentioned above with pure thermal oil, that is, 67.71%, the thermal efficiency enhancement by about 5.5%, is achieved. Moreover, it is discussed how the thermal efficiency achieved from GO nanosheets surpasses the ones obtained from the application of particle shape nanomaterials, or carbon nanotubes in the same conditions.

A theoretical and experimental investigation of continuous oil–water gravity separation

In this study, we have developed a mathematical model for a three-phase separator. The model consists of two sections: the inlet section and the separation section, separated by a perforated calming baffle. In the inlet section, two dispersion layers undergo droplet size evolution due to turbulent breakage and coalescence, described by a spatially homogeneous PBE. In the separation section, the two dispersion layers flow alongside each other and interact at an interface. The volumetric flow and velocity profiles are influenced by interfacial coalescence, with considerations for plug and laminar flow assumptions. The model incorporates droplet gravity-driven transport using the Kumar and Hartland model, binary and interfacial coalescence employing a film drainage model, and an effective diffusion term to account for the formation of the dense packed layer which ensures a physical volume fraction range of 0–1. Steady-state and transient numerical solvers are developed to solve the resulting advection–diffusion equations. Additionally, a series of experiments were conducted using a lab-scale multi-parallel pipes separator to investigate the impact of varying volume fractions and flow rates on the separation efficiency of the equipment. The model results are compared with the experimental data which shows relatively good agreement.

Micropolar effects on the effective shear viscosity of nanofluids

The modified size-dependent Einstein's and Brinkman's solutions are established for the effective shear viscosity of rigid particle suspensions taking into account the micropolar effects in the base fluid. Solutions are obtained based on the homogenization approach and allow us to take into account the influence of the particle size. Two non-classical parameters arise in the considered micropolar solutions: the length scale parameter and the coupling (micropolarity) number of the base fluid. The solutions developed are validated using tests performed with polydimethylsiloxane based TiO2 nanofluids as well as other published data on the size-dependent shear viscosity of different nanofluids. Good agreement between the predictions and the experimental data is established across a wide range of volume fractions and size of nanoparticles. The possibility for unique identification (at given temperature) of the micropolar parameters of the base fluids is shown. Temperature-dependent values of non-classical rotational and spin viscosities of polydimethylsiloxane, ethylene glycol, and water are evaluated.

Heat Transfer and Entropy Generation for Mixed Convection of Al2O3–Water Nanofluid in a Lid-Driven Square Cavity with a Concentric Square Blockage

The present numerical investigation is focused on analyzing the characteristics of steady laminar mixed convection flow in a lid-driven square cavity, specifically considering the utilization of Al2O3–water nanofluid. The Al2O3–water nanofluid is assumed to be Newtonian and incompressible. Within the cavity, a square blockage is positioned at its center, which is subjected to isothermal heating. The blockage ratio of the square is B = 1/4, and the Grashof number is Gr = 100. The walls of the cavity are maintained at a constant temperature, Tc, while the square blockage remains at a constant temperature, Th. The primary objective of this study is to investigate the flow and heat transfer mechanisms, as well as the entropy generation within the cavity. This investigation is conducted for a range of Richardson numbers (0.01 ≤ Ri ≤ 100) and volume fractions of the nanofluid (0 ≤ ϕ ≤ 0.05). Several parameters are obtained and analyzed, including streamlines, isotherms, velocity variations on the vertical and horizontal midplanes, local Nusselt number variations on the surfaces of the square blockage, the average Nusselt number on the square blockage, and the total dimensionless entropy generation of the system. The results of the investigation revealed that both the average Nusselt number on the square blockage and the total dimensionless entropy generation of the system exhibit an increasing trend with an increasing volume fraction of the nanofluid and a decreasing Richardson number. Furthermore, correlations for the average Nusselt number and the total dimensionless entropy generation with the Richardson number, and the nanofluid volume fraction are derived.

Optical tunability with superlattice hyperbolic metamaterial coatings

Optical tunability is demonstrated with multi-metal hyperbolic metamaterial (HMM) structures on varying substrate surfaces. A systematic uniaxial modeling methodology is adapted from classical approaches to extract the anisotropic permittivity of the films to identify epsilon-near-zero (ENZ) behavior over a wide range of metal volume fractions (φ). The anisotropic model accuracy is quantified by a mean squared error (MSE) with the presented modeling routine resulting in a MSE < 35 for all samples. The optical model thicknesses were verified with transmission electron microscopy (TEM) imaging and measurements. This study also demonstrates the ability to tune the optical responses in the visible-to-infrared frequencies with surface microtexturing and applied strain with HMM coatings on flexible Kapton substrates. Furthermore, the structured films and modeling procedure lay the groundwork for future studies on coupling the anisotropic optical and thermal properties for control over advanced multifunctional thin-film coatings.

Poly(ethylene oxide)- and Polyzwitterion-Based Thermoplastic Elastomers for Solid Electrolytes.

In this article, ABA triblock copolymer (tri-BCP) thermoplastic elastomers with poly(ethylene oxide) (PEO) middle block and polyzwitterionic poly(4-vinylpyridine) propane-1-sulfonate (PVPS) outer blocks were synthesized. The PVPS-b-PEO-b-PVPS tri-BCPs were doped with lithium bis-(trifluoromethane-sulfonyl) imide (LiTFSI) and used as solid polyelectrolytes (SPEs). The thermal properties and microphase separation behavior of the tri-BCP/LiTFSI hybrids were studied. Small-angle X-ray scattering (SAXS) results revealed that all tri-BCPs formed asymmetric lamellar structures in the range of PVPS volume fractions from 12.9% to 26.1%. The microphase separation strength was enhanced with increasing the PVPS fraction (fPVPS) but was weakened as the doping ratio increased, which affected the thermal properties of the hybrids, such as melting temperature and glass transition temperature, to some extent. As compared with the PEO/LiTFSI hybrids, the PVPS-b-PEO-b-PVPS/LiTFSI hybrids could achieve both higher modulus and higher ionic conductivity, which were attributed to the physical crosslinking and the assistance in dissociation of Li+ ions by the PVPS blocks, respectively. On the basis of excellent electrical and mechanical performances, the PVPS-b-PEO-b-PVPS/LiTFSI hybrids can potentially be used as solid electrolytes in lithium-ion batteries.

Modelling effective thermal conductivity in polymer composites: A simple cubic structure approach

In this study, we propose the simple cubic model, a distinctive thermal-conductive mathematics for modelling the effective thermal conductivity in polymer composites, taking both filler size and interface thermal resistance into account. This model is constructed by delineating heat transport paths within simple cubic structural units, leveraging principles involving Fourier's law, minimum thermal resistance, specific equivalent thermal conductivity, and thermal resistance network. Demonstrating broad applicability, the simple cubic model accurately predicts effective thermal conductivity within a 0–40 % volume fraction range of filler in polymer composites, maintaining less than 15 % error. Its robustness is validated across over 100 experimental datasets, encompassing various polymer matrices and granular filler types. This extensive validation underscores the model's efficacy, both with our experimental data and existing literature. The simple cubic model's insightful predictions make it valuable in designing and preparing thermally conductive polymer composites.

A microstructure-based parameterization of the effective anisotropic elasticity tensor of snow, firn, and bubbly ice

Abstract. Quantifying the link between microstructure and effective elastic properties of snow, firn, and bubbly ice is essential for many applications in cryospheric sciences. The microstructure of snow and ice can be characterized by different types of fabrics (crystallographic and geometrical), which give rise to macroscopically anisotropic elastic behavior. While the impact of the crystallographic fabric has been extensively studied in deep firn, the present work investigates the influence of the geometrical fabric over the entire range of possible volume fractions. To this end, we have computed the effective elasticity tensor of snow, firn, and ice by finite-element simulations based on 391 X-ray tomography images comprising samples from the laboratory, the Alps, Greenland, and Antarctica. We employed a variant of Eshelby's tensor that has been previously utilized for the parameterization of thermal and dielectric properties of snow and utilized Hashin–Shtrikman bounds to capture the nonlinear interplay between density and geometrical anisotropy. From that we derive a closed-form parameterization for all components of the (transverse isotropic) elasticity tensor for all volume fractions using two fit parameters per tensor component. Finally, we used the Thomsen parameter to compare the geometrical anisotropy to the maximal theoretical crystallographic anisotropy in bubbly ice. While the geometrical anisotropy clearly dominates up to ice volume fractions of ϕ≈0.7, a thorough understanding of elasticity in bubbly ice may require a coupled elastic theory that includes geometrical and crystallographic anisotropy.

Large strain micromechanics of thermoplastic elastomers with random microstructures

Thermoplastic polyurethanes (TPU) are block copolymeric materials composed of plastomeric “hard” and elastomeric “soft” domains, by which they exhibit highly resilient yet dissipative large deformation features depending on volume fractions and microstructures of the two distinct domains. Here, we develop a new methodology to explore the microscopic deformation mechanisms in TPU materials with highly disordered microstructures. We propose new micromechanical models for randomly dispersed (or occluded) as well as randomly continuous hard domains (and mixtures of both dispersed and continuous hard domains), each within a continuous soft structure as widely found in representative TPU materials over a wide range of volume fractions, vhard = 26.9% to 52.2%. The micromechanical modeling results are compared to experimental data on the macroscopic large strain behaviors reported previously (Cho et al., 2017). We explore the role of the dispersed vs. continuous nature of the geometric features of the random microstructures on shape recovery and energy dissipation at the microstructural level in these phase-separated copolymeric materials.

On the effective properties of random microstructures and cross-property connections for them

Effective elastic and conductive properties of 2-D random (“disordered”) mixtures of several types are examined by computational means. It is found that an “equivalent” material of simple microgeometry – a continuous matrix with elliptical inhomogeneities – can be identified, that matches both the elastic and the conductive properties, in the entire range of property contrast between constituents. Moreover, the ellipse eccentricities are almost the same for different types of the random mixtures in the volume fraction range (0.3 – 0.7); in this range, there is no need in specifying the type of a mixture, as far as the effective properties are concerned. It is also found that the effective properties of the considered random mixtures are well described by the Mori-Tanaka-Benveniste model (in spite of the fact that this model was not intended for them).We also examined the effect of inhomogeneity interactions in a matrix composite on the cross-property connections between the elastic and conductive properties. Whereas the interactions generally produce strong effect on each of the properties, their effect on the connections is negligible (the latter can be taken from the non-interaction approximation).It is argued that most findings related to 2-D random mixtures should apply to 3-D ones as well.

The influence of magneto-hydrodynamics and vortex generators on nanofluids heat transfer

This paper investigates the effects of a vortex generator (VG) and magneto-hydrodynamics (MHD) on the thermal properties of nanofluids in a microchannel. A variety of test scenarios within the laminar flow regimes are numerically examined: nanofluids in a hot-walled simple channel (SC); nanofluids in a heated-walled channel where a circular cylinder is embedded within the channel and functions as a vortex generator (VG); nanofluids in a heated-walled channel that incorporates both a vortex generator and magneto-hydrodynamics (VG-MHD). The channel has a circular cylinder with a diameter of D that is fixed inside the channel with various gap ratios (GR = G/D) ranging from 0.5 to 4.0. Numerical investigations for laminar flow with Re ≤ 1,000 are carried out. The nanoparticle volume fractions range from 0 % to 7 %, and the magnetic field is set at 0.05 T. The best heat transmission conditions with the lowest skin friction coefficient are evaluated for the optimal GR. It is found that heat transfer is enhanced by approximately 20 % when MHD and VG effects are employed, in contrast to a traditional channel that does not utilize the MHD effect.

Characterization of multiphase flow through Venturi nozzle using gamma-ray tomography

Venturi-based differential pressure flow meters have proven to be robust and well suited to measure the flowrate of multiphase flow in combination with other measurement techniques. However, important challenges remain in order to reduce the effect of flow regime dependent measurement uncertainties from non-homogeneous flow.Understanding the complexities of multiphase flow through a Venturi is critical, not only for the Venturi flow measurement but also for the potential implications it might have on adjacent measurements affected by the constriction-induced flow perturbations.In this study, we examine the evolution of multiphase flow through a vertically oriented Venturi situated downstream of a T-bend, with a particular emphasis on the effects this might have on associated measurements within a multiphase metering context. Using Gamma-ray tomography, we conducted measurements at the inlet, throat, outlet, and downstream of the Venturi across a wide range of flow rates and Gas Volume Fractions (GVFs). We evaluated gas fraction (GF), slip, and cross-sectional distribution, quantified using measures of asymmetry and annularity.Our findings suggest that deviations between GF and GVF, relative slip velocity, annularity, and asymmetry are generally less at the outlet and downstream of the Venturi compared to the inlet and throat. Notably, annularity exhibits a greater impact than asymmetry on the estimation of bulk fractions from cord measurements.Overall, the study suggests that there may be more favorable conditions for measurements that require a homogeneous mix and less difference between GF and GVF at the outlet or a short distance downstream of the Venturi. However, despite the inlet results showing larger deviations due to inhomogeneous flow compared to the outlet and downstream, these results demonstrate a more predictable pattern in line with predictive models, offering potential benefits for the application of corrective models.

Experimental study of a dense stream of particles impacting on an inclined surface

We present measurements of the impact process of gravity-driven flows of particles against inclined surfaces for a range of particle loadings in the four-way coupled regime. These were investigated with particle image velocimetry (PIV) for a range of particle curtain thicknesses, volume fractions, velocities and mass flow rates using a series of hoppers of various aperture sizes, following impact on a steel plate at a range of angles from 15° to 75°. In addition, micro-shadowgraphy was used to provide new details of the region of impact, providing the first direct evidence of the formation of layer of particles that slide along the surface for sufficiently high particle volume fractions. Statistical measurements of particle impact and rebound velocities, together with rebound angle and coefficient of restitution, were obtained from the PIV analysis, which revealed that an increase in particle loading leads to increase in the probability that a layer of particles at the surface is formed at the point of impact. This layer acts to absorb energy for all impact angles, thereby influencing the rebound processes. For impact angles close to the normal direction the layer also increases the range of rebound angles, while it causes particles to slide along the surface as a chute-like flow for large inclination angles.

Micromechanical Analysis of GFRP Composite with Micro-Level Defects

Fiber-reinforced plastic (FRP) composites are subjected to micro-level defects such as fiber-matrix debond and/or matrix cracks after a period of their service due to the increasing brittleness of matrix material. Prediction of the degraded elastic properties of a lamina through micromechanical studies by incorporating micro-level defects gives an idea of the health condition of such structures. Due to the limitations of classical mathematical approaches in solving complex structures, numerical mathematical methods like the finite element method (FEM) can be employed. The present investigation deals with the micromechanical analysis of Glass fiber-reinforced plastic (GFRP) composite with micro-level defects to predict some of the elastic properties. The composite is idealized as an array of square unit cells, and the micromechanical behavior of one such unit cell is simulated in ANSYS software using the three-dimensional finite element method to predict Young’s moduli and Poisson’s ratios in principal material directions. The converged finite element solution for longitudinal modulus is validated by the rule of mixtures and the other properties using the Maxwell–Betti reciprocal theorem. Variations of Young’s moduli and Poisson’s ratios due to an incremental internal failure of composite such as low-level, medium-level, and high-level defects at an expected range of fiber volume fractions (50% - 60%) are evaluated and estimated the percentage degradation with respect to a corresponding defect-free composite.

Investigation of forced convection of a novel hybrid nanofluid containing NEPCM in a square microchannel: Application of single-phase and Eulerian-Eulerian two-phase models

In the present study, laminar forced convection flow and heat transfer of novel hybrid nanofluid of Al 2 O 3 -n-octadecane/water through a horizontal microchannel under a constant wall heat flux condition are investigated. N-octadecane is regarded as a nano-encapsulated phase change material (NEPCM). Simulations are performed utilizing single-phase and Eulerian-Eulerian two-phase models. Governing equations are discretized by finite volume method and then solved using SIMPLE algorithm. Effects of nanoparticles volume fraction ( φ ), Reynolds number ( Re ), and melting range ( T mr ) on thermal and hydrodynamic parameters of hybrid nanofluid are evaluated. It is shown that predictions by Eulerian-Eulerian approach are more accurate than those by single-phase approach when compared to available experimental data. Addition of Al 2 O 3 and n-octadecane nanoparticles to water-based fluid leads to a reduction in fluid and wall temperatures, which is intensified at higher φ and Re . Also, these nanoparticles do not have a significant effect on hydrodynamic development of flow, while they delay its thermal development. NEPCM with a higher T mr only slightly improves thermal performance of hybrid nanofluid, which is more noticeable in single-phase procedure. Total efficiency of hybrid nanofluid ( η hnf ) is amplified by raising φ for both approaches. This augmentation is more evident in Eulerian-Eulerian model due to better thermal and hydrodynamic performances. Maximum increases in η hnf concerning single-phase and Eulerian-Eulerian models are 27% and 60%, respectively, occurring at φ Al 2 O 3 = 1 % and φ n ‐ octadecane = 10 % . Therefore, this type of hybrid nanofluids, because of its enhanced thermo-physical properties, can be considered as a suitable candidate for thermal energy storage, heat transfer, and renewable energy applications.

Optical absorbance profilometry for tracking time-resolved particle redistribution in high volume fraction colloidal droplets

The distribution of components within colloidal suspensions is important in many complex biological and industrial fluids. A convenient method of measuring such distributions in low-volume-fraction suspensions is that of optical absorbance. Here we introduce a time-dependent validity criterion allowing extended use of optical absorbance to track colloidal distribution in high volume fraction suspensions. We define our validity criterion and show its use on a range of volume fractions from 15 to 55%, and also on larger micron sized particles, common for biological cells. Within the validity criterion, we establish the evaporative time duration in which the material’s intrinsic coefficient of extinction can be treated as constant. This method enables rapid, low-cost, time-based study of the advective flow of suspended particulates, enabling advection to be straightforwardly measured from digital imaging. The residue profile predicted using our method in two test systems is compared with conventional laser profilometry measurements of the final evaporated residue, with good agreement at most radial positions.

Numerical simulations of proppant transportation in cryogenic fluids: Implications on liquid helium and liquid nitrogen fracturing for subsurface hydrogen storage

The over dependence on fossil fuels for human energy requirements together with the resultant adverse environmental effects in the form of greenhouse gas discharges has redirected our attention towards renewable energy sources. Researchers have identified hydrogen, a non-carbonaceous energy source holding the capacity to substitute fossil fuels, as a viable fuel option that has the potential to be generated utilizing eco-friendly techniques. Studies have identified underground sites that are operational or have the potential to be used for hydrogen storage. Shale formations, characterized by their low permeability, offer promising opportunities for underground hydrogen storage. These formations require stimulation techniques to generate flow channels. Pumping frac-fluid into these formations at high pressure induces fractures in them and the engineered fractures are supported by the proppants injected along with the fluid. Propped fractures form a vital conduit in unconventional gas reservoirs, which are a potential medium for storage of hydrogen. Cryogenic fracturing is an innovative approach that aims to enhance and broaden the capabilities of conventional hydraulic fracturing processes. The transmission and settlement of proppants are influenced by certain critical aspects including their density, size and volume fraction and fluid velocity, which are investigated in this contribution. This study incorporates water and cryogenic fluids like liquid nitrogen (LN2) and liquid helium (LHe) as fracturing fluids. The primary objective of this effort is to analyze proppant transportation phenomenon and the key influential factors in LN2 and LHe. The proppant volume fraction contour, equilibrium dune level (EqDL) and dune height (EqDH) data are illustrated in this research for better understanding of proppant migration. It was observed that when the fracturing fluid is given a higher velocity, the proppant grains experience increased drag force, causing them to penetrate deeper into the fracture. The desired range of proppant volume fraction for improved grain transmission was determined as 0.45 to 0.50 and the critical proppant density that significantly affected the EqDL as 187.2839 lb/ft3.

Pairing-specific microstructure in depletion gels of bidisperse colloids.

We report the ensemble-averaged and pairing-specific network microstructure formed by short-range depletion attractions in hard sphere-like colloidal systems. Gelation is induced by adding polystyrene molecules at a fixed concentration to colloids with different colloid bidispersity ratios (α = 1, 0.72, and 0.60) across a range of volume fractions (0.10 ≤ ϕ ≤ 0.40). 3D confocal microscopy imaging combined with a scale-invariant feature transform algorithm show that monodisperse colloids pack more efficiently, whereas increasing the size disparity leads to looser, more disordered, and sub-isostatic packings. Categorizing the structures formed by small and large particles reveal that certain cluster configurations may be favored due to the complex interplay between the differences in particle surface areas and attractive potentials. These pairwise bonds assemble to affect the density of tetrahedral and poly-tetrahedral clusters in bidisperse systems. With the exception of non-percolating samples at ϕ = 0.10, increasing the gel volume fraction leads to an increase in the number of nearest neighbors. However, the internal density within each cluster decreases, possibly due to kinetic arrest from the deeper potential wells of tetrahedral clusters at low volume fractions in which vertices are primarily made out of larger particles.