Large 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.

Discontinuous shear thickening (DST) transition with spherical iron particles coated by adsorbed brush polymer

We explore the rheology of very concentrated (0.55 < Φ < 0.67) suspensions of carbonyl iron particles coated by a small polymer. A strong discontinuous shear thickening (DST) is observed in a large range of volume fraction presenting some specific behaviors in comparison with other systems. In particular, the DST transition can appear suddenly without being preceded by shear thickening. The presence of a frictional network of particles is confirmed by a simultaneous measurement of the electric resistance of the suspension and of the rheological curve. Using the Wyart–Cates (W–C) model, we show that with increasing the volume fraction, the fraction of frictional contacts increases more quickly with the stress, contrary to the prediction of numerical simulations. The same behavior is observed in the presence of a magnetic field with a strong increase in the viscosity before the DST transition. We interpret this behavior by the interpenetration of the polymer layer under the effect of the shear stress—and of the magnetic stress—followed by the expulsion of the polymer out of the surfaces between two particles in contact. We point out that above the DST transition, we do not observe a jamming in the range of volume fraction, whereas it is predicted by the W–C model. The frictional contacts are created by a shear stress and not by a static stress, so in the absence of shear flow, the polymer can adsorb again on the surface and lubricate the frictional contacts. We thus predict an asymptotic non-zero shear rate reproducing the experimental behavior.

Elastic response of hollow truss lattice micro-architectures

Elastic meta-materials, which we will treat herein as synonymous with elastic micro-architected materials, derive their unique combination of properties from the fine scale geometry of their solid and void regions. Recent advances in additive manufacturing have made the fabrication of such micro-architected materials feasible, and have driven interest in their properties. We consider the class of elastic meta-materials whose micro-architectures are composed of a network of straight struts connected at nodes arranged within a repeating unit cell; the octet truss is one well-known example of such truss lattices. Heretofore, the majority of work characterizing such truss lattices has considered solid struts and has been based on rod theory, a simplification of continuum elasticity which is accurate in the limit of low relative densities. In this paper, we use full continuum theory, solved with finite element analysis on adaptively refined meshes, to characterize the elastic performance of seven truss lattices with cubic geometric symmetry, and whose struts and nodes are hollow; we consider a wide range of strut wall thicknesses and truss relative densities. Varying the wall thickness provides an additional dimension of control, so that stiffness and anisotropy can, to an extent, be decoupled from the relative density of a given truss lattice. We show that a truss’ stiffness can be increased at fixed relative density, with bend-dominated truss lattices showing significantly greater improvement than stretch-dominated designs. Increases in stiffness by a factor of greater than five are observed, and increases by a factor of 100 or more are obtainable. Bend-dominated structures with hollow struts can be found that are stiffer than stretch-dominated ones at nearly all relative densities, contradicting a common rule of thumb. For some trusses, including the octet truss, choosing the wall thickness appropriately allows one to obtain isotropic response over a large range of volume fractions. We use topology optimization to find maximally stiff multiscale structures comprised of micro-architected materials and find that all the trusses we consider perform similarly, with anisotropic trusses resulting in slightly stiffer structures for a given load.

Combined Lattice–Boltzmann and rigid-body method for simulations of shear-thickening dense suspensions of hard particles

We present a high-fidelity simulation model for dense suspensions of spherical and non-spherical particles suspended in a Lattice–Boltzmann Method (LBM) based fluid. The non-spherical particles are composed of an arbitrary number of overlapping spheres of different sizes and arbitrary relative positions in the particle reference frame which stay fixed during the simulation. This approach allows to approximate a wide range of rigid particle shapes. Fluid Structure Interactions (FSI) are realized using a hybrid of immersed-boundary methods and bounce-back schemes, that employs coupling coefficients dependent upon particle overlap with the fluid lattice, resulting in smooth hydrodynamic interactions when particles move over the lattice. Numerical lubrication breakdown is overcome by applying appropriate corrections for small inter-particle gaps and hydrodynamic interactions are resolved down to scales much smaller than the LBM lattice spacing. For improved numerical stability in the limit of stiff particle-particle interactions, a generalized-α method together with a dynamically refined time-step is used for rigid body dynamics. An unbounded shear flow with large shear rates is realized by splitting the computational domain into multiple co-moving reference frames coupled through Galilean transformations of both fluid and particle phase. For fast simulations of hundreds of particles over physical times-spans of seconds, the LBM sub-model and FSI computations are accelerated on GPUs and MPI/OpenMP are used to parallelize the computation over networked/shared-memory resources. All these innovations together lead to a very powerful simulation environment for sheared dense suspensions, facilitating study of rheology close to the jamming limit. In this paper we present benchmark results and simulations of continuous and discontinuous shear-thickening of dense polydisperse frictional suspensions, demonstrating the accuracy and predictive power of the model over a large range of volume fractions of suspended particles and a large range of shear rates.

A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in Newtonian fluids

We propose a new, minimal tensorial model attempting to clearly represent the role of microstructure on the viscosity of noncolloidal suspensions of rigid particles. Qualitatively, this model proves capable of reproducing several of the main rheological trends exhibited by concentrated suspensions: Anisotropic and fore-aft asymmetric microstructure in simple shear and transient relaxation of the microstructure toward its stationary state. The model includes only few constitutive parameters, with clear physical meaning, that can be identified from comparisons with experimental data. Hence, quantitative predictions of the complex transient evolution of apparent viscosity observed after shear reversals are reproduced for a large range of volume fractions. Comparisons with microstructural data show that not only the depletion angle, but the pair distribution function, are well predicted. To our knowledge, it is the first time that a microstructure-based rheological model is successfully compared to such a wide experimental dataset.We propose a new, minimal tensorial model attempting to clearly represent the role of microstructure on the viscosity of noncolloidal suspensions of rigid particles. Qualitatively, this model proves capable of reproducing several of the main rheological trends exhibited by concentrated suspensions: Anisotropic and fore-aft asymmetric microstructure in simple shear and transient relaxation of the microstructure toward its stationary state. The model includes only few constitutive parameters, with clear physical meaning, that can be identified from comparisons with experimental data. Hence, quantitative predictions of the complex transient evolution of apparent viscosity observed after shear reversals are reproduced for a large range of volume fractions. Comparisons with microstructural data show that not only the depletion angle, but the pair distribution function, are well predicted. To our knowledge, it is the first time that a microstructure-based rheological model is successfully compared to such a wid...

Normal stress differences, their origin and constitutive relations for a sheared granular fluid

The rheology of the steady uniform shear flow of smooth inelastic spheres is analysed by choosing the anisotropic/triaxial Gaussian as the single-particle distribution function. An exact solution of the balance equation for the second-moment tensor of velocity fluctuations, truncated at the ‘Burnett order’ (second order in the shear rate), is derived, leading to analytical expressions for the first and second ($\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$) normal stress differences and other transport coefficients as functions of density (i.e. the volume fraction of particles), restitution coefficient and other control parameters. Moreover, the perturbation solution at fourth order in the shear rate is obtained which helped to assess the range of validity of Burnett-order constitutive relations. Theoretical expressions for both $\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$ and those for pressure and shear viscosity agree well with particle simulation data for the uniform shear flow of inelastic hard spheres for a large range of volume fractions spanning from the dilute regime to close to the freezing-point density (${\it\nu}\sim 0.5$). While the first normal stress difference $\unicode[STIX]{x1D615}_{1}$ is found to be positive in the dilute limit and decreases monotonically to zero in the dense limit, the second normal stress difference $\unicode[STIX]{x1D615}_{2}$ is negative and positive in the dilute and dense limits, respectively, and undergoes a sign change at a finite density due to the sign change of its kinetic component. It is shown that the origin of $\unicode[STIX]{x1D615}_{1}$ is tied to the non-coaxiality (${\it\phi}\neq 0$) between the eigendirections of the second-moment tensor $\unicode[STIX]{x1D648}$ and those of the shear tensor $\unicode[STIX]{x1D63F}$. In contrast, the origin of $\unicode[STIX]{x1D615}_{2}$ in the dilute limit is tied to the ‘excess’ temperature ($T_{z}^{ex}=T-T_{z}$, where $T_{z}$ and $T$ are the $z$-component and the average of the granular temperature, respectively) along the mean vorticity ($z$) direction, whereas its origin in the dense limit is tied to the imposed shear field.

Acid-induced aggregation and gelation of natural rubber latex particles

Coagulation of natural rubber latex suspensions into an elastic gel is the first step of their processing into rubber. We studied this transition under controlled acidification conditions with the aim of identifying the main parameters controlling gel formation. The onset of aggregation and the percolation events observed during continuous acidification were monitored on a large range of volume fractions by a combination of light-scattering techniques adapted to the different degrees of suspension opacity (namely, diffusing wave spectroscopy, static light scattering and turbidimetry) and by rheology. We consequently established the state diagram of NRL particles in the pH–ϕv space during acidification. Within this diagram, we identified three states: a suspension, a two-phase macroscopically separated system in between a gel and a suspension, and a gel. The rheological properties of the gels were characterized as a function of the volume fraction ϕv. The elastic modulus scale with ϕv3.35, it shows remarkable consistency independently of the acidification kinetics and final pH.

The Impact of Blue Inorganic Pigments on the Microwave Electrical Properties of Polymer Composites

We present the results of the measurement of complex dielectric permittivity, in the microwave frequency region, on glass reinforced polybutylene terephthalate (PBT) with blue inorganic pigments. The cavity resonant method had been used in order to measure the shift in the resonant frequency of the cavity, caused by the insertion of a sample, which can be related to the real part of the complex permittivity. Also, the quality factor of the cavity decreases with the insertion of a sample. The changes in the inverse of this quality factor give the imaginary part. In order to predict the dielectric behavior of this composite, we had developed a program of numerical simulation to calculate the complex permittivity of the inclusion. By using some of dielectric mixture laws (Maxwell-Wagner-Sillars, Hanai, Looyenga, inverse and direct Wiener, and Bruggemann), we can predict the dielectric behavior of the composite in a large range of volume fraction of inclusions.

Demixing and orientational ordering in mixtures of rectangular particles

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyze the stability of phases with orientational order and the demixing phase behavior of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilized, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares, in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard disks or discorectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behavior, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.

A mean-field description of two-phase flows with phase changes

A new version of the two-fluid model is developed, specially devoted to liquid–vapour two-phase mixtures, but also relevant to liquid-gas and liquid–liquid mixtures. It is well-known that, over a large range of volume fractions, liquid–vapour mixtures behave as dispersions of particles in a carrier fluid. But the “particles” belong to one phase at the beginning of the phase change, and to the second phase at the end. Within the present model, the dispersed phase is not prescribed at the outset but is merely the one with the lower volume fraction. To simplify the issue, surface tension and interfacial properties are neglected. However, the differences of pressure, temperature and velocity between the two phases are taken into account. The exchanges of mass, momentum and energy between phases are split into a “mean-field” part corresponding to the average conditions imposed by the whole mixture on the dispersed phase, and a part specifically due to the disturbances created by the particles. Constraints on constitutive relations are obtained from the overall dissipation rate, and result in a closed set of seven equations for seven state variables including one volume fraction. We insist on the general form of the equations but not on the details of the closure relations. The limits of this simple model are clearly stated, and we discuss possible improvements, including a better account of small-scale kinetic phenomena, as well as an eighth equation for the density of interfaces.

Fabrication process and electrical behavior of novel pressure-sensitive composites

Abstract A novel route was developed to fabricate a new pressure-sensitive composite by dispersing homogeneously conductive carbon particles in an insulating silicone rubber matrix. The composites showed a gradual change in electrical resistivity with applied pressure within percolation threshold region at a constant temperature. This type of gradual fall of resistivity with applied pressure is very important to fabricate pressure sensors. Various amounts of carbon particles were dispersed in a rubber matrix to understand the effect of volume fraction of conductive filler with applying external pressure on resistivity. A quantitative general effective media (GEM) theory was used to understand the resistivity of carbon–rubber composites system over a large range of volume fraction of carbon with applied pressure. The use of two different sizes of silicon rubber particles showed a significant effect in gradual fall of resistivity with applied pressure in the narrow range of percolation threshold. However, a large variation in resistivity from 1st measuring to 10th measuring was observed. A significant improvement in successive measuring of resistivity variation from 1st measuring to 10th measuring was observed when composites were fabricated in hexane solvent media. Finally, nano-sized Al2O3 was dispersed to control the resistivity variation upon successive measurement and to improve the mechanical properties of the composites. The material was suggested to use as unique materials as pressure sensors in practical applications mainly for robots.

Approach of the critical point of gas–liquid transitions in an electrostatically stabilized colloidal suspension

We report on the study of the critical point of gas–liquid transitions in an electrostatically stabilized colloidal suspension. Suspensions are constituted of spherical magnetic nanoparticles dispersed in water and stabilized by electrostatic repulsions. The coexistence line is constructed on the Π-V diagram (Π: osmotic pressure, Φ: volume fraction) by the determination of transitions’ threshold by optical microscopy on a large range of volume fractions. This coexistence line presents a maximum that corresponds to a “critical area” where density fluctuations are seen at the microscopic scale. The measurement of these density fluctuations when reaching transitions by small angle neutron scattering (SANS) shows that the transition is of the second order in the critical area and of the first order out of the critical area. SANS measurements also allow to conclude that the interparticle potential is attractive at long range near the coexistence lines of the phase diagram. Long-range attractions are due to dipolar magnetic interactions between particles. Such a potential authorizes gas–liquid transitions and thus the existence of a liquid colloidal phase.

Accuracy of cancellous bone volume fraction measured by micro-CT scanning

Volume fraction, the single most important parameter in describing trabecular microstructure, can easily be calculated from three-dimensional reconstructions of micro-CT images. This study sought to quantify the accuracy of this measurement. One hundred and sixty human cancellous bone specimens which covered a large range of volume fraction (9.8–39.8%) were produced. The specimens were micro-CT scanned, and the volume fraction based on Archimedes’ principle was determined as a reference. After scanning, all micro-CT data were segmented using individual thresholds determined by the scanner supplied algorithm (method I). A significant deviation of volume fraction from method I was found; both the y-intercept and the slope of the regression line were significantly different from those of the Archimedes-based volume fraction ( p<0.001). New individual thresholds were determined based on a calibration of volume fraction to the Archimedes-based volume fractions (method II). The mean thresholds of the two methods were applied to segment 20 randomly selected specimens. The results showed that volume fraction using the mean threshold of method I was underestimated by 4% ( p=0.001), whereas the mean threshold of method II yielded accurate values. The precision of the measurement was excellent. Our data show that care must be taken when applying thresholds in generating 3-D data, and that a fixed threshold may be used to obtain reliable volume fraction data. This fixed threshold may be determined from the Archimedes-based volume fraction of a subgroup of specimens. The threshold may vary between different materials, and so it should be determined whenever a study series is performed.

Interactions between Polymer-Grafted Membranes in Concentrated Solutions of Free Polymer

Polymers grafted or otherwise immobilized at surfaces are often used to stabilize particle suspensions in situations where nonspecific colloidal forces or specific chemical bonds act to coagulate the particles. Although the motivation is clear, criteria for steric stabilization are not well established for environments that contain large amounts of free polymer which can induce strong attraction through depletion forces. To examine these criteria, we have performed micromechanical tests of adhesion between pairs of large vesicles with membranes made from mixtures of phospholipids and phospholipids grafted with poly(ethylene oxide) PEO chains in aqueous solutions of free (nonadsorbing) PEO chains. Solutions were made with two free polymer fractions (Np ≈ 114 and 444 monomers in average length) over a large range of volume fractions between 0.01 and 0.2. Three graft chain lengths (Ng ≈ 45, 114, and 273 monomers) and several surface densities were used to extend the scale of surface roughness from ∼0.5 nm for smooth bilayers to nearly 16 nm for the most prominent graft. On the basis of established theory, the grafted polymers were expected to form structures that varied from dilute noninteracting chains to semidilute marginal brushes with mean volume fractions of up to 0.06. Surprisingly, we found a consistent pattern of interaction for all graft lengths and surface densities; i.e., there was no adhesion below a threshold level of free polymer concentration and adhesion energy increased strongly with free polymer concentration above the threshold. Moreover, there was no tendency toward stabilization even at the highest volume fractions of 0.15−0.2. When both surfaces carried grafts (symmetric interactions), the stabilization threshold was proportionally higher than when one of the two surfaces was bare (asymmetric interactions). Significantly, these features were independent of free and graft polymer molecular weights. Correlation of the energy scale for free polymer depletion at the threshold to the graft surface density and symmetry of the steric interaction implies a simple criterion for stabilization of surfaces grafted with homopolymers in semidilute solutions of nonadsorbing free polymer and good solvent.

Elasticity of Compressed Emulsions.

The elastic shear modulus of monodisperse emulsions is shown to exhibit a universal dependence on droplet volume fraction $\ensuremath{\varphi}$ when scaled by the Laplace pressure of the droplets, increasing as $\ensuremath{\varphi}(\ensuremath{\varphi}\ensuremath{-}{\ensuremath{\varphi}}_{c})$, where ${\ensuremath{\varphi}}_{c}\ensuremath{\approx}0.635$, the value of random close packing of solid spheres. Surprisingly the osmotic pressure required to compress the emulsions to increase $\ensuremath{\varphi}$ is nearly the same as the shear modulus over a large range of volume fraction, while the bulk osmotic modulus differs significantly. Models based on the structural disorder of the emulsions are discussed to account for these data.

Study of the volume fraction, temperature, and pressure dependence of the resistivity in a ceramic-polymer composite using a general effective media theory equation

A quantitative general effective media (GEM) equation is used to describe quantitatively the resistivity of an Fe3O4-epoxy composite system over a large range of volume fractions in terms of the resistivities of each component and two percolation morphology parameters. One parameter is the critical (percolation) volume fraction, φc, and the other is an exponent,t. Preliminary models, also based on the GEM equation, are used to describe the positive temperature coefficient of resistivity (PTC) and the piezoresistivity (uniaxial pressure) of the composite when the composition is near the percolation threshold.