Suspensions Of Spheres Research Articles

Sedimentation path theory for mass-polydisperse colloidal systems.

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Solvents govern rheology and jamming of polymeric bead suspensions

Despite their apparent simplicity, suspensions of hard spheres in a Newtonian fluid show complex non-Newtonian behaviors and remain poorly understood. Recent works have pointed out the crucial role of interparticle contact forces in these behaviors. Here, we show that the same (polystyrene) particles, when immersed in different Newtonian solvents, show different behaviors at both the microscopic and macroscopic scales. Thanks to interparticle force measurements in each solvent together with rheological measurements, we show how the fine details of the pairwise particle interactions impact the macroscopic behavior. The rheological properties (shear thinning, shear thickening, jamming solid fraction value) of the suspensions, made up of same particles, are shown to depend on the nature of the solvent. Here, we highlight several mechanisms at the particle scale: the swelling of polymeric particles in an organic solvent, the role of colloidal repulsive forces and inertia for particles in a water solution, and the variation of the friction coefficient as a function of the load for particles immersed in silicone oils. Our study provides new quantitative data to test micromechanical models and simulations. It questions the interpretation of previous experimental works. Finally, it shows the need to systematically characterize the interparticle normal and tangential forces when studying a given suspension of hard spheres in a Newtonian fluid

Number Concentration Measurements of Polystyrene Submicrometer Particles.

The number of techniques to measure number concentrations and size distributions of submicrometer particles has recently increased. Submicrometer particle standards are needed to improve the accuracy and reproducibility of these techniques. The number concentrations of fluorescently labeled polystyrene submicrometer sphere suspensions with nominal 100 nm, 200 nm and 500 nm diameters were measured using seven different techniques. Diameter values were also measured where possible. The diameter values were found to agree within 20%, but the number concentration values differed by as much as a factor of two. Accuracy and reproducibility related with the different techniques are discussed with the goal of using number concentration standards for instrument calibration. Three of the techniques were used to determine SI-traceable number concentration values, and the three independent values were averaged to give consensus values. This consensus approach is proposed as a protocol for certifying SI-traceable number concentration standards.

Ordered domains in sheared dense suspensions: The link to viscosity and the disruptive effect of friction

Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over 105 particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for Pe>1, the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering and planar order, and we determine that particles are packed into hexagonal crystal layers (with numerous defects) that slide past each other. By computing local ψ6 and ψ4 order parameters, we determine that the defects correspond to chains of particles in a squarelike lattice. We compute the individual particle contributions to the stress tensor and discover that the largest contributors to the shear stress are primarily located in these lower density, defect regions. The defect structure enables the formation of compressed chains of particles to resist the shear, but these chains are transient and short-lived. The inclusion of a contact friction force allows the stress-bearing structures to grow into a system-spanning network, thereby disrupting the order and drastically increasing the suspension viscosity.

High-resolution patterning of silica nanoparticle-based ionogels by reverse-offset printing and its characterization

In this study, nanoparticle-based, high-resolution patternable ionogels are presented to provide a route for realizing printed solid-state ionic devices. By incorporating an ionic liquid (IL) into a spherical silica nanoparticle suspension, a quasi-solid ionogel layer compatible with reverse-offset printing (ROP) with a spatial resolution of approximately 5 μm was realized. In situ near-infrared (NIR) spectroscopic analysis revealed the drying kinetics of the ionogel ink during printing, and a temporal margin for successful patterning in relation to its dry state was provided. In contrast to polymer-based gels, the present ionogel can be regarded as a porous medium of silica filled with ionic liquids with a certain degree of saturation. By optimizing the ink formulations, ROP patterning was successful for saturation up to 102%, indicating the nanoscale pores between silica nanoparticles can be fully used as an ion-conductive phase in the proposed patternable gel. The conductivity depends drastically on saturation, with a saturation exponent of approximately −7 according to Archie’s law. From a complementary scratch test, an ionogel at a saturated condition still exhibited fragile but solid-like characteristics. As a demonstration, planar micro-supercapacitors fully printed with reverse-offset printable ionogel and carbon inks were fabricated. A comparison with a drop-casted IL showing a similar capacitance indicates a limited ability of the carbon nanoparticle material used here, while a relatively high resistance of the silica-nanoparticle-based ionogel hinders a fast cyclic voltammetry response.

Anisotropic stresslet and rheology of stick–slip Janus spheres

A Janus sphere with a stick–slip pattern can behave quite differently in its hydrodynamics compared with a no-slip or uniform-slip sphere. Here, using the Lorentz reciprocal theorem in conjunction with surface harmonic expansion, we rigorously derive the extended Faxén formula for the stresslet of a weakly stick–slip Janus sphere, capable of describing the anisotropic nature of the stresslet with an arbitrary axisymmetric stick–slip pattern in an arbitrary background flow. We find that slip anisotropy not only causes a variety of additional contributions to the stresslet, but also naturally renders a stresslet–rotation coupling that may turn a suspension of couple-free stick–slip Janus spheres into a dipolar one under the actions of an external couple. Moreover, to correctly account for the impacts of slip anisotropy on the stresslet, it is necessary to include at least the first four surface harmonic contributions. As a result, the anisotropies of both the stresslet and torque on the sphere in a linear flow field are purely reflected by a symmetric quadrupole and hexadecapole. These hydrodynamic quantities can be further mediated by an antisymmetric dipole and octupole due to the gradients of the imposed strain field. The average bulk stress and effective viscosity for a suspension of stick–slip spheres are also determined, showing characteristics quite distinct from those of a suspension of near spheres. If the spheres possess permanent dipole moments, in particular, additional stresslets and couplets can be generated by an applied external couple on each sphere and added into the bulk stress, accompanied by non-Jeffery orientational orbits of such dipolar stick–slip spheres. In addition to the above, the extended Faxén stresslet and torque relations found in this work will also provide the formulae needed for tackling problems involving hydrodynamically interacting stick–slip spheres on which small slip anisotropy may have profound impacts.

Anomalous rheological aging of a model thermoreversible colloidal gel following a thermal quench.

We investigate the aging behavior in a well-studied model system comprised of a colloidal suspension of thermoreversible adhesive hard spheres (AHS) but thermally quenched below the gel transition to much larger depths than previously studied. The aging behavior in the model AHS system is monitored by small amplitude oscillatory shear rheology measurements conducted while rapidly quenching from the liquid state at 40 °C to a temperature below the gel temperature, and new, anomalous aging behaviors are observed. Shallow quenches lead to monotonic development of the elastic modulus with time, consistent with prior reports for the development of a homogeneous gel [Gordon et al., J. Rheol. 61, 23-34 (2017)]. However, for deeper quenches, a unique and new phenomenon is reported, namely, after an initial rise in the modulus, a reproducible drop in the modulus is observed, followed by a plateau in the modulus value. This drop can be gradual or sudden and the extent of the drop depends on the quench depth. After this drop in the modulus, AHS gel evolves toward a quench-path independent state over the experimental timescale. These effects of the extent of quenching on aging behavior are hypothesized to be a consequence of quenching into different underlying thermodynamic states of colloidal gels and the possible influence of the adhesive glass dynamical arrest for the deepest quenches. The research connects homogeneous gelation with heterogeneous gel formation due to phase separation and shows that the extent of quench can be used as an independent parameter to govern the rheological response of the arrested gel.

Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds

We prove that if M is a closed n-dimensional Riemannian manifold, n ge 3, with mathrm{Ric}ge n-1 and for which the optimal constant in the critical Sobolev inequality equals the one of the n-dimensional sphere mathbb {S}^n, then M is isometric to mathbb {S}^n. An almost-rigidity result is also established, saying that if equality is almost achieved, then M is close in the measure Gromov–Hausdorff sense to a spherical suspension. These statements are obtained in the mathrm {RCD}-setting of (possibly non-smooth) metric measure spaces satisfying synthetic lower Ricci curvature bounds. An independent result of our analysis is the characterization of the best constant in the Sobolev inequality on any compact mathrm {CD} space, extending to the non-smooth setting a classical result by Aubin. Our arguments are based on a new concentration compactness result for mGH-converging sequences of mathrm {RCD} spaces and on a Pólya–Szegő inequality of Euclidean-type in mathrm {CD} spaces. As an application of the technical tools developed we prove both an existence result for the Yamabe equation and the continuity of the generalized Yamabe constant under measure Gromov–Hausdorff convergence, in the mathrm {RCD}-setting.

Hard Sphere Crystal Nucleation Rates: Reconciliation of Simulation and Experiment.

Over the past two decades, a large number of studies addressed the topic of crystal nucleation in suspensions of hard spheres. The shared result of all these efforts is that, at low supersaturations, experimentally observed nucleation rates and numerically computed ones differ by more than 10 orders of magnitude. We present precise simulation results of crystal nucleation rate densities in the metastable hard sphere liquid. To compare these rate densities to experimentally measured ones, we propose an interpretation of the experimental data as a combination of nucleation and crystal growth processes (rather than purely the nucleation process). This interpretation may resolve the long-standing dispute about the differing rates.

Screen-Printed Carbon Electrodes with Macroporous Copper Film for Enhanced Amperometric Sensing of Saccharides.

A porous layer of copper was formed on the surface of screen-printed carbon electrodes via the colloidal crystal templating technique. An aqueous suspension of monodisperse polystyrene spheres of 500 nm particle diameter was drop-casted on the carbon tracks printed on the substrate made of alumina ceramic. After evaporation, the electrode was carefully dipped in copper plating solution for a certain time to achieve a sufficient penetration of solution within the polystyrene spheres. The metal was then electrodeposited galvanostatically over the self-assembled colloidal crystal. Finally, the polystyrene template was dissolved in toluene to expose the porous structure of copper deposit. The morphology of porous structures was investigated using scanning electron microscopy. Electroanalytical properties of porous copper film electrodes were evaluated in amperometric detection of selected saccharides, namely glucose, fructose, sucrose, and galactose. Using hydrodynamic amperometry in stirred alkaline solution, a current response at +0.6 V vs. Ag/AgCl was recorded after addition of the selected saccharide. These saccharides could be quantified in two linear ranges (0.2–1.0 μmol L−1 and 4.0–100 μmol L−1) with detection limits of 0.1 μmol L−1 glucose, 0.03 μmol L−1 fructose, and 0.05 μmol L−1 sucrose or galactose. In addition, analytical performance of porous copper electrodes was ascertained and compared to that of copper film screen-printed carbon electrodes, prepared ex-situ by the galvanostatic deposition of metal in the plating solution. After calculating the current densities with respect to the geometric area of working electrodes, the porous electrodes exhibited much higher sensitivity to changes in concentration of analytes, presumably due to the larger surface of the porous copper deposit. In the future, they could be incorporated in detectors of flow injection systems due to their long-term mechanical stability.

A novel method for investigating the isotropy of response for randomly generated unit cells of particulate composites

This work investigates the isotropy of mechanical response of randomly generated unit cells of particulate composites. We propose a novel algorithm for assessing the isotropic behavior of such microstructures by applying different loading in random planes in space. The Random Plane Evaluation of Isotropy (RPEI) is based on calculating the averaged stress and strain under periodic boundary conditions and finding the maximum angle difference between the principal directions of them as a measure for deviation from coaxiality/isotropy. We show that an average of such data at a statistical level can be used for assessing closeness to isotropy. To put the RPEI in use, we have also proposed a new method for generating unit cells containing a random distribution of ellipsoidal particles. Then the isotropy of mechanical behavior for various unit cells enclosing random suspensions of spheres and ellipsoids was investigated. Our results show that (i) Merely random distribution of particles does not guarantee the isotropy of the response (ii) Checking the isotropy in limited directions can be misleading and data at a statistical level is needed (iii) RPEI proves a reliable tool for checking the isotropy of response of unit cells of heterogeneous materials for a variety of behaviors.

Torque scaling at primary and secondary bifurcations in a Taylor–Couette flow of suspensions

The Taylor–Couette flow of non-colloidal, neutrally buoyant spherical particle suspensions in the $\phi =0\,\%-28\,\%$ concentration range and (17–250) Reynolds number ( $\mathcal {R})$ range is studied using synchronized flow visualization and torque measurements. Both methods are applied in ramp-up/down (acceleration/deceleration of the inner cylinder) experiments to detect the various flow structure states and bifurcation natures, their critical conditions and their lifetime in $\mathcal {R}$ range. Torque measurement allows us to discuss the evolution of the (pseudo) Nusselt number, $\mathcal {N}$ , and friction coefficient with $\mathcal {R}$ or alternatively the Taylor number, Ta. Flow visualization brings additional information on the unsteady dynamics of flow states. For concentrations higher than $\phi =6\,\%$ , two unsteady (spiral vortex flow, wavy vortex flow) and one steady (Taylor vortex flow) flow state are observed in both ramp-up/down experiments. Hysteretic behaviour is reported for some primary, secondary and tertiary bifurcations, which are thus found to be subcritical. A critical concentration is observed at $\phi =15\,\%$ for the range of $\mathcal {R}$ at which spiral vortex flow is encountered. Characteristic frequencies of unsteady flow state (spiral vortex flow, wavy vortex flow) for different suspension concentrations are evaluated. Finally, three hydrodynamic concentration subregimes are identified for the first time, with their distinct sets of concentration-dependent critical conditions, torque scaling exponents and friction coefficients.

Synthesis of standard reference materials of particle size in liquid medium based on aqueous suspensions of polystyrene latex spheres

Synthesis of standard reference materials of particle size in liquid medium based on aqueous suspensions of polystyrene latex spheres

Tissue Engineering of Canine Cartilage from Surgically Debrided Osteochondritis Dissecans Fragments

This study in dogs explored the feasibility of using cartilage fragments removed and discarded during routine palliative surgery for osteochondritis dissecans (OCD) as a source of primary chondrocytes for scaffold-free cartilage tissue-engineering. Primary chondrocytes were obtained from three OCD donors and one age-matched healthy articular cartilage (HAC) donor. After monolayer expansion of primary cells, a three-dimensional spherical suspension culture was implemented. Following this stage, cells were seeded at a high density into custom-made agarose molds that allowed for size and shape-specific constructs to be generated via a method of cellular self-assembling in a scaffold-free environment. Fifty-eight neocartilage constructs were tissue-engineered using this methodology. Neocartilage constructs and native cartilage from shoulder joint were subjected to histological, mechanical, and biochemical testing. OCD and HAC chondrocytes-sourced constructs had uniformly flat morphology and histology consistent with cartilage tissue. Constructs sourced from OCD chondrocytes were 1.5-times (32%) stiffer in compression and 1.3 times (23%) stronger in tension than constructs sourced from HAC chondrocytes and only 8.7-times (81%) less stiff in tension than native tissue. Constructs from both cell sources consistently had lower collagen content than native tissue (22.9%/dry weight [DW] for OCD and 4.1%/DW for HAC vs. 51.1%/DW native tissue). To improve the collagen content and mechanical properties of neocartilage, biological and mechanical stimuli, and thyroid hormone (tri-iodothyronine) were applied to the chondrocytes during the self-assembling stage in two separate studies. A 2.6-fold (62%) increase in compressive stiffness was detected with supplementation of biological stimuli alone and 5-fold (81%) increase with combined biological and mechanical stimuli at 20% strain. Application of thyroid hormone improved collagen content (1.7-times, 33%), tensile strength (1.8-times, 43%), and stiffness (1.3-times, 21%) of constructs, relative to untreated controls. Collectively, these data suggest that OCD chondrocytes can serve as a reliable cell source for cartilage tissue-engineering and that canine chondrocytes respond favorably to biological and mechanical stimuli that have been shown effective in chondrocytes from other animal species, including humans.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Infrared-spectroscopic, dynamic near-field microscopy of living cells and nanoparticles in water

Infrared fingerprint spectra can reveal the chemical nature of materials down to 20-nm detail, far below the diffraction limit, when probed by scattering-type scanning near-field optical microscopy (s-SNOM). But this was impossible with living cells or aqueous processes as in corrosion, due to water-related absorption and tip contamination. Here, we demonstrate infrared s-SNOM of water-suspended objects by probing them through a 10-nm thick SiN membrane. This separator stretches freely over up to 250 µm, providing an upper, stable surface to the scanning tip, while its lower surface is in contact with the liquid and localises adhering objects. We present its proof-of-principle applicability in biology by observing simply drop-casted, living E. coli in nutrient medium, as well as living A549 cancer cells, as they divide, move and develop rich sub-cellular morphology and adhesion patterns, at 150 nm resolution. Their infrared spectra reveal the local abundances of water, proteins, and lipids within a depth of ca. 100 nm below the SiN membrane, as we verify by analysing well-defined, suspended polymer spheres and through model calculations. SiN-membrane based s-SNOM thus establishes a novel tool of live cell nano-imaging that returns structure, dynamics and chemical composition. This method should benefit the nanoscale analysis of any aqueous system, from physics to medicine.

Modulation of elasto-inertial transitions in Taylor–Couette flow by small particles

Particle suspensions in non-Newtonian liquid matrices are frequently encountered in nature and industrial applications. We here study the Taylor–Couette flow (TCF) of semidilute spherical particle suspensions (volume fraction $\leq 0.1$ ) in viscoelastic, constant-viscosity liquids (Boger fluids). We describe the influence of particle load on various flow transitions encountered in TCF of such fluids, and on the nature of these transitions. Particle addition is found to delay the onset of first- and second-order transitions, thus stabilising laminar flows. It also renders them hysteretic, suggesting an effect on the nature of bifurcations. The transition to elasto-inertial turbulence (EIT) is shown to be delayed by the presence of particles, and the features of EIT altered, with preserved spatio-temporal large scales. These results imply that particle loading and viscoelasticity, which are known to destabilise the flow when considered separately, can on the other hand compete with one another and ultimately stabilise the flow when considered together.

Numerical Study on Proppant Transport in Hydraulic Fractures Using a Pseudo-3D Model for Multilayered Reservoirs

Summary In this paper, we incorporated a kinematic proppant transport model for spherical suspensions in hydraulic fractures developed by Dontsov and Peirce (2014) in a pseudo-3D hydraulic-fracture simulator for multilayered rocks to capture a different proppant transport speed than fluid flow and abridged fracture channel by highly concentrated suspensions. For pressure-driven proppant transport, the bridges made of compact proppant particles can lead to both proppant distribution discontinuity and increased fracture aperture and height because of the higher pressure. The model is applied to growth of a fracture from a vertical well, which can contain thin-bedded intervals and more than one opened hydraulic-fracture interval, because the fracture plane extends in height through layers with contrasts in stress and material properties. Three numerical examples demonstrate that a loss of vertical connectivity can occur among multiple fracture sections, and proppant particles are transported along the more compliant layers. The proppant migration within a narrow fracture in a thin soft rock layer can result in bridging and formation of a proppant plug that strongly limits fluid speed. This generates an increase of injection pressure associated with fracture screenout, and these screenout events can emerge at different places along the fracture. Next, because of the lack of pretreatment geomechanical data, the values of layer stress and leakoff coefficient are adjusted for a field case so that the varying bottomhole pressure and fracture length are in line with the field measurements. This paper provides a useful illustration for hydraulic-fracturing treatments with proppant transport affected by and interacting with reservoir lithological complexities.

Capillary flow of magnetic fluids with effect of hydrodynamic dispersion

A theoretical study is conducted on the influence of a shear-induced dispersion on the rheological response of a magnetic suspension. A capillary geometry is considered, in which a dilute ferrofluid flows under the action of a longitudinal applied magnetic field. The shear-induced dispersion is assumed to arise either due to particle roughness or non-sphericity (i.e., shape anisotropy). A new asymptotic solution for a suspension of rough spheres in the limit of weak flows is developed. The numerical results indicate that the dispersive flux by shear rate gradient produces a particle migration toward the center of the tube. In the case of smooth prolate spheroidal particles, the shape anisotropy may either intensify or reduce the viscous dissipation according to the non-dimensional physical parameters. For weak applied fields and weak shear rates, the relative viscosity presented a rising dependence with the aspect ratio. In contrast, at strong flows and/or large applied fields, the net result was a relative viscosity reduction in comparison with a suspension of spheres. The results provide useful insights into the rheology of ferrofluids in quadratic flows, especially to suspensions designed for biomedical applications, such as hyperthermia and magnetic drug targeting in the blood vessels.

Photocatalytic degradation of Red 2G on the suspended TiO2-hollow glass sphere

Photocatalytic degradation of Red 2G on the suspended TiO2-hollow glass sphere