Suspensions Of Spheres Research Articles

Shear thickening of suspensions of dimeric particles

In this article, I study the shear thickening of suspensions of frictional dimers by the mean of numerical simulations. I report the evolution of the main parameters of shear thickening, such as the jamming volume fractions in the unthickened and thickened branches of the flow curves, as a function of the aspect ratio of the dimers. The explored aspect ratios range from $1$ (spheres) to $2$ (dimers made of two kissing spheres). I find a rheology qualitatively similar than the one for suspensions of spheres, except for the first normal stress difference $N_1$, which I systematically find negative for small asphericities. I also investigate the orientational order of the particles under flow. Overall, I find that dense suspensions of dimeric particles share many features with dry granular systems of elongated particles under shear, especially for the frictional state at large applied stresses. For the frictionless state at small stresses, I find that suspensions jam at lower volume fraction than dry systems, and that this difference increases with increasing aspect ratio. Moreover, in this state I find a thus far unobserved alignment of the dimers along the vorticity direction, as opposed to the commonly observed alignment with a direction close to the flow direction.

Pipe flow of sphere suspensions having a power-law-dependent fluid matrix

Measurement and prediction of suspension flow properties in cylindrical geometries represent a significant challenge for both the experimentalist and modeler. In this paper, results of a computational study of the suspension flow in a pipe geometry using a computational method based on the smoothed particle hydrodynamics are presented. Flow fields and the spatial distribution of solid spherical inclusions for the case of pipe flow will be shown as a function of the matrix fluid properties (including Newtonian, shear thinning, and shear thickening), driving force, and volume fraction of particles. Simulation results of suspension flow are consistent with a previous work of suspensions with a Newtonian fluid matrix. A strong effective slip phenomenon is shown for the case of a suspension with a shear thinning fluid matrix despite adherence to no-slip boundary conditions. A simple scaling ansatz is given to describe the change of flow rate with driving force. At a volume fraction of approximately 40 % and higher, there is strong evidence of ordering. This feature is illuminated using a small-angle scattering algorithm and compared to experimental studies using neutron scattering. Issues related to proper experimental characterization of rheological properties for pumping and printing of cement-based materials are discussed.Measurement and prediction of suspension flow properties in cylindrical geometries represent a significant challenge for both the experimentalist and modeler. In this paper, results of a computational study of the suspension flow in a pipe geometry using a computational method based on the smoothed particle hydrodynamics are presented. Flow fields and the spatial distribution of solid spherical inclusions for the case of pipe flow will be shown as a function of the matrix fluid properties (including Newtonian, shear thinning, and shear thickening), driving force, and volume fraction of particles. Simulation results of suspension flow are consistent with a previous work of suspensions with a Newtonian fluid matrix. A strong effective slip phenomenon is shown for the case of a suspension with a shear thinning fluid matrix despite adherence to no-slip boundary conditions. A simple scaling ansatz is given to describe the change of flow rate with driving force. At a volume fraction of approximately 40 % and ...

A model to assess visibility in scattering environments

A numerical evaluation of visibility through a scattering medium was performed with the underlying idea of application to media involving water mist and/or smoke. The model uses the principles of incoherent imaging which is based on the Point Spread Function (PSF) concept. This PSF corresponds to the image of a single object point produced by an optical system. Here the light propagates through a scattering and possibly absorbing medium between the object and the imaging system, that leads to a supplementary spreading of the PSF. In this work the PSF was calculated by a Monte-Carlo Method (MCM) and it was applied to the image reconstruction of a USAF1951 resolution pattern. The results of the model were validated through comparison with an experiment in which the USAF1951 pattern was imaged through a cell containing a mixture of silica spheres in suspension in water, the optical properties of this medium being fully characterized. The experiment was made in two limit cases: a luminous object in a dark room and a reflecting object in a luminous room. A good agreement was observed in these two cases and the distance of visibility was found close to the prediction given by the T. Jin's correlation.

Universal Relaxation Dynamics of Sphere Packings below Jamming.

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic timescale that diverges at jamming. This slow timescale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.

Chord-length distributions cannot generally be obtained from small-angle scattering

The methods used to extract chord-length distributions from small-angle scattering data assume a structure consisting of spatially uncorrelated and disconnected convex regions. These restrictive conditions are seldom met for a wide variety of materials such as porous materials and semicrystalline or phase-separated copolymers, the structures of which consist of co-continuous phases that interpenetrate each other in a geometrically complex way. The significant errors that would result from applying existing methods to such systems are discussed using three distinct models for which the chord-length distributions are known analytically. The models are a dilute suspension of hollow spheres, the Poisson mosaic and the Boolean model of spheres.

Spectral determination of μa, μs and g from single and multiple scattering signals with one optically thick sample

Development of robust and easy-to-implement methods for quantitative turbidity characterization by inherent properties of absorption and scattering can have wide applications. We report a new method for multiparameter characterization of turbid samples with three photodiodes based on the radiative transfer (RT) theory. Instead of acquiring collimated transmittance by spatial filtering and scattered light signals by integrating spheres, the method determines RT parameters from forward transmittance dominated by light of single scattering and non-hemispherical diffuse reflectance and transmittance dominated by light of multiple scattering. A Monte Carlo based inverse algorithm has been developed to rapidly obtain absorption coefficient μa, scattering coefficient μs and anisotropy factor g at multiple wavelengths. The method has been validated with different sphere suspensions against the Mie theory. RT parameters for suspensions of spheres of 0.966 µm and 11 µm in nominal diameter values has been determined in a spectral region of 460–1000 nm and the uniqueness of the inverse solutions has been proved at selected wavelengths.

Force chains and networks: wet suspensions through dry granular eyes

Recent advances in shear-thickening suspension rheology suggest a relation between (wet) suspension flow below jamming and (dry) granular physics. To probe this connection, we simulated the contact force networks in suspensions of non-Brownian spheres using the discrete element method, varying the particle friction coefficient and volume fraction. We find that force networks in these suspensions show quantitative similarities to those in jammed dry grains. As suspensions approach the jamming point, the extrapolated volume fraction and coordination number at jamming are similar to critical values obtained for isotropically compressed spheres. Similarly, the shape of the distribution of contact forces in flowing suspensions is remarkably similar to that found in granular packings, suggesting potential refinements for analytical mean field models for the rheology of shear thickening suspensions.Graphic abstract

Influence of particle modulus (softness) and matrix rheology on the sensory experience of ‘grittiness’ and ‘smoothness’

The perception of particles that arises during food oral processing, described using sensory terms such as gritty, powdery, chalky and rough, is critical to sensory perception and consumer satisfaction. Here, a relationship between particle modulus (softness), particle concentration, matrix phase viscosity and sensory experience of grittiness and smoothness is elucidated using well-defined model systems. The systems consist of a model set of fifteen suspensions of micro-hydrogel agar spheres of around 100 μm in size that vary in modulus and are dispersed in aqueous mediums with varying rheological properties. A key finding is that, for suspensions with the same particle concentration and matrix phase viscosity, increasing particle modulus across the range of 100–600 kPa, causes an increase in in-mouth detectability along with an increase in sensory perception of particles, termed size of particles and a decrease in smoothness perception. It is also found that particle concentration (10–80 w/w %) and matrix phase rheology have little influence on particle detectability for both the lowest and highest modulus particles. The results provide support to the notion that for heterogeneous food and beverages samples, micromechanical properties (i.e. level of the individual constituents) play a key role in their perceived texture and mouthfeel in conjunction with bulk properties such as rheology. The insights from this can be used in understanding how heterogeneity, which includes that arising from particle addition or as a by-product of the manufacturing process, may be considered in the rational design and development of products without compromising consumer acceptance.

Rheology of non-colloidal suspensions with viscoelastic matrices.

The rheology of non-colloidal suspensions of spheres in a viscoelastic matrix, including the viscometric, G', G' and uniaxial extensional responses, is explored. Volume fractions of 50% and less were used. By recognizing that filament stretching between beads begins at a distance comparable to the sphere diameter the unexpected large stresses seen in the uniaxial extension experiments can be understood, and a model is presented. In the experiments there is little variation of the dimensionless elongational stresses with the volume fraction φ. For a volume fraction of 50% the behaviour was different from the other concentrations. An essential finding is that a single-mode model of the Oldroyd-B type is not able to describe the elongational experiments at all-at least two modes are needed. There is clearly a difference between behaviour in elongation and in shear with regards to the action of interparticle friction. With negligible rotation of the particles in elongation the kind of vigorous interparticle rubbing possible in shear does not happen.

Nonlinear Behavior of a Suspended Particle in Single-Axis Acoustic Levitators

The nonlinear behavior of a suspended sphere in a single-axis acoustic levitator was studied. Spontaneous oscillations of the sphere in this levitator were experimentally analyzed recording its positions using a high speed camera. A mathematical model based on acoustic radiation forces and real parameters is proposed to describe the dynamics of the sphere movement and its stability. The stability of the motion was investigated via a Lyapunov exponent diagram. We observed that the axial and radial movements of small spheres under levitation may present regular stability and chaotic ones. The Lyapunov exponent diagram for the model shows a complexity structure sharing different regions of stability according to the model parameters.

Light scattering in monodisperse systems – from suspensions to transparent ceramics

Predicting the in-line transmittance of transparent ceramics via model calculations is a useful guide for materials design and optimization of preparation process. However, the absence of reliable input information (volume fractions and size) usually precludes the direct verification of these calculations. On the other hand, suspensions, which can be prepared with well controlled volume fractions of the solids selected, may serve as model systems that are amenable to verification. This paper describes the procedure to perform these calculations, and compares calculated data for suspensions of monodisperse spheres of amorphous silica with spectrophotometric measurements of silica monosphere suspensions with four different concentrations. Moreover, completely analogous model calculations are performed for bubbles in silica glass and pores in spinel ceramics. The results are discussed on the basis on 3D graphs, the use of which is highly recommended. The results may be considered as a benchmark for future model calculations for polydisperse systems.

Hybrids of Bowl-like and Crumpled Hollow Carbon Particles Synthesized through Encapsulation Templating.

The one-pot synthesis of hybrid hollow nanoparticles of symmetric and asymmetric shapes is a challenging task and has rarely been reported. This work proposes a method for a high-yield synthesis of hybrid hollow carbon particles. In the first step, hexadecane/styrene (HD/St) is encapsulated in a silica shell. Then, by the polymerization of St, a silica/polystyrene double shell is formed. Finally, hollow carbon particles with bowl-like and crumpled shapes are obtained by carbonization. The results show that the ratio of diameter to thickness (D/H) for obtaining crumpled particles is ∼4-12, whereas this ratio is ∼7-18 for bowl-like particles. We study the effects of HD and St concentrations on the D/H ratio and the composition of hybrid particles. In contrast to suspensions of hollow carbon spheres, the suspensions of hybrid nanoparticles show shear-thinning behavior over the examined range of shear rates, which is attributed to their enhanced packing. The shape effect of hybrid particles also increases their adsorption on human mesenchymal stem cells (hMSCs) compared to the hollow carbon spheres.

Effect of compact spherical potassium 12-tungstosilicate and lithium heteropolytungstate additives on the rheology and surface chemistry of washed spherical and platelet α-Al2O3 suspensions: Patch charge bridging

The zeta potential data confirmed the adsorption of the large compact Keggin [Si(W12O40)]4- and heteropolytungstate (LST) anions on both α-Al2O3. The adsorbed [Si(W12O40)]4- ions should form a thick steric barrier, ~1 nm, but this effect was not reflected in the yield stress results. A relatively strong additional attractive force explained the increasing maximum yield stress. A similar result was observed with LST. For the spherical α-Al2O3 the largest maximum yield stress (at zero charge) occurred at 0.6 dwb% additive. This attractive force was attributed to patch charge attraction between the negative additive patch and the positive surface site. For the low surface area platelet α-Al2O3 suspensions, complete surface coverage occurred at a low additive concentration as reflected by an almost identical all negative zeta potential-pH behaviour at all additive concentrations at low pH. The slightly larger yield stress at pH 2.5 could be due to this patch charge bridging attraction.

Coincidence of the freezing and the onset of caging in hard sphere and Lennard-Jones fluids.

In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium.

Time-dependent electrokinetic processes in porous colloidal particles

This paper is concerned with effects that arise from the electric charge on the surface of porous colloidal particles. When an external disturbance is applied, for example a change in the concentration of the surrounding electrolyte or an applied electric field, a complicated interaction ensues between the electric field, the liquid pressure field and the ion concentration fields in these particles. In this paper we derive the governing equations for these electrokinetic interactions for a general pore geometry and particle shape, and we present a procedure for solving these equations in the case of a general binary electrolyte. As an illustration, we obtain a new result: a formula for the complex electrical conductivity spectrum of a dilute suspension of porous spheres.

Effects of particle-size distribution and solid additives in the apparent viscosity of drilling fluids

The rheological behavior of drilling fluids depends on the physicochemical characteristics of viscosifying, weighting and bridging agents, such as particle size distribution, charges, chemical composition and density. The accurate controlling of the viscosity profile ensures a higher performance in the drilling process. In this work, the influence of polymers and the particle-size of barite, calcite and glass spheres in the apparent viscosity of suspensions was evaluated. Carboxymethyl cellulose (CMC) and xanthan gum (XG) dissolved in water were used as viscosifying agents. The rheological characteristics of suspensions were evaluated, as well as their zeta potential and microstructure properties. The suspensions of fine material particles presented higher values of shear stress. The CMC polymer increased apparent viscosity at more significant levels than XG and the polymer chain characteristic was predominant over the solid effect. Barite and glass spheres suspensions presented higher zeta potential and lower shear stresses values when compared to calcite suspensions which presented a stronger electrostatic interaction with polymers. Statistical tests were performed using the analysis of variance and results were validated inside 95% of confidence level.

Settling dynamics of two spheres in a suspension of Brownian rods

We investigate via numerical simulations the settling dynamics of two non-Brownian rigid spheres in a dilute suspension of Brownian rods at low Reynolds numbers. Specifically, this work focuses on how the overall settling dynamics is affected by the coupling between the flow field around the spheres and the orientation of the rods. The Brownian motion introduces a finite relaxation time in the suspending medium which is modeled as a continuum. When the spheres fall along their centerline, the spheres experience two contributions: one Newtonian and a non-Newtonian contribution due to the presence of the Brownian rods. The interactions between the two settling spheres are evaluated as a function of Péclet number (Pe) and the distance between the centers of the spheres. Repulsive interactions are found, and these interactions are affected by Pe and the distance between the centers of the spheres. An analysis of the flow fields highlights the origin of these repulsive interactions in non-Newtonian elongational effects.

Experimental and numerical studies on the flow characteristics and separation properties of dispersed liquid-liquid flows

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

Viscoelastic properties of suspensions of noncolloidal hard spheres in a molten polymer

We report an experimental study on suspensions of solid particles in a viscoelastic polymer matrix. A commercial entangled poly(ε-caprolactone) was used as the suspending fluid. Noncolloidal solid spheres (diameter = 15 μm) made of polymethylmethacrylate were dispersed in the polymer via a solvent casting method. The volume fraction of the spheres was varied from 5% to 30%, thus allowing to explore both dilute and concentrated regimes. Electron scanning microscopy demonstrated homogeneous dispersion of the spheres in the matrix. We measured the rheological properties of the suspensions both in linear and nonlinear regimes with both dynamic and transient tests. The experimental results demonstrate the reinforcement effect of the particles. Both viscous and elastic moduli increase as the concentration of the particles is increased. The results show good agreement with available theories, simulations, and previous experimental data. In particular, the second order parameter of the quadratic equation that describes the dependence of the shear viscosity of the suspension upon the volume fraction of particles is in agreement with the predicted value found by Batchelor [G. K. Batchelor and J. T. Green, “The hydrodynamic interaction of two small freely-moving spheres in a linear flow field,” J. Fluid Mech. 56, 375–400 (1972); G. K. Batchelor and J. T. Green, “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech. 56, 401–427 (1972); and G. K. Batchelor, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97–117 (1977)]. We probe experimentally that the linear rheological behavior of suspensions of particles in viscoelastic fluids is the same as for Newtonian fluids.

Quantitative study of the rheology of frictional suspensions: Influence of friction coefficient in a large range of viscous numbers

A numerical study of sheared suspensions of frictional and frictionless rigid spheres finds that macroscopic friction in granular suspensions is nearly independent of interparticle contact friction, and besides contact lubrication, the viscous contribution of the pore fluid is negligibly small.