Suspensions Of Spheres Research Articles

Spark-generated bubble near an elastic sphere

The interaction between a spark-generated bubble and an elastic sphere is investigated. A spark-generated bubble is created at various distances horizontally away from a suspended elastic sphere made of silicone rubber or super absorbent polymer (of shear modulus of elasticity G of between 5 and 312kPa), using a low-voltage spark discharge method. We observe pronounced deformation and elongation of the elastic sphere when the spark-bubble is generated very close to a sphere. This happens when the elastic sphere has a small modulus of elasticity and a small size ratio R’ between the bubble and the elastic sphere (i.e. the bubble and the sphere have similar radii). Numerical simulations are also conducted using a Boundary Element Method (BEM) model coupled with a Finite Element Method (FEM) solver. The simulation results compare well with the experimental data. The numerical model is then extended to study the effects of elasticity and experimental parameters, such as the dimensionless stand-off distance H’, and size ratio R’, on the degree of deformation of the elastic cell and the dynamics of the bubble.

Elongational flows of some non-colloidal suspensions

The rheology of a system must be explored not only in viscometric flows, but also in other flow classes, and so, we present some results for the axisymmetric elongational flow of non-colloidal suspensions of spheres. We compare our results with data from shear flows using the same matrices and spheres. We have experimented with non-colloidal suspensions of 40-μm diameter polystyrene spheres with volume fractions (ϕ) varying from 0.3 to 0.5. Two matrix fluids were used—one was a near-Newtonian polydimethyl siloxane of 12 Pa-s viscosity and the other was a variant of the M1 Boger fluid sample of Sridhar which we call M1*. We did not find that the Trouton ratio for either of these fluids was 3; generally, the ratio was larger. We investigated the role of sphere roughness using spheres roughened to 5.3 % of the radius in a 50 % suspension in silicone oil and found an increase of elongational viscosity of about 65 % which is comparable with the 60 % increase in shear viscosity with roughness noted previously. For the silicone oil matrix, we found no rate effect, with very little strain-hardening. By contrast, the M1-type matrix suspensions showed strain-hardening and an increase of elongational viscosity with elongation rate.

Increasing entropy for colloidal stabilization.

Stability is of paramount importance in colloidal applications. Attraction between colloidal particles is believed to lead to particle aggregation and phase separation; hence, stability improvement can be achieved through either increasing repulsion or reducing attraction by modifying the fluid medium or by using additives. Two traditional mechanisms for colloidal stability are electrostatic stabilization and steric stabilization. However, stability improvement by mixing attractive and unstable particles has rarely been considered. Here, we emphasize the function of mixing entropy in colloidal stabilization. Dispersion stability improvement is demonstrated by mixing suspensions of attractive nanosized titania spheres and platelets. A three-dimensional phase diagram is proposed to illustrate the collaborative effects of particle mixing and particle attraction on colloidal stability. This discovery provides a novel method for enhancing colloidal stability and opens a novel opportunity for engineering applications.

Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

We prove that if $(X,\mathsf{d},\mathfrak{m})$ is a metric measure space with $\mathfrak{m}(X)=1$ having (in a synthetic sense) Ricci curvature bounded from below by $K>0$ and dimension bounded above by $N\in [1,\infty)$, then the classic L\'evy-Gromov isoperimetric inequality (together with the recent sharpening counterparts proved in the smooth setting by E. Milman for any $K\in \mathbb{R}$, $N\geq 1$ and upper diameter bounds) hold, i.e. the isoperimetric profile function of $(X,\mathsf{d},\mathfrak{m})$ is bounded from below by the isoperimetric profile of the model space. Moreover, if equality is attained for some volume $v \in (0,1)$ and $K$ is strictly positive, then the space must be a spherical suspension and in this case we completely classify the isoperimetric regions. Finally we also establish the almost rigidity: if the equality is almost attained for some volume $v \in (0,1)$ and $K$ is strictly positive, then the space must be mGH close to a spherical suspension. To our knowledge this is the first result about isoperimetric comparison for non smooth metric measure spaces satisfying Ricci curvature lower bounds. Examples of spaces fitting our assumptions include measured Gromov-Hausdorff limits of Riemannian manifolds satisfying Ricci curvature lower bounds and Alexandrov spaces with curvature bounded from below; the result seems new even in these celebrated classes of spaces.

A review on particle dynamics simulation techniques for colloidal dispersions: Methods and applications

Colloidal dispersions have attracted much attention both from academia and industry due to industrial significance and complex dynamic properties. Accordingly, a variety of attempts have been made to understand the complicated physics of colloidal dispersions. Particle dynamics simulation has been playing an important role in exploring colloidal systems as a strong complement to experimental approaches from which it is hard to get exact microscopic information. Our aim is to provide a well-organized and up-to-date guide to particle dynamics simulation of colloidal dispersions. Among diverse particle dynamics simulation techniques, we focus on Brownian dynamics, Stokesian dynamics, multi-particle collision dynamics, and self-consistent particle simulation techniques. First, the concept of the simulation techniques will be described. Then, for each simulation technique, pros and cons are discussed with a broad range of applications, including concentrated hard sphere suspensions and biological systems. It is expected that this article helps to identify and motivate research challenges.

Direct numerical simulation of particle alignment in viscoelastic fluids

Rigid particles suspended in viscoelastic fluids under shear can align in string-like structures in the flow direction. Although this phenomenon was first reported almost four decades ago by Michele et al. [J. Michele, R. Pätzold, R. Donis, Alignment and aggregation effects in suspensions of spheres in non-Newtonian media, Rheologica Acta 16 (1977) 317–321.], the exact mechanism of particle alignment is not completely understood. Initially, it was believed that normal stress differences are responsible for the alignment of particles, but recent experimental work by van Loon et al. [S. Van Loon, J. Fransaer, C. Clasen, J. Vermant, String formation in sheared suspensions in rheologically complex media: The essential role of shear thinning, Journal of Rheology 58(1) (2014) 237–254.] showed particle alignment in a shear-thinning fluid without significant normal stress differences.To unravel the phenomenon of particle alignment, we present for the first time 3D direct numerical simulations of the alignment of two and three rigid, non-Brownian particles in a viscoelastic shear flow, with the shear rate denoted by γ˙. The equations are solved on moving, boundary-fitted meshes, which are locally refined to accurately describe the polymer stresses around and in between the particles. A small minimal gap size between the particles is introduced. The Giesekus model, with a relaxation time λ, is used for the viscoelastic fluid, and the effect of the Weissenberg number Wi=λγ˙, shear thinning parameter α and ratio between the solvent viscosity and zero-shear viscosity β is investigated.The numerical method allows for the detailed investigation of particles interacting in viscoelastic flows. Alignment of two and three particles is observed in the simulations. Morphology plots were created for various values of α, β and Wi. Alignment is mainly governed by the value of the elasticity parameter S, defined as half of the ratio between the first normal stress difference and shear stress of the suspending fluid. Alignment appears to occur above a critical value of S, which decreases with increasing α, thus shear thinning promotes alignment. Furthermore, three particles align at lower S than two particles. Finally, simulations were performed in a shear-thinning Carreau fluid, where we never observed alignment of the particles. These results lead us to the conclusion that the presence of normal stress differences is essential for particle alignment to occur, although it is strongly promoted by shear thinning.

Spheres from cervical cancer cells display stemness and cancer drug resistance.

Cervical cancer is one of the most common gynecological malignant tumors and is the cause of a serious health problem worldwide. An increasing amount of evidence has shown that cancer stem cells (CSCs) are present in tumors, and that these CSCs may be responsible for tumor metastasis and relapse. The present study aimed to identify and characterize a CSC population from the CaSki cell line. First, a stem cell culture medium was used to selectively expand the cancer stem-like cell spheres, and the putative stemness markers, Oct4 and Sox2, were identified. These markers were all highly expressed in the CaSki sphere-forming cells. Next, target region amplified polymorphism-polymerase chain reaction was performed and the CaSki sphere-forming cells were found to exhibit higher telomerase activity than the CaSki control cells cultured in non-stem cell medium. Using the 3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2H-tetrazolium assay, it was found that the CaSki sphere-forming cells were more resistant to chemotherapeutic drugs than the control CaSki cells. Using the tumor invasive assay, it was shown that the CaSki sphere-forming cells were more invasive than the control CaSki cells. These characteristics all suggested that the tumor sphere-forming cells mirrored the acknowledged CSC phenotypes. Overall, the use of a suspended sphere culture of CaSki cells may be an easy and feasible approach for enriching cancer stem-like cells in cervical cancer research.

A rheological and microstructural characterisation of bigels for cosmetic and pharmaceutical uses

Bigels are biphasic systems formed by water-based hydrogels and oil-based organogels, mainly studied, in the last few years, for pharmaceutical and cosmetic application focused on the controlled delivery of both lipophilic and hydrophilic active agents. The rheological properties of bigels depend on both the amount and the rheological characteristics of single structured phases. Moreover, it can be expected that, at large fractions of one of the starting gels, systems more complex than oil-in-water or water-in-oil can be obtained, yielding bicontinuous or matrix-in-matrix arrangement. Model bigels were investigated from a microstructural (i.e. microscopy and electrical conductivity tests) and rheological point of view. The hydrogel was prepared by using a low-methoxyl pectin whereas the organogel was prepared by using olive oil and, as gelator, a mixture of glyceryl stearate and policosanol. Model bigels were obtained by increasing the amount of organogel mixed with the hydrogel, and microstructural characterisation evidenced an organogel-in-hydrogel behaviour for all investigated samples, even though at the highest organogel content a more complex structure seems to arise. A semi-empirical model, based on theoretical equations developed for suspensions of elastic spheres in elastic media, was proposed to relate bigel rheological properties to single phase properties and fractions.

Particle roughness and rheology in noncolloidal suspensions

We explore the effect of deliberately increased particle roughness on the rheology of noncolloidal suspensions of spheres, both in Newtonian (polydimethylsiloxane or silicone oil) and non-Newtonian (Boger fluid) matrices. The object of the experiment is to change only the roughness of the spheres, while leaving the density and the material of the particles unchanged, so as to isolate the effect of roughness on rheology. Two sphere materials, polystyrene (PS) and polymethylmethacrylate (PMMA) were used. The PS spheres were of 40 and 80 μm nominal diameters, and the PMMA spheres were 40 μm in diameter. Roughness ratios (average roughness/sphere radius) of 0.1%–5% were explored. With silicone matrices, there was up to 50% increase in viscosity with a 50% volume fraction suspension and an increase in the normal stress differences of a similar magnitude. Two polybutene-based Boger fluids were also used. The increases of viscosity with the polybutene matrices were somewhat larger than those with the Newtonian matrix; at 40% volume concentration, we saw approximately a 35% increase in viscosity with a roughness ratio of 5.3%. We compared the experimental results with computations for spheres in Newtonian matrices, and we found reasonable agreement with the computations of Mari et al. [J. Rheol. 58, 1693–1724 (2014)] if a friction coefficient of about 0.5 was assumed. We conclude that friction and roughness must be considered in computational work, or no agreement with experiment will be found. We suggest that the shear-thinning seen with Newtonian matrices is due to a lessening of friction with shear rate. We also show that the unexpected success of the Maron–Pierce formula for Newtonian suspensions is due to the fact that it mimics well a frictional suspension with a friction coefficient of ∼0.5.

Analytical solution for the lubrication force between two spheres in a bi-viscous fluid

An analytical solution for the calculation of the normal lubrication force acting between two moving spheres embedded in a shear-thinning fluid represented by a bi-viscous model is provided. The resulting force between the suspended spheres exhibits a consistent transition between the Newtonian constant-viscosity limits and it reduces to the well-known standard Newtonian lubrication theory for viscosity-ratio approaching one. Effects of several physical parameters of the theory are analyzed under relevant physical conditions, i.e., for a prototypical case of two non-colloidal spheres immersed in a non-Newtonian fluid with rheology parameterized by a bi-viscosity model. Topological results for high/low-viscosity regions in the gap between spheres are also analyzed in detail showing a rich phenomenology. The presented model enables the extension of lubrication dynamics for suspensions interacting with non-Newtonian matrices and provides a clean theoretical framework for new numerical computations of flow of dense complex particulate systems.

Nonlinear interaction between a gas bubble and a suspended sphere

The fully nonlinear interaction between a gas bubble and a suspended sphere is studied using boundary integral method. The violently expanding and collapsing bubble would cause the sphere to move, in reverse, the sphere response can strongly affect the bubble dynamics. Differing from previous studies, we use the auxiliary function method to decouple the mutual dependence between the force and the sphere motion. To validate our model, two experiments are carried out for a spark-generated bubble interacting with a suspended sphere, captured by using a high speed camera. Our numerical results agree well with the experimental data for both cases, in terms of bubble shapes and sphere displacement. We further conduct convergence and sensitivity studies, in which consistent results have been achieved. Then, the effects of two parameters are investigated, i.e., the stand-off parameter (defined as γ=d/Rm, where d is the minimum distance between initial bubble center and the sphere surface, Rm is the maximum equivalent bubble radius) and the size ratio (defined as θ=Rs/Rm, where Rs is the sphere radius). The sphere is pushed away by the expanding bubble and gets attracted towards the collapsing bubble. Bubble motion varies greatly with different parameters. We found the maximum jet impact pressure on the sphere is realized when θ is around 2.

Dipolar colloids in apolar media: direct microscopy of two-dimensional suspensions.

Spherical colloids, in an absence of external fields, are commonly assumed to interact solely through rotationally-invariant potentials, u(r). While the presence of permanent dipoles in aqueous suspensions has been previously suggested by some experiments, the rotational degrees of freedom of spherical colloids are typically neglected. We prove, by direct experiments, the presence of permanent dipoles in commonly used spherical poly(methyl methacrylate) (PMMA) colloids, suspended in an apolar organic medium. We study, by a combination of direct confocal microscopy, computer simulations, and theory, the structure and other thermodynamical properties of organic suspensions of colloidal spheres, confined to a two-dimensional (2D) monolayer. Our studies reveal the effects of the dipolar interactions on the structure and the osmotic pressure of these fluids. These observations have far-reaching consequences for the fundamental colloidal science, opening new directions in self-assembly of complex colloidal clusters.

Rheology of non-colloidal suspensions with corn syrup matrices

We explore the rheology of corn syrup and non-colloidal suspensions of spheres in matrices based on corn syrup. We also comment on the effect of sphere roughness on suspension rheology. Two sphere materials, polystyrene (PS) and polymethyl methacrylate (PMMA), were used. The spheres were of 40 μm nominal diameter. Roughness ratios (average roughness/sphere radius) of 0.15 to 5 % were explored. The viscosity increase with the corn syrup matrix was very large and appears to be due to drying of the corn syrup at the free surfaces of the sample. A corn syrup/glycerine/polyacrylamide Boger fluid was also used. The increases of viscosity with the Boger fluid matrix were again large with the roughened spheres. This appears to be due to the deformation of the long polyacrylamide molecules in the narrow channels between the roughened spheres.

Modeling the viscosity of polydisperse suspensions: Improvements in prediction of limiting behavior

The present study develops a fully consistent extension of the approach pioneered by Farris [“Prediction of the viscosity of multimodal suspensions from unimodal viscosity data,” Trans. Soc. Rheol. 12, 281–301 (1968)] to describe the viscosity of polydisperse suspensions significantly improving upon our previous model [P. M. Mwasame, N. J. Wagner, and A. N. Beris, “Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions,” J. Rheol. 60, 225-240 (2016)]. The new model captures the Farris limit of large size differences between consecutive particle size classes in a suspension. Moreover, the new model includes a further generalization that enables its application to real, complex suspensions that deviate from ideal non-colloidal suspension behavior. The capability of the new model to predict the viscosity of complex suspensions is illustrated by comparison against experimental data.

Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear

We present a 3D numerical investigation of the viscometric functions for suspensions in viscoelastic fluids under steady shear including comparisons with theoretical predictions in the dilute regime and experimental results for non-colloidal suspensions in a Boger fluid. The comparison with dilute suspension theoretical predictions resolves a discrepancy in the literature regarding the second normal stress difference calculated using the Landau–Lifshitz averaging procedure versus using the ensemble averaging procedure. We also determine that the particle contribution to the stress in a dilute suspension in viscoelastic fluids shear-thickens in all viscometric material properties and we present the scaling of the viscometric functions with the Weissenberg number (Wi). This shear-thickening behavior is fundamentally different from that shown in 2D numerical simulations which are attributed to elongation flow effects between particles. Comparisons with experimental results at volume fraction ϕ=0.05, which is the lowest volume fraction available in existing experimental measurements of bulk viscometric functions, highlight the important role of long range hydrodynamic interactions between particles to fully describe the suspension rheology even at low volume fractions. We investigate the effect of hydrodynamic interactions in the flow, vorticity, and gradient directions and show that these interactions can greatly enhance or decrease the viscometric functions as well as change the shear rate dependent behavior of the suspension.

Colloidal Suspensions of Rodlike Nanocrystals and Magnetic Spheres under an External Magnetic Stimulus: Experiment and Molecular Dynamics Simulation.

Using experiments and molecular dynamics simulations, we explore magnetic field-induced phase transformations in suspensions of nonmagnetic rodlike and magnetic sphere-shaped particles. We experimentally demonstrate that an external uniform magnetic field causes the formation of small, stable clusters of magnetic particles that, in turn, induce and control the orientational order of the nonmagnetic subphase. Optical birefringence was studied as a function of the magnetic field and the volume fractions of each particle type. Steric transfer of the orientational order was investigated by molecular dynamics (MD) simulations; the results are in qualitative agreement with the experimental observations. By reproducing the general experimental trends, the MD simulation offers a cohesive bottom-up interpretation of the physical behavior of such systems, and it can also be regarded as a guide for further experimental research.

Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers

A theoretical analysis shows that polymers interacting with particles in a shear flow experience enhanced streamwise stretch that grows in amplitude and spatial extent with increasing Deborah number. This results in shear thickening of the viscosity and first normal stress coefficient of a particle suspension in a Boger fluid.

Thermal connection and vibrational isolation: an elegant solution for two problems

Schenberg is a detector of gravitational waves resonant mass type, with a central frequency of operation of 3200 Hz. Transducers located on the surface of the resonating sphere, according to a distribution half-dodecahedron, are used to monitor a strain amplitude. To improve the performance of the detector it is essential to decrease the temperature, then it will be cooled down, this temperature could reach as low as 50 mK. This refrigerator produces vibration noise that could compromise the performance of Schenberg detector. In this work we the study such vibration noise and how it could be minimized proposing a new connection from the dilution refrigerator to the sphere suspension. The vibration attenuation is studied by finite element modeling (FEM) and an attenuation higher than 1024 is found, higher enough to note compromise the performance of Schenberg detector.

Electrophoresis and electric conduction in a suspension of charged soft particles

A thorough analytical study of the electrophoresis and electric conduction in a suspension of charged soft particles in an arbitrary electrolyte solution is presented through the use of a unit cell model. Each soft particle is a spherical hard core of radius r 0 and constant surface charge density σ covered with a permeable porous layer of constant thickness a − r 0 and uniform fixed charge density Q. Solving the relevant electrostatic and electrokinetic differential equations, we obtain closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension. These results are expressed as linear functions of σ and Q for arbitrary values of r 0/a, λa, κa, and the particle volume fraction of the suspension, where λ is the reciprocal of the Brinkman permeation length of the surface layer of each particle, and κ is the reciprocal of the Debye screening length. The effects of the surface layer characteristics and particle interactions on the electrophoretic mobility and effective conductivity are interesting, significant, and complicated. The general results for a suspension of charged soft spheres, which reduce to those of hard spheres and porous spheres in the limits r 0 = a and r 0 = 0, respectively, provide valuable information for interpreting experimental data.

Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear

We present a 3D numerical investigation of the viscometric functions for suspensions in viscoelastic fluids under steady shear including comparisons with theoretical predictions in the dilute regime and experimental results for non-colloidal suspensions in a Boger fluid. The comparison with dilute suspension theoretical predictions resolves a discrepancy in the literature regarding the second normal stress difference calculated using the Landau–Lifshitz averaging procedure versus using the ensemble averaging procedure. We also determine that the particle contribution to the stress in a dilute suspension in viscoelastic fluids shear-thickens in all viscometric material properties and we present the scaling of the viscometric functions with Weissenberg number (Wi). This shear-thickening behavior is fundamentally different from that shown in 2D numerical simulations which are attributed to elongation flow effects between particles. Comparisons with experimental results at volume fraction ϕ=0.05, which is the lowest volume fraction available in existing experimental measurements of bulk viscometric functions, highlight the important role of long range hydrodynamic interactions between particles to fully describe the suspension rheology even at low volume fractions. We investigate the effect of hydrodynamic interactions in the flow, vorticity, and gradient directions and show that these interactions can greatly enhance or decrease the viscometric functions as well as change the shear rate dependent behavior of the suspension.