A General Expression for the Ordered-Packed Volume Fraction of Hard Spheres of Different Diameters

2002 ◽  
Vol 41 (5) ◽  
pp. 1122-1128 ◽  
Author(s):  
Cyrus Ghotbi ◽  
Juan H. Vera
Keyword(s):  
General Expression ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Different Diameters ◽  
Packed Volume

scholarly journals Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1543
Author(s):  
Luka Sturtewagen ◽  
Erik van der Linden
Keyword(s):  
Phase Behavior ◽  
Critical Point ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Two Phase ◽  
Different Types ◽  
Asymmetric Partitioning ◽  
Average Size ◽  
Liquid Liquid Phase Separation

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

scholarly journals Effects of Pumice-Based Porous Material on Hydration Characteristics and Persistent Shrinkage of Ultra-High Performance Concrete (UHPC)

Materials ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 11 ◽  
Author(s):  
Kaizhi Liu ◽  
Rui Yu ◽  
Zhonghe Shui ◽  
Xiaosheng Li ◽  
Xuan Ling ◽  
...  
Keyword(s):  
High Performance ◽  
High Performance Concrete ◽  
Volume Fraction ◽  
Energy Dispersive Spectrometer ◽  
Effective Area ◽  
Mineral Admixtures ◽  
Ultra High Performance Concrete ◽  
Composition And Structure ◽  
Different Diameters ◽  
Hydration Characteristics

In this paper, two kinds of pumice particles with different diameters and water absorption rates are employed to substitute the corresponding size of river sands by volume fraction, and their effects on the hydration characteristics and persistent shrinkage of Ultra-High Performance Concrete (UHPC) are investigated. The obtained experimental results show that adopting a low dosage of 0.6–1.25 mm saturated pumice as the internal curing agent in UHPC can effectively retract the persistent shrinkage deformation of concrete without a decrease of strength. Heat flow calorimetry results demonstrate that the additional water has a retarding effect and promotes the hydration process. X-ray Diffraction (XRD) and Differential Thermal Gravimetry (DTG) are utilized to quantify the Ca(OH)2 content in the hardened paste, which can confirm that the external moisture could accelerate the early cement hydration and secondary hydration of active mineral admixtures. The Ca/Si ratio of C–S–H calculated by the Energy Dispersive Spectrometer (EDS) reveals that the incorporation of wet pumice can transform the composition and structure of hydration products in its effective area.

scholarly journals Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness

2015 ◽  
Vol 9 (6) ◽  
pp. 2101-2117 ◽  
Author(s):  
H. Löwe ◽  
G. Picard
Keyword(s):  
Correlation Function ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Microwave Emission ◽  
Scattering Coefficient ◽  
Equivalent Diameter ◽  
Emission Model ◽  
Data Set ◽  
Point Correlation ◽  
Point Correlation Function

Abstract. The description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents measured input parameters from being used for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomography. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres, we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally, our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from tomography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors.

scholarly journals The non-Newtonian rheology of dilute colloidal suspensions

2002 ◽  
Vol 456 ◽  
pp. 239-275 ◽  
Author(s):  
J. BERGENHOLTZ ◽  
J. F. BRADY ◽  
M. VICIC
Keyword(s):  
Boundary Layer ◽  
Normal Stress ◽  
Volume Fraction ◽  
Hydrodynamic Lubrication ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Colloidal Suspensions ◽  
Brownian Diffusion ◽  
Concentrated Suspensions ◽  
Stokesian Dynamics

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions.

Phenomenological Approach of the Effective Viscosity of Hard Sphere Suspensions in Shear-Thinning Media

2006 ◽  
Vol 16 (3) ◽  
pp. 145-151 ◽  
Author(s):  
Y. Peysson ◽  
T. Aubry ◽  
M. Moan
Keyword(s):  
Effective Viscosity ◽  
Phenomenological Study ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Rheological Behaviour ◽  
Phenomenological Approach ◽  
Shear Thinning ◽  
Packing Fraction ◽  
Solid Content ◽  
Power Law Index

Abstract In this work we investigate the rheological behaviour of macroscopic buoyant hard spheres dispersed in a shear-thinning suspending fluid. We focus on the phenomenological study of the influence of the shear-thinning behaviour of the suspending medium on the effective apparent suspension viscosity at different volume fractions. In the oil industry, the effective viscosity concept is widely used and very useful to quickly characterize a change of viscosity due to an increase of the solid content. Viscosity measurements are compared to the effective viscosity of a suspension of hard spheres in an Ostwald fluid. The power law index of the suspending fluid is shown, both experimentally and theoretically, to influence strongly the volume fraction dependence of the suspension effective viscosity. All experimental results are shown to be quite correctly plotted on a master curve, with only one adjustable parameter, the maximum packing fraction fm. The best fit is obtained for fm = 0.57, corresponding to the theoretical maximum random packing volume fraction.

Numerical Study on Momentum Transfer Between Droplets and Carrier-Phase in Wave-Type Plate Separators

2017 ◽  
Author(s):  
Li Yuzheng ◽  
Liu Qianfeng ◽  
Bo Hanliang
Keyword(s):  
Momentum Transfer ◽  
Carrier Phase ◽  
Volume Fraction ◽  
Numerical Study ◽  
Euler Method ◽  
Coupling Method ◽  
Low Velocity ◽  
Wave Type ◽  
The One ◽  
Different Diameters

The steam flow is simulated by FLUENT. The Lagrange-Euler method is used to simulate the droplet-laden flow in wave-type separators. Two-way coupling method is used to study the influence of the momentum transfer between droplets and carrier-phase in wave-type plate separators. A group of the trajectories of droplets with different diameters are performed in wave-type plate separator flow field. The result shows that the momentum transfer has tiny impact on the behaviors of droplets in a low velocity flow. However, the momentum transfer affects the behaviors of droplets more significantly with rising flow velocity. The one-way coupling method overestimates the diffusion of droplets. In addition, the momentum transfer affects the total pressure loss more significantly with rising volume fraction. The conclusion verifies the importance of the momentum transfer in droplet-laden flows, which could be used to simulate the behavior of droplets moving in a separator.

Processing, Microstructure and Mechanical Properties of SiCp/AZ91 Mg Matrix Composites Fabricated by Squeeze Casting

2007 ◽  
Vol 546-549 ◽  
pp. 499-502
Author(s):  
X. Qiu ◽  
Xiao Jun Wang ◽  
Ming Yi Zheng ◽  
Kun Wu
Keyword(s):  
Mechanical Properties ◽  
Tensile Properties ◽  
Squeeze Casting ◽  
Volume Fraction ◽  
Matrix Alloy ◽  
Matrix Composites ◽  
Magnesium Matrix Composites ◽  
The Matrix ◽  
Az91 Magnesium ◽  
Different Diameters

The fabrication processing, mechanical properties and fracture characters of SiCp/AZ91 magnesium matrix composites fabricated by squeeze casting were investigated. The SiC particles with different diameters (5μm, 20μm and 50μm) were employed as the reinforcement in the composites, the volume fraction of them was 50% in all cases. Experimental results showed that when the size of SiC particle decreased, the tensile properties of the composite increased. The tensile properties of SiCp/AZ91 composite with small particles are controlled by the properties of matrix alloy and the strength of the interface between the matrix and reinforcements, but the composites reinforced by large particles are controlled by the fracture of the particles.

scholarly journals Refractive index matched, nearly hard polymer colloids

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180763 ◽  
Author(s):  
Gregory N. Smith ◽  
Matthew J. Derry ◽  
James E. Hallett ◽  
Joseph R. Lovett ◽  
Oleksander O. Mykhaylyk ◽  
...  
Keyword(s):  
Refractive Index ◽  
Diblock Copolymer ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Scattered Light ◽  
Degree Of Polymerization ◽  
Model Systems ◽  
Binary Solvent ◽  
Solvent Mixtures ◽  
Crucial Difference

Refractive index matched particles serve as essential model systems for colloid scientists, providing nearly hard spheres to explore structure and dynamics. The poly(methyl methacrylate) latexes typically used are often refractive index matched by dispersing them in binary solvent mixtures, but this can lead to undesirable changes, such as particle charging or swelling. To avoid these shortcomings, we have synthesized refractive index matched colloids using polymerization-induced self-assembly (PISA) rather than as polymer latexes. The crucial difference is that these diblock copolymer nanoparticles consist of a single core-forming polymer in a single non-ionizable solvent. The diblock copolymer chosen was poly(stearyl methacrylate)–poly(2,2,2-trifluoroethyl methacrylate) (PSMA–PTFEMA), which self-assembles to form PTFEMA core spheres in n -alkanes. By monitoring scattered light intensity, n -tetradecane was found to be the optimal solvent for matching the refractive index of such nanoparticles. As expected for PISA syntheses, the diameter of the colloids can be controlled by varying the PTFEMA degree of polymerization. Concentrated dispersions were prepared, and the diffusion of the PSMA–PTFEMA nanoparticles as a function of volume fraction was measured. These diblock copolymer nanoparticles are a promising new system of transparent spheres for future colloidal studies.

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