Brownian diffusion of hard spheres at finite concentrations

AIChE Journal ◽  
1993 ◽  
Vol 39 (1) ◽  
pp. 3-16 ◽  
Author(s):  
M. Sami Selim ◽  
M. A. Al-Naafa ◽  
M. C. Jones
Keyword(s):  
Hard Spheres ◽  
Brownian Diffusion ◽  
Finite Concentrations

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.

The influence of third-order interactions on the density profile of associating hard spheres

1997 ◽  
Vol 91 (4) ◽  
pp. 761-767 ◽  
Author(s):  
D. HENDERSON ◽  
S. SOKOŁOWSKI ◽  
R. ZAGORSKI ◽  
A. TROKHYMCHUK
Keyword(s):  
Density Profile ◽  
Hard Spheres ◽  
Third Order

Glass transition for dipolar hard spheres: a mode-coupling approach

1998 ◽  
Vol 77 (2) ◽  
pp. 305-311 ◽  
Author(s):  
Thomas Scheidsteger, Rolf Schilling
Keyword(s):  
Glass Transition ◽  
Mode Coupling ◽  
Hard Spheres ◽  
Coupling Approach

Quantum effects in a system of Boltzmann hard spheres

2018 ◽  
Vol 189 (06) ◽  
pp. 659-664
Author(s):  
Sergei M. Stishov
Keyword(s):  
Hard Spheres ◽  
Quantum Effects

Quantum-chemical analysis of small silver clusters

1987 ◽  
Vol 52 (7) ◽  
pp. 1652-1657 ◽  
Author(s):  
Grigorii V. Gadiyak ◽  
Yurii N. Morokov ◽  
Mojmír Tomášek
Keyword(s):  
Hard Spheres ◽  
Electronic Configuration ◽  
Close Packing ◽  
Basis Sets ◽  
Silver Clusters ◽  
Quantum Chemical Analysis ◽  
Spin Distribution ◽  
Spin Polarized ◽  
Atomic Silver ◽  
Equilibrium Geometries

Total energy calculations of three- and four-atomic silver clusters have been performed by the spin-polarized version of the CNDO/2 method to get the most stable equilibrium geometries, atomization energies, and charge and spin distribution on the atoms for three different basis sets: {s}, {sp}, and {spd}. When viewed from the equilateral triangle and square geometries, the last electronic configuration, i.e. the {spd} one, appears to be most stable with respect to the geometrical deformations considered. In this case, the behaviour of the atoms of both clusters resembles that of hard spheres (i.e. close-packing).

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

Study of Sedimentation Velocity of Block Copolymer Micelles

1993 ◽  
Vol 58 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Minmin Tian ◽  
C. Ramireddy ◽  
Stephen E. Webber ◽  
Petr Munk
Keyword(s):  
Block Copolymer ◽  
Methacrylic Acid ◽  
Mixed Solvent ◽  
Hard Spheres ◽  
Sedimentation Velocity ◽  
Hydrodynamic Coefficient ◽  
Block Copolymer Micelles ◽  
Copolymer Micelles ◽  
Size Heterogeneity ◽  
Good Agreement

No anomalies were observed during the measurement of sedimentation coefficients of block copolymer micelles formed by copolymers of styrene and methacrylic acid in a mixed solvent; 80 vol.% of dioxane and 20 vol.% of water. The shapes of the sedimenting boundaries suggest that the size heterogeneity of the micelles is small. Linear relations between 1/s and c were obtained. The value of the hydrodynamic coefficient κ was between 2 and 4 in a good agreement with the value 2.75 or 2.86 that was obtained by combining Burgers' or Fixman's values of the coefficient of the concentration dependence kvs for hard spheres with Einstein's value of [η] for spheres.

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