New bounds on the sedimentation velocity for hard, charged and adhesive hard-sphere colloids

2011 ◽  
Vol 667 ◽  
pp. 403-425 ◽  
Author(s):  
W. TODD GILLELAND ◽  
SALVATORE TORQUATO ◽  
WILLIAM B. RUSSEL
Keyword(s):  
Brownian Motion ◽  
Upper Bound ◽  
Hard Sphere ◽  
Large Scale ◽  
Hard Spheres ◽  
Colloidal Dispersions ◽  
Sedimentation Velocity ◽  
Close Packing ◽  
Interparticle Potential ◽  
Equilibrium Microstructure

The sedimentation velocity of colloidal dispersions is known from experiment and theory at dilute concentrations to be quite sensitive to the interparticle potential with attractions/repulsions increasing/decreasing the rate significantly at intermediate volume fractions. Since the differences necessarily disappear at close packing, this implies a substantial maximum in the rate for attractions. This paper describes the derivation of a robust upper bound on the velocity that reflects these trends quantitatively and motivates wider application of a simple theory formulated for hard spheres. The treatment pertains to sedimentation velocities slow enough that Brownian motion sustains an equilibrium microstructure without large-scale inhomogeneities in density.

scholarly journals The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition

1987 ◽  
Vol 42 (3) ◽  
pp. 231-235
Author(s):  
Hyearn-Maw Koo ◽  
Siegfried Hess
Keyword(s):  
Hard Sphere ◽  
Solid Phase ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Transition Density ◽  
Colloidal Dispersions ◽  
Number Density ◽  
Relative Pair ◽  
Hard Sphere Fluid ◽  
Solid Phase Transition

Solution of the Kirkwood-Smoluchowski equation for a hard sphere fluid yields an expression for the viscosity which shows a dramatic pretransitional increase and a divergence at a number density close to that one observed in computer simulations and in colloidal dispersions. The value for the transition density stems from a boundary condition at the surface of the hard sphere in the configurational relative pair-space and makes use of the density dependence of the pair-correlation function and of its derivative at the point of contact.

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).

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.

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

scholarly journals Upper-Bound General Circulation of the Ocean: a Theoretical Exposition

2021 ◽  
Author(s):  
Hsien-Wang Ou
Keyword(s):  
Ocean Circulation ◽  
Upper Bound ◽  
First Principles ◽  
General Circulation ◽  
Large Scale ◽  
Companion Paper ◽  
Jet Stream ◽  
Equatorial Undercurrent ◽  
Macroscopic Motion ◽  
Dynamical Principle

This paper considers the general ocean circulation within the thermodynamical closure of our climate theory, which aims to deduce the generic climate state from first principles. The preceding papers of the theory have reduced planetary fluids to warm/cold masses and determined their bulk thermal properties, which provide prior constraints for the derivation of the upper-bound circulation when the potential vorticity is homogenized in moving masses. In a companion paper on the atmosphere, this upper bound is seen to reproduce the prevailing wind, forsaking therefore previous discordant explanations of the easterly trade and the polar jet stream. In this paper on the ocean, we again show that this upper bound may replicate broad features of the observed circulation, including a western-intensified subtropical gyre and a counter-rotating tropical gyre feeding the equatorial undercurrent. Together, we posit that PV homogenization may provide a unifying dynamical principle of the large-scale planetary circulation, which may be interpreted as the maximum macroscopic motion extractable by microscopic stirring --- within the confine of the thermal differentiation.

On the computability of a construction of Brownian motion

2013 ◽  
Vol 23 (6) ◽  
pp. 1257-1265 ◽  
Author(s):  
GEORGE DAVIE ◽  
WILLEM L. FOUCHÉ
Keyword(s):  
Brownian Motion ◽  
Lower Bound ◽  
Rate Of Convergence ◽  
Upper Bound ◽  
Binary Sequence ◽  
Computable Analysis

We examine a construction due to Fouché in which a Brownian motion is constructed from an algorithmically random infinite binary sequence. We show that although the construction is provably not computable in the sense of computable analysis, a lower bound for the rate of convergence is computable in any upper bound for the compressibilty of the sequence, making the construction layerwise computable.

scholarly journals Event-Driven Molecular Dynamics Simulation of Hard-Sphere Gas Flows in Microchannels

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Volkan Ramazan Akkaya ◽  
Ilyas Kandemir
Keyword(s):  
Molecular Dynamics ◽  
Hard Sphere ◽  
Stokes Equations ◽  
Hard Spheres ◽  
Flow Characteristics ◽  
Dynamics Simulation ◽  
Navier Stokes ◽  
Gas Flows ◽  
Linearized Boltzmann Equation ◽  
Event Driven

Classical solution of Navier-Stokes equations with nonslip boundary condition leads to inaccurate predictions of flow characteristics of rarefied gases confined in micro/nanochannels. Therefore, molecular interaction based simulations are often used to properly express velocity and temperature slips at high Knudsen numbers (Kn) seen at dilute gases or narrow channels. In this study, an event-driven molecular dynamics (EDMD) simulation is proposed to estimate properties of hard-sphere gas flows. Considering molecules as hard-spheres, trajectories of the molecules, collision partners, corresponding interaction times, and postcollision velocities are computed deterministically using discrete interaction potentials. On the other hand, boundary interactions are handled stochastically. Added to that, in order to create a pressure gradient along the channel, an implicit treatment for flow boundaries is adapted for EDMD simulations. Shear-Driven (Couette) and Pressure-Driven flows for various channel configurations are simulated to demonstrate the validity of suggested treatment. Results agree well with DSMC method and solution of linearized Boltzmann equation. At low Kn, EDMD produces similar velocity profiles with Navier-Stokes (N-S) equations and slip boundary conditions, but as Kn increases, N-S slip models overestimate slip velocities.

Structural properties of dense hard sphere systems near random close packing

2011 ◽  
Author(s):  
B. A. Klumov ◽  
S. A. Khrapak ◽  
G. E. Morfill ◽  
Vladimir Yu. Nosenko ◽  
Padma K. Shukla ◽  
...  
Keyword(s):  
Structural Properties ◽  
Hard Sphere ◽  
Close Packing ◽  
Random Close Packing

Structure of chemically reacting particles near a hard wall from integral equations and computer simulations

1996 ◽  
Vol 74 (1-2) ◽  
pp. 65-76 ◽  
Author(s):  
A. Trokhymchuk ◽  
D. Henderson ◽  
S. Sokołowski
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Hard Spheres ◽  
Total Density ◽  
Hard Wall ◽  
Monte Carlo Data ◽  
Density Profiles ◽  
Interparticle Potential ◽  
Theoretical Predictions ◽  
Chemically Reacting

We performed Monte-Carlo computer simulations of a fluid of chemically reacting, or overlapping, hard spheres near a hard wall. The model of the interparticle potential is that introduced by Cummings and Stell. This investigation is directed to the determination of the structure of the fluid at the wall, and the orientation of the dimers in particular. In addition, we applied the singlet Percus–Yevick, hypernetted chain and Born–Green–Yvon equations to calculate the total density profiles of the particles. A comparison with the Monte-Carlo data indicates that the singlet Percus–Yevick theory is superior and leads to results that are in reasonable agreement with simulations for all the parameters investigated. We also calculated the average numbers of dimers formed in the bulk part of the system and the results are compared with different theoretical predictions.

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