Universal effects of collective interactions on long-time self-diffusion coefficients in hard-sphere systems

2003 ◽  
Vol 328 (3-4) ◽  
pp. 367-379 ◽  
Author(s):  
Michio Tokuyama ◽  
Hiroyuki Yamazaki ◽  
Yayoi Terada
Keyword(s):  
Diffusion Coefficients ◽  
Hard Sphere ◽  
Self Diffusion ◽  
Long Time ◽  
Collective Interactions

Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow

1994 ◽  
Vol 281 ◽  
pp. 51-80 ◽  
Author(s):  
Chingyi Chang ◽  
Robert L. Powell
Keyword(s):  
Diffusion Coefficients ◽  
Cluster Size ◽  
Near Field ◽  
Spherical Particles ◽  
Random Structure ◽  
Shearing Flow ◽  
Self Diffusion ◽  
Long Time ◽  
Mobility Matrix ◽  
Many Body Interactions

We study the average mobilities and long-time self-diffusion coefficients of a suspension of bimodally distributed spherical particles. Stokesian dynamics is used to calculate the particle trajectories for a monolayer of bimodal-sized spheres. Hydrodynamic forces only are considered and they are calculated using the inverse of the grand mobility matrix for far-field many-body interactions and lubrication formulae for near-field effects. We determine both the detailed microstructure (e.g. the pair-connectedness function and cluster formation) and the macroscopic properties (e.g. viscosity and self-diffusion coefficients). The flow of an ‘infinite’ suspension is simulated by considering 25, 49, 64 and 100 particles to be one ‘cell’ of a periodic array. Effects of both the size ratio and the relative fractions of the different-sized particles are examined. For the microstructures, the pair-connectedness function shows that the particles form clusters in simple shearing flow due to lubrication forces. The nearly symmetric angular structures imply the absence of normal stress differences for a suspension with purely hydrodynamic interactions between spheres. For average mobilities at infinite Péclet number, Ds0, our simulation results suggest that the reduction of Ds0 as concentration increases is directly linked to the influence of particle size distribution on the average cluster size. For long-time self-diffusion coefficients, Ds∞, we found good agreement between simulation and experiment (Leighton & Acrovos 1987 a; Phan and Leighton 1993) for monodispersed suspensions. For bimodal suspensions, the magnitude of Ds∞, and the time to reach the asymptotic diffusive behaviour depend on the cluster size formed in the system, or the viscosity of the suspension. We also consider the effect of the initial configuration by letting the spheres be both organized (size segregated) and randomly placed. We find that it takes a longer time for a suspension with an initially organized structure to achieve steady state than one with a random structure.

p, T Dependence of the Self Diffusion Coefficients and Densities in Liquid Silicone Oils

1996 ◽  
Vol 51 (3) ◽  
pp. 192-196 ◽  
Author(s):  
A. Thern ◽  
H.-D. Lüdemann
Keyword(s):  
Diffusion Coefficients ◽  
Hard Sphere ◽  
The Self ◽  
Hard Sphere Model ◽  
Tait Equation ◽  
Sphere Model ◽  
Rouse Model ◽  
Self Diffusion ◽  
Silicone Oils ◽  
Liquid Silicone

Abstract Self diffusion coefficients and densities from a series of commercial silicones have been studied in the temperature range between 290 and 410 K at pressures up to 200 MPa. The densities are fitted to a modified Tait equation. The self diffusion coefficients are discussed in terms of the rough hard sphere model and tested against the Rouse-model.

Long-time self-diffusion in binary colloidal hard-sphere dispersions

1995 ◽  
Vol 52 (6) ◽  
pp. 6344-6357 ◽  
Author(s):  
A. Imhof ◽  
J. K. G. Dhont
Keyword(s):  
Hard Sphere ◽  
Self Diffusion ◽  
Long Time

Long-time self-diffusion coefficients of suspensions

1992 ◽  
Vol 46 (8) ◽  
pp. 5012-5019 ◽  
Author(s):  
Grzegorz Szamel ◽  
Jan A. Leegwater
Keyword(s):  
Diffusion Coefficients ◽  
Self Diffusion ◽  
Long Time

Application of the Hard Sphere Theory to the Diffusion of Binary Liquid Alloy Systems

1981 ◽  
Vol 36 (11) ◽  
pp. 1225-1232 ◽  
Author(s):  
G. Schwitzgebel ◽  
G. Langen
Keyword(s):  
Melting Temperature ◽  
Liquid Alloy ◽  
Diffusion Coefficients ◽  
Hard Sphere ◽  
Liquid Alloys ◽  
Particle Interactions ◽  
Self Diffusion ◽  
Binary Liquid ◽  
Pure Metals ◽  
Better Than

On the basis of the van der Waals concept of Ascarelli and Paskin the hard sphere theory of self diffusion is extended to binary liquid alloys. Using only the melting temperature of the pure metals and the densities, component self-diffusion coefficients and, with the help of Darken’s equation, mutual diffusion coefficients were calculated. Agreement with experimental results is good in (Bi, Sn), and excellent in (Sn, Zn) and (Li, Ag). Impurity diffusion in liquid Cu, Sn and Pb is predicted better than by the theory of Protopapas et al. Deviations in (Hg, Zn) and (Li, Pb) are tentatively attributed to strong particle interactions in one component (Hg) or in the alloy (Li, Pb).

scholarly journals Modelling the Diffusion Coefficients of Dilute Gaseous Solutes in Hydrocarbon Liquids

2021 ◽  
Vol 42 (10) ◽  
Author(s):  
Yasser A. Aljeshi ◽  
Malyanah Binti Mohd Taib ◽  
J. P. Martin Trusler
Keyword(s):  
Carbon Dioxide ◽  
Diffusion Coefficients ◽  
Hard Sphere ◽  
Tracer Diffusion ◽  
Pure Component ◽  
Viscosity Data ◽  
Polar Liquids ◽  
Self Diffusion ◽  
Coefficient Measurement ◽  
Tracer Diffusion Coefficients

AbstractIn this work, we present a model, based on rough hard-sphere theory, for the tracer diffusion coefficients of gaseous solutes in non-polar liquids. This work extends an earlier model developed specifically for carbon dioxide in hydrocarbon liquids and establishes a general correlation for gaseous solutes in non-polar liquids. The solutes considered were light hydrocarbons, carbon dioxide, nitrogen and argon, while the solvents were all hydrocarbon liquids. Application of the model requires knowledge of the temperature-dependent molar core volumes of the solute and solvent, which can be determined from pure-component viscosity data, and a temperature-independent roughness factor which can be determined from a single diffusion coefficient measurement in the system of interest. The new model was found to correlate the experimental data with an average absolute relative deviation of 2.7 %. The model also successfully represents computer-simulation data for tracer diffusion coefficients of hard-sphere mixtures and reduces to the expected form for self-diffusion when the solute and solvent become identical.

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