scholarly journals Diffusion microrheology of ferrofluids

2018 ◽  
Vol 64 (1) ◽  
pp. 82 ◽  
Author(s):  
R. Peredo-Ortíz ◽  
M. Hernández-Contreras
Keyword(s):  
Statistical Mechanics ◽  
Computer Simulations ◽  
Magnetic Fluid ◽  
Structure Factor ◽  
Diffusion Coefficients ◽  
Magnetic Particles ◽  
Particle Concentration ◽  
Thermal Fluctuations ◽  
Self Diffusion ◽  
Viscous Modulus

We provide a statistical mechanics approach to study the linear microrheology of thermally equilibrated and homogeneous ferrofluids. Theexpressions for the elastic and loss moduli depend on the bulk microstructure of the magnetic fluid determined by the structure factor of thesuspension of magnetic particles. The comparison of the predicted microrheology with computer simulations confirms that as a function ofrelaxation frequency of thermal fluctuations of the particle concentration both theory and simulations have the same trends. At very shortfrequencies the viscous modulus relates to the translational and rotational self-diffusion coefficients of a ferro-particle.

Brownian Motion

2018 ◽  
pp. 1-24
Author(s):  
Giovanni Zocchi
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Concentration Gradient ◽  
Nonequilibrium Statistical Mechanics ◽  
Thermal Fluctuations ◽  
Nonequilibrium System ◽  
Individual Particle ◽  
Equilibrium Concept ◽  
Self Diffusion ◽  
Main Ideas

This chapter provides an introduction to the main ideas of Brownian motion. Brownian motion connects equilibrium and nonequilibrium statistical mechanics. It connects diffusion—a nonequilibrium phenomenon—with thermal fluctuations—an equilibrium concept. More precisely, diffusion with a net flow of particles, driven by a concentration gradient, pertains to a nonequilibrium system, since there is a net current. Without a concentration gradient, the system is macroscopically in equilibrium, but each individual particle undergoes self-diffusion just the same. In this sense, Brownian motion is at the border of equilibrium and nonequilibrium statistical mechanics.

A magnetic super lattice

1987 ◽  
Vol 45 ◽  
pp. 360-361 ◽  
Author(s):  
M.D. Bentzon ◽  
J. v. Wonterghem ◽  
A. Thölén
Keyword(s):  
Thermal Decomposition ◽  
Oleic Acid ◽  
Magnetic Fluid ◽  
Magnetic Particles ◽  
Carbon Film ◽  
Thick Layer ◽  
Amorphous Iron ◽  
Super Lattice ◽  
Carrier Liquid ◽  
Median Diameter

We report on the oxidation of a magnetic fluid. The oxidation results in magnetic super lattice crystals. The “atoms” are hematite (α-Fe2O3) particles with a diameter ø = 6.9 nm and they are covered with a 1-2 nm thick layer of surfactant molecules.Magnetic fluids are homogeneous suspensions of small magnetic particles in a carrier liquid. To prevent agglomeration, the particles are coated with surfactant molecules. The magnetic fluid studied in this work was produced by thermal decomposition of Fe(CO)5 in Declin (carrier liquid) in the presence of oleic acid (surfactant). The magnetic particles consist of an amorphous iron-carbon alloy. For TEM investigation a droplet of the fluid was added to benzine and a carbon film on a copper net was immersed. When exposed to air the sample starts burning. The oxidation and electron irradiation transform the magnetic particles into hematite (α-Fe2O3) particles with a median diameter ø = 6.9 nm.

scholarly journals Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges

2021 ◽  
Vol 11 (11) ◽  
pp. 5070
Author(s):  
Xesús Prieto-Blanco ◽  
Carlos Montero-Orille
Keyword(s):  
Ion Exchange ◽  
Diffusion Coefficients ◽  
Molten Salts ◽  
Theoretical Modelling ◽  
Copper Films ◽  
Theoretical Frameworks ◽  
Self Diffusion ◽  
Exchange Processes ◽  
The One ◽  
Made In

In the last few years, some advances have been made in the theoretical modelling of ion exchange processes in glass. On the one hand, the equations that describe the evolution of the cation concentration were rewritten in a more rigorous manner. This was made into two theoretical frameworks. In the first one, the self-diffusion coefficients were assumed to be constant, whereas, in the second one, a more realistic cation behaviour was considered by taking into account the so-called mixed ion effect. Along with these equations, the boundary conditions for the usual ion exchange processes from molten salts, silver and copper films and metallic cathodes were accordingly established. On the other hand, the modelling of some ion exchange processes that have attracted a great deal of attention in recent years, including glass poling, electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles, has been addressed. In such processes, the usual approximations that are made in ion exchange modelling are not always valid. An overview of the progress made and the remaining challenges in the modelling of these unique processes is provided at the end of this review.

scholarly journals Self-Diffusion Coefficients, Aggregation Numbers and the Range of Existence of Spherical Micelles of Oxyethylated Alkylphenols

2021 ◽  
Author(s):  
Victor P. Arkhipov ◽  
Natalia A. Kuzina ◽  
Andrei Filippov
Keyword(s):  
Aqueous Solutions ◽  
Diffusion Coefficients ◽  
The Self ◽  
Self Diffusion ◽  
Aggregation Numbers ◽  
Temperature Ranges ◽  
Spherical Micelles ◽  
Limiting Values

AbstractAggregation numbers were calculated based on measurements of the self-diffusion coefficients, the effective hydrodynamic radii of micelles and aggregates of oxyethylated alkylphenols in aqueous solutions. On the assumption that the radii of spherical micelles are equal to the lengths of fully extended neonol molecules, the limiting values of aggregation numbers corresponding to spherically shaped neonol micelles were calculated. The concentration and temperature ranges under which spherical micelles of neonols are formed were determined.

scholarly journals Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4030
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Surface Effect ◽  
Bulk Water ◽  
Self Diffusion ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Chain Lengths ◽  
Fluid Diffusion ◽  
Self Diffusion Coefficient

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH2)3CH3, –(CH2)7CH3, and –(CH2)11CH3 nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.

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.

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