Yoshihisa Enomoto

Finite volume fraction effects on Ostwald ripening

Abstract We investigate the effect of a finite droplet volume fraction on the Ostwald ripening on the basis of the statistical theory recently developed by us. The theory takes into account both the competitive growth and soft-collision effect of droplets arising from statistical correlations among them. The Lifshitz-Slyozov-Wagner scaling law is found to hold. The scaled droplet size distribution function and the average droplet size are determined self-consistently, up to order Q 1 2 , Q being the volume fraction, by numerically solving the kinetic equation of the theory for long times. The results are in excellent agreement with those of the computer by Voorhees and Glicksman within the data scatter, which is not the case if soft-collision processes are omitted as in all the previous theories.

Statistical theory of Ostwald ripening with elastic field interaction

Effects of elastic field interactions between precipitate droplets are incorporated in the statistical theory of Ostwald ripening developed by Tokuyama and the present authors. We find that the elastic effects begin to play important roles in coarsening behavior when the average droplet radius reaches the size α/|B|φ where α is the capillary length, φ is the droplet volume fraction and B is the dimensionless strength of the elastic misfit between the precipitate and the matrix. We see that when the elastic field interactions are attractive, coarsening slows down and simultaneously the droplet size distribution tends to become narrow and symmetrical. When the elastic interactions are repulsive the coarsening is accelerated and the droplet size distribution broadens with positive skewness.

Computer modelling of Ostwald ripening

Abstract On the basis of the multiparticle diffusion equation in the Ostwald ripening, we construct a new effective model by using three simplifications: 1. (1) explicit consideration of the screening effect of the diffusion field, 2. (2) the dimensional reduction, 3. (3) the expansion in the volume fraction. We simulate this model for various values of the volume fraction, and obtain the droplet size distribution functions, coarsening rates, the standard deviations and the skewness of the distribution function, which are compared with those of the earlier theories and the recent direct computer simulations of the multiparticle diffusion equation. The present results are in good agreement with those of the theory by Tokuyama and Kawasaki, which have pointed out the importance of the soft-collision processes.

Kinetic equations for Ostwald ripening

A new viewpoint on the kinetics of Ostwald ripening is presented by studying the kinetic equation recently derived for the late stage of phase separation. It is shown that the average droplet radius grows as t13 and the number density of droplets decays as t-1. An important effect of a soft (distant) collision on coarsening is discussed. Thus the relative droplet size distribution function is found to obey a second-order differential equation. The coarsening rate is also expressed in terms of the distribution function, leading to a dependence on the volume fraction of the minority phase.

The time dependent behavior of the ostwald ripening for the finite volume fraction

Abstract On the basis of the theory of Tokuyama and Kawasaki on the Ostwald ripening, we investigate the time dependent behavior from the late stage into the scaling region. We calculate numerically the transient behavior of the droplet size distribution function and the average droplet radius for various initial conditions. Moreover we compare the obtained results with the experiments in which the transient behavior of the Al-Li, Ni-Al and Ni-Si alloy systems were investigated for various ageing temperatures. The present theoretical results are in good agreement with these experimental results.

Computer simulation of Ostwald ripening with elastic field interactions

Abstract Effects of elastic field interactions between precipitating droplets on coarsening behavior (Ostwald ripening) have been studied by simulating the droplet growth equations with elastic interactions which have been recently put forward by the present authors. Attractive elastic inter-droplet interactions lead to suppression of coarsening with sharp droplet size distributions, whereas repulsive interactions accelerate coarsening with broadened droplet size distributions. For a small droplet volume fraction, Q = 0.01, the simulation results are in good agreement with our earlier theoretical predictions. The finite Q -effects on coarsening are also investigated for Q = 0.1, and are found to delay the onset time after which elastic interactions play important roles in coarsening, by comparing the simulation result with our earlier theoretical prediction for the same Q value. This is explained by correlation effects. The broadened droplet size distribution is found to be in good agreement with experimental results for fatigued Al-Zn alloys.

Dynamics of fluctuations in ostwald ripening: A new equation of motion for the structure function

Abstract A new method of finding an equation of motion for the structure function S k ( t ) from the kinetic equations recently derived for the late stage of phase separation is presented. S k ( t ) is shown to be scaled by two kinds of characteristics lengths, the average droplet radius R (t) and the screening length l ( t ), as S k (t)∝ R (t) 3 S(x, q; Q) 1 2 ) with x=k R (t) and q = kl ( t ) where Q is the volume fraction of the minority phase, and R (t) and l(t) satisfy the power laws (t)∼Q −1 2 R (t) and R (t)∼t 1 3 . The scaled structure function S(x, q; Q 1 2 ) is found to obey a first-order differential equation with two source terms which originate from two kinds of fluctuations; initial thermal fluctuations and nonthermal fluctuations generated by soft collisions among droplets. The soft-collision process is shown to produce a new type of narrowing of S(x, q; Q 1 2 ) which is different from the usual one that occurs as Q increases. The results are compared with other theories.

Elementary derivation of kinetic equations for Ostwald ripening

A direct and elementary derivation is presented for the kinetic equation of the single droplet distribution function and the variance equation that describe Ostwald ripening. The derivation is basically algebraical and the screening effects of diffusional interactions among droplets is taken into account automatically by a projection technique. The results correct up to the square root of the volume fraction confirm the kinetic equations derived previously by Tokuyama and Kawasaki except for a correction to the variance equation.

Simulation study on microstructure formations in magnetic fluids

We propose the Langevin-type microscopic equations of motion for magnetic fluids. Magnetic fluids are modeled as an ensemble of interacting ferromagnetic nanoparticles suspended in a viscous fluid. The present model is described in terms of position vectors of nanoparticles and orientation vectors of their magnetic dipole moments. In this model, forces and torques arising from the magnetic origin and the surrounding fluid flow are included. Effects of non-spherical particle shape are also taken into account. From the Brownian dynamics simulations of the model, it is found that the present model exhibits various microstructure formation processes in magnetic fluids.

SLOW DYNAMICS OF SUPERCOOLED COLLOIDAL FLUIDS : SPATIAL HETEROGENEITIES AND NONEQUILIBRIUM DENSITY FLUCTUATIONS

The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient DS(Φ) becomes zero at the glass transition volume fraction φg as DS(Φ)∼D0|1−Φ(x,t)/φg|γ with γ=2 where Φ(x,t) is the local volume fraction of colloids, D0 the single-particle diffusion constant, and φg=(43)3/(7ln3−8ln2+2). This dynamic anomaly results from the many-body correlations due to the long-range hydrodynamic interactions. Then, it is shown how small initial disturbances can be enhanced by this anomaly near φg, leading to long-lived, spatial heterogeneities. Those heterogeneities are responsible for the slow relaxation of nonequilibrium density fluctuations. In fact, the self-intermediate scattering function is shown to obey a two-step relaxation around the β-relaxation time tβ∼|1−φ/φg|−1, and also to be well approximated by the Kohlrausch–Williams–Watts function with an exponent β around the α-relaxation time tα∼|1−φ/φg|−η, where η=γ/β, and φ is the particle volume fraction. Thus, the nonexponential α relaxation is shown to be explained by the existence of long-lived, spatial heterogeneities.