Kengo Ichiki

Dynamical simulation of fluidized beds: Hydrodynamically interacting granular particles

A numerical simulation of a gas-fluidized bed is performed without introduction of any empirical parameters. Realistic bubbles and slugs are observed in our simulation. It is found that the convective motion of particles is important for the bubbling phase and there is no convection in the slugging phase. From the simulation results, non-Gaussian distributions are found in the particle velocities and the relation between the deviation from Gaussian and the local density of particles is suggested. It is also shown that the power spectra of particle velocities obey power laws. A brief explanation of the relationship between the simulation results and the Kolmogorov scaling argument is discussed.

Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics

It is shown that the method of reflections in resistance form (with truncated multipoles) is one of many possible iterative methods to obtain the inverse of the mobility matrix (with the same truncation) in low-Reynolds-number hydrodynamics. Although the method of reflections in the mobility form is guaranteed to converge, it is found that in the resistance form the method may fail to converge. This breakdown is overcome by conjugate-gradient-type iterative methods, and the implications of the iterative method for low-Reynolds-number hydrodynamics are discussed.

Faxen-like relations for a nonuniform suspension

The first part of the paper shows how ensemble averages that correspond to a prescribed statistically nonuniform spatial distribution of particles can be evaluated starting from a statistically uniform ensemble. The method consists of attributing to each realization of the uniform ensemble a suitable weight which is explicitly constructed. As an application of this general procedure, in the second part of the paper, the behavior of particles subjected to force or torque in a statistically nonuniform suspension and the behavior of a suspension subjected to a uniform shear are studied. In particular, it is shown how the average translational and angular velocities of the particles with respect to the mixture satisfy Faxen-like relations. Furthermore, it is pointed out that several quantities which vanish in an identical way in the case of a uniform suspension are nonzero in the presence of spatial nonuniformities.

The stress system in a suspension of heavy particles: antisymmetric contribution

The nature of the stress in a suspension of equal homogeneous spheres all subject to the same force, such as weight, is considered; inertial effects are neglected. This study builds upon some of the well-known work devoted to this problem by the founder of the Journal of Fluid Mechanics, Professor George K. Batchelor. After developing a general theory, the antisymmetric part of the stress tensor is considered in detail. It is shown that, in addition to a term already found by Batchelor and characterized by an axial vector, the antisymmetric stress contains another term characterized by the curl of a polar vector. As a consequence, a suspension will possess, in addition to an axial vortex viscosity, a polar vortex viscosity. Appendix C presents a calculation of the hindrance function for rotation correct to the first order in the particle volume fraction.

On the computation of ensemble averages for spatially non-uniform particle systems

When there is no clear separation between micro- and macro-scales, ergodicity cannot be invoked to transform ensemble into volume averages. In such cases it is necessary to use ensemble averaging directly. A straightforward calculation of such averages converges slowly and therefore requires a large number of realizations of the system. This paper describes a much more efficient method based on the use of a Fourier expansion of the quantity to be averaged. The advantages of the Fourier approach are estimated in general terms and demonstrated explicitly with several examples for the specific problem of equal spheres in a viscous fluid. The analytical estimates suggest that similar results can be expected for other situations as well. It is shown both analytically and numerically that the variance of the Fourier coefficients is in many cases significantly smaller than that of the direct method, which leads to a much faster convergence of the former. The paper also describes a method by which the probability distribution of a uniform ensemble can be biased so as to mimic that of a non-uniform one with prescribed properties.

SIMULATION OF GRANULAR PARTICLES IN FLOW BY THE STOKESIAN-DYNAMICS METHOD

We apply the Stokesian-dynamics method for colloidal particles to simulate motion of granular particles in uniform flow. Our preliminary result suggests that inhomogeneity of flow including the boundary condition of flow is important to get fluidized motion of granular particles.

Fast Calculation of Hydrodynamic Interaction among Particles in the Stokes Flows

The aim of this work is to present an efficient computational method of hydrodynamic interaction among spherical particles in low-Reynolds-number flows. A standard method called Stokesian Dynamics 1) has two main difficulties: the heavy computational load which is scaled by O(N ) with the number of particle N , and no systematic way to improve approximation. These will overcome in terms of multipole expansion, iterative scheme and fast multipole method.