arXiv subjects
Publications and source records attributed to Hisao Hayakawa.
We present a thermodynamic theory of weakly excited two-dimensional granular systems from the view point of elementary excitations of spinless Fermion systems. We introduce a global temperature T that is associated with the acceleration amplitude Γin a vibrating bed. We show that the configurational statistics of weakly excited granular materials in a vibrating bed obey the Fermi statistics.
We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations.
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 on the relationship between the simulation results and the Kolmogorov scaling argument is discussed.
An analytical treatment for the sedimentation rate of disordered suspensions is presented in the context of a resistance problem. From the calculation it is confirmed that the lubrication effect is important in contrast to the suggestion by Brady and Durlofsky (Phys.Fluids Vol.31, 717 (1988)). The calculated sedimentation rate agrees well with the experimental results in all range of the volume fraction.