DYNAMICS OF FLUIDIZED SUSPENSIONS OF SPHERES OF FINITE-SIZE

We propose a one-dimensional theory of fluidized suspensions in which the fluids and solids momentum equations are decoupled by using a new mean drag law for the particles. Our mean drag law differs from the st andard drag laws frequently used in that the drag is assumed to depend on the area fraction rather than the number density. For a monodisper se suspension of spheres of radius R, the area fraction and the number density are related by a simple geometrical construction that takes i nto account the area of intersection of the spheres with a plane perpe ndicular to the flow. For the linearized theory uniformly fluidized su spension is unstable but not Hadamard unstable. However, there is a di stinguished set of marginally stable modes belonging to a countable se t of blocked wave numbers alpha: alpha = 4.493/R, 7.7253/R, 10.904/R,. .. The nonlinear theory contains bounded solutions when a certain dime nsionless ''growth rate'' parameter is below a critical value. The pow er spectrum of these bounded solutions is broad banded in both space a nd time, and is very low for the wave numbers that are marginally stab le in the linear theory. These results agree with our experiments, as well as with the previous experimental results from diffraction studie s.