FULLY-DEVELOPED TRAVELING-WAVE SOLUTIONS AND BUBBLE FORMATION IN FLUIDIZED-BEDS

It is well known that most gas fluidized beds of particles bubble, whi le most liquid fluidized beds do not. It was shown by Anderson, Sundar esan & Jackson (1995), through direct numerical integration of the vol ume-averaged equations of motion for the fluid and particles, that thi s distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and in terphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate crit erion for separating bubbling and non-bubbling systems. To this end, w e have computed, making use of numerical continuation techniques as we ll as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parame ter values, and examined the evolution of these travelling wave soluti ons through direct numerical integration. It is demonstrated that whet her bubbles form or not is dictated by the value of Omega = (rho(s) nu (t)(3)/Ag)(1/2), where rho(s) is the density of particles, nu(t) is th e terminal settling velocity of an isolated particle, g is acceleratio n due to gravity and A is a measure of the particle phase viscosity. W hen Omega is large (> similar to 30), bubbles develop easily. It is th en suggested that a natural scale for A is rho(s) nu(t) d(p), so that Omega(2) is simply a Froude number.