Ordered pattern formation and chaos-order transitions in pulsed fluidized beds

Gas-solid fluidized beds are technologically very important. They are normally operated by continuously injecting gas through a distributor plate at the bottom of the bed of solid particles. We discovered that, when the gas is injected in a pulsating way, remarkably regular patterns may under certain conditions emerge. In a two-dimensional (2D) bed, a rising regular hexagonal pattern of bubbles may form between the bottom plate and a critical bed height. Higher up, the ordered patterns disappear and the bubble flow turns chaotic. Interestingly, prior industrial research has shown positive effects of applying pulsating flow on, e.g,, conversions of chemical processes, yet such regular patterns were never reported. In our laboratory, through an initial investigation with a research fellow and two masters students, the parameter space (average gas flow, frequency and amplitude of the gas pulses, type of particles, ...) was briefly probed to measure the conditions under which the regular patterns form in 2D, and more recently also in a 3D bed. We now wish to more generally investigate this fascinating phenomenon: when, why and how does the pattern formation occur in two- and three-dimensional fluidized beds ? Considering the success of applying pulsating flow or a vibrating distributor plate in industry, this should also be of practical interest, because mass and heat transfer may be larger in such 'structured fluidized beds'. Using optical and pressure probes, video analysis, and y-ray tomography, we will perform a detailed experimental study of the conditions leading to regular patterns in two- and three-dimensional beds. The modeling will consist of a dimensional analysis - which parameter groups play a role -, perturbation analysis, and CFD. An as simple as possible macroscopic model will in the first place be searched for, because of the macroscopically ordered pattern. The perturbation analysis will start with the two-phase equations of Anderson, Sundaresan and Jackson (1995); the mathematical ("virtual") sine wave perturbation used in stability analysis is indeed similar to our physical ("real") pulse.