Multi-scale modeling, bubble

Bauer, M. and Eigenberger, G. (1999), A concept for multi-scale modeling of bubble columns and loop reactors, Chem. Eng. ScL, 54, 5109-5117. 

All the models proposed for fluidized bed membrane reactors have the same limitations. These models are phenomenological models that make use of closure equations originally derived for fluidized bed without internals. Although it is known that the presence of internals (membranes and permeation of gas through them) may vary the behavior of bubbles, mass transfer and solid circulation inside the bed, reliable closure equations for membrane assisted fluidized bed are not yet available. A way to solve this problem is to use a so-called multi-scale modeling of dense gas-solid systems, where low level... 

Albeit originally proposed for gas-solid fluidization, the concepts of structure resolution and compromise between dominant mechanisms embodied in the EMMS model can be generalized into the so-called variational multi-scale methodology (Li and Kwauk, 2003) and extended to other complex systems (Ge et al., 2007). One typical example out of these extensions is the Dual-Bubble-Size (DBS) model for gas-liquid two-phase flow in bubble columns (Yang et al., 2007, 2010). 

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