Structure-dependent analysis of energy dissipation in gas-solid flows: Beyond nonequilibrium thermodynamics

- Structure-dependent analysis of energy dissipation rate is presented for fluidization.
- Minimum energy dissipation rate applies to homogeneous flow state.
- EMMS predicts the choking transition but minimum energy dissipation rate fails.

Gas-solid fluidized bed is a typical dissipative system, featuring meso-scale structures with bimodal distribution of parameters. The energy-minimization multi-scale (EMMS) model focuses on such dissipative characteristics and has shown many successful applications. In previous work, through structure-dependent analysis of mass, momentum and energy conservation, we have discussed the consistency between the hydrodynamic equations of two-fluid model (TFM) and those of the EMMS model. In this work, we extend this structure-dependent analysis to the extremum behavior of dissipation processes, revealing that the solution based on the minimum energy dissipation rate applies only to homogeneous, dilute flow states, but fails in the particle-fluid compromising fluidization regime, in particular, fails to predict choking transition. By comparison, the EMMS variational stability condition that is based on the principle of compromise in competition between dominant mechanisms well describes the flow regimes of fluidization. This work unfolds a fresh viewpoint to understand the EMMS stability condition that is beyond the analysis of extremum of energy dissipation. And it is expected to boost the development of EMMS-based meso-scale modeling in broader realm of multiphase flow systems.