New game theoretical model and GNE results for the flow structure in bubble columns

The mechanism of the meso-scale structure in the gas-liquid system in bubble columns is of great significance in chemical engineering. Based on the multi-objective problem indwelling the EMMS(energy-minimization-multi-scale) model, we studied the problem from a novel point of the noncooperative game theory. In our previous works, we formulated the problem as a game between different dominant mechanisms of particles and the conservation equations of system state variables were considered as constraints. Then we chose several free state variables as strategies for each player for some reason. The system state at GNE(generalized Nash equilibrium) seems quite coincident with the model prediction and the experimental results in the literature. In this paper, we will choose different free variables as strategies of the players and thus will build a different game model for the same problem. Then we will see different GNE results about the steady states as well as the important parameters of the system, which implies that the problem is not so simple or naive as we regarded before. Actually it involves much tough and fundamental issues that we must consider very carefully.