Analytical multi-scale method for multi-phase complex systems in process engineering—Bridging reductionism and holism

Multi-scale spatio-temporal structures, the dominant feature for all complex systems, are identified and discussed as a common challenge and frontier in process engineering, as well as in science and technology of many different fields and disciplines. Emphasis is paid to the correlation between different scales, which is one of the focuses in complexity science. The energy minimization multi-scale (EMMS) model for particle–fluid flow is revisited as an implementation of the analytical multi-scale method to elucidate its principles, in which the correlation between scales is established by analyzing the compromise between dominant mechanisms. This strategy has been extended to six other systems, covering single-phase flow, gas–liquid flow, granular flow and emulsions. A general framework of the method and the common feature of the compromise processes are then presented together with an introduction to some practical applications of the analytical multi-scale method and its extensions. We conclude with prospects on the multi-scale method as a reasonable approach to complex systems that bridges reductionism and holism.