Focusing on the meso-scales of multi-scale phenomena—In search for a new paradigm in chemical engineering

To celebrate the 90th birthday of Professor Mooson Kwauk, who supervised the multi-scale research at this Institute in the last three decades, we dedicate this paper outlining our thoughts on this subject accumulated from our previous studies. In the process of developing, improving and extending the energy-minimization multi-scale (EMMS) method, we have gradually recognized that meso-scales are critical to the understanding of the different kinds of multi-scale structures and systems. It is a common challenge not only for chemical engineering but also for almost all disciplines of science and engineering, due to its importance in bridging micro- and macro-behaviors and in displaying complexity and diversity. It is believed that there may exist a common law behind meso-scales of different problems, possibly even in different fields. Therefore, a breakthrough in the understanding of meso-scales will help materialize a revolutionary progress, with respect to modeling, computation and application.