微反应器分形流道中物质利用效率优化研究

The optimization of material utilization efficiency in fractal flow channels of the microreactor

自然界广泛存在的分形流道能够实现物质的高效率输运和利用,对分形流道的研究在医学、化学以及社会学等诸多领域具有非常重要的意义.本文采用理论分析和数值模拟相结合的方法,从物质最优化利用角度出发,讨论分形流道中各级流道的作用和末端流道发育极限.研究结果表明,随着流道内Péclet数(Pe)不断增大,流道内物质利用率先增大后减小,可分为3种状态:对流限制状态、过渡状态和扩散限制状态.过渡状态对应的物质利用率最高,而扩散限制状态下物质输运速率最大.不同限制状态下,影响物质利用率的因素不同,物质利用率与Pe数分别呈现不同标度关系.通过优化算法获得分形流道和其流场信息,与局部分析结果对比发现,流道从初级向末端发育过程中,流道逐级收窄, Pe数降低,流体状态从扩散限制状态逐步转变为过渡状态.综合上述分析,分形流道中物质输运和利用分别在初级流道和末级流道中完成,各层级分工协作高效率地完成输运和利用的任务,并且过渡状态是流道发育的最优极限.本文的研究结果有助于对分形流道的深入理解,可为页岩油气缝网设计、高效催化反应器设计以及高灵敏传感器设计等应用领域提供理论指导.

The fractal flow channels widely existed in nature can realize the efficient transport and utilization of materials. The research on fractal flow channels is of great significance to many fields such as medicine, chemistry, and sociology. Through theoretical analysis and numerical simulations from the perspective of material optimization, this paper has discussed the role of each channel in the fractal channels and the development limit of the final channels. The results show that as the Péclets number(Pe) in the channels increases, the rate of material utilization increases first and then decreases. Three states can be clarified: convection-limited state,transition state, and diffusion-limited state. The rate of material utilization in the transition state is the highest, and the rate of material transport in the diffusion-limited state is the highest. Under different limited states, the factors that affect the material utilization rate are different, and the material utilization rate and Pe number show different scaling relations. The fractal channels and its flow field are obtained through the optimization algorithm and compared with the local analysis. It is found that during the development of the flow channels from the primary to the end, the flow channels are gradually narrowed, the Pe number is reduced, and the fluid state changes from the diffusion-limited state to the transition state. Based on the above analysis, the material transport and utilization in the fractal flow channels are completed in the primary flow channels and the final flow channels, respectively, the transport and utilization are performed efficiently by the cooperation of all levels of channels, and the transition state is the optimal limit of the flow channels development. The results can help to understand the fractal flow channels and provide theoretical guidance for applications such as the design of shale oil and gas seam, high-efficiency catalytic reactor, and highly sensitive sensor.