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

Abstract

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 Peclets 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.