Geometric structure of segmented flow networks
Segmented flows consist of two immiscible fluids which travel along a channel in a segmented arrangement due to an imposed pressure difference. In this paper, the geometric structure of segmented flow networks is examined and fundamental design rules are established for two-phase flow without phase change. These rules provide a basis for mini- and microfluidic architectures that minimize flow resistance for a global system. The focus of the theoretical analysis is on T-shaped constructs which are frequently used to transport slugs/bubbles to multiple sites. When the global pressure difference is dominated by the single-phase flow, i.e. approaching infinitely long slugs, geometric ratios for the T-shaped construct follow the well-established Murrays rule. However, when the global pressure difference is dominated by the presence of a second phase, the geometric ratios follow alternative rules. Using the constructal method, these rules are shown to evenly distribute flow resistance over the area occupied by the T-shaped construct. A simplified surface energy analysis has also been conducted to estimate the work requirements during transport of a bubble from the primary to the daughter channels of the network before breakup occurs. This work input becomes important as the svelteness of the flow network decreases and a critical svelteness has been outlined by considering the channel and junction pressure scales. The design guidelines presented are useful for the optimization of microscale chemical processes and heat exchanger technologies involving two-phase flows.