Principle-based design of distributed two-phase flow for fluid and heat transport

The design of real systems incorporating multiphase flows remains a significant challenge for applications including biofluidics, microreactors and heat exchangers. Segmented two-phase flow without phase change is common to such applications, for the purpose of distributing biological samples from one site to many and for enhancing heat and mass transport over conventional laminar single phase flow. This paper theoretically examines flow configurations that can efficiently transport a segmented gas-liquid flow over an area. In the first part, fundamental design rules have been determined using the constructal method to minimize flow resistance of elemental bifurcations. It was determined that the geometric diameter ratio follows an alternative to the established Murray's law (also known as the Hess-Murray law) when the global pressure difference is dominated by short liquid slugs and the gas bubble phase. Using the findings for an elemental bifurcation, the second part investigates both single scale and multiple scale hierarchical configurations for combined fluid and heat transport. The multiple scale tree-shaped design can be advantageous in the controlled transport of segmented phases over an area and for low thermal resistance and pumping power requirements compared to a single scale serpentine channel layout. The principle-based method and results from this study can be used to reduce the design space in high-fidelity investigations of mini- and microscale segmented flows for fluid and heat transport purposes.