The design of systems incorporating multiphase flows remains a significant challenge for applications including lab-on-chip and microreactors. Segmented two-phase flow is used for the purpose of distributing biological samples from one site to many, enhancing heat and mass transport over laminar single phase flow and rapid chemical synthesis. This paper examines hierarchical designs, regularly utilised in such applications, that transport a segmented gas-liquid flow over an area with maximal thermodynamic performance. Fundamental design rules, predicted using the constructal method, minimize flow resistance of elemental bifurcations. The predicted geometric configuration follows an alternative to the established Murray's law (or Hess-Murray law) when the global pressure difference is dominated by short liquid slugs and dispersed gas phase. Breakup of phases in the junction region was examined numerically with a volume-of-fluid approach to develop a general criteria where junction losses are non-negligible. Although this loss is periodic, the interfacial pressure during the necking stage of the dispersed phase dominates. Using the findings for an elemental bifurcation, multiple scale hierarchical configurations for combined fluid and heat transport were assessed. The multiple scale tree-shaped design can be advantageous for low thermal resistance and pumping power requirements compared to a single scale serpentine layout. The principle-based method and results can reduce the design space in high-fidelity investigations of microscale segmented flows. (C) 2016 Elsevier Ltd. All rights reserved.