| Summary: | Ramifying networks of tubes for delivery and multipoint distribution of fluids pervade engineered and living systems. Bifurcating (pairing) is the basic building blocks of all these trees. Comprehensively characterizing of ramified networks requires optimization rules for the sizes of the bifurcating tubes. In this paper, we derive generalized rules applicable to branching of both straight and curved tubes, impermeable and permeable tubes for fluid flows that exhibit different properties (Newtonian and non-Newtonian, laminar and turbulent). Key characteristics of design resulting of these rules are also discussed and compared with analytical expressions for the optimum daughter–parent sizes available in the literature. Here we also report the influence of individual slug/bubbles on flows in optimal branching tubes that is of practical importance, since they are found in both engineered and living systems.
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