Vascular structures with flow uniformity and small resistance

The drive toward vascular smart materials calls for novel flow architectures that bathe and serve entire volumes and areas as uniformly as possible. Here, we show that vascular designs consisting of trees matched canopy to canopy can be configured so that they have two qualities: small flow resistance (ψ) and small volumetric flow nonuniformity (μ). In the past, the only quality sought was small flow resistance. Two classes of architectures are explored: (a) matched trees with diagonal channels through the core and (b) matched trees with orthogonal channels. First, we show that flow architectures can be developed and selected for minimum flow nonuniformity alone. Second, in the ψ − μ design space the best of designs (b) lie close to the best of designs (a), although the best of designs (b) offer slightly better configurations (low ψ and μ) than the best of designs (a). Comparisons with similar architectures generated based on genetic algorithms show that the minimum global flow resistance ψ of designs (a, b) is 2–5 times smaller than the genetic-algorithm values. The flow nonuniformities μ corresponding to the minimum ψ of designs (a, b) are 2–70 times smaller than the flow nonuniformities of the genetic-algorithm results.