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A generalised optimisation principle for asymmetric branching in fluidic networks
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Stephenson, David and Lockerby, Duncan A. (2016) A generalised optimisation principle for asymmetric branching in fluidic networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2191). 20160451. doi:10.1098/rspa.2016.0451 ISSN 1364-5021.
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Official URL: http://dx.doi.org/10.1098/rspa.2016.0451
Abstract
When applied to a branching network, Murray’s law states that the optimal branching of vascular networks is achieved when the cube of the parent channel radius is equal to the sum of the cubes of the daughter channel radii. It is considered integral to understanding biological networks and for the biomimetic design of artificial fluidic systems. However, despite its ubiquity, we demonstrate that Murray’s law is only optimal (i.e. maximises flow conductance per unit volume) for symmetric branching, where the local optimisation of each individual channel corresponds to the global optimum of the network as a whole. In this paper, we present a generalised law that is valid for asymmetric branching, for any cross-sectional shape, and for a range of fluidic models. We verify our analytical solutions with the numerical optimisation of a bifurcating fluidic network for the examples of laminar, turbulent, and non-Newtonian fluid flows.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||||
Library of Congress Subject Headings (LCSH): | Non-Newtonian fluids -- Mathematical models, Biomimetics | ||||||||
Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||||
Publisher: | The Royal Society Publishing | ||||||||
ISSN: | 1364-5021 | ||||||||
Official Date: | 24 July 2016 | ||||||||
Dates: |
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Volume: | 472 | ||||||||
Number: | 2191 | ||||||||
Article Number: | 20160451 | ||||||||
DOI: | 10.1098/rspa.2016.0451 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 11 July 2016 | ||||||||
Date of first compliant Open Access: | 24 August 2016 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/I011927/1, EP/N016602/1 and EP/K038664/1 | ||||||||
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