title: Optimal counter-current exchange networks.
abstract: We present a general analysis of exchange devices linking their efficiency to the geometry of the exchange surface and supply network. For certain parameter ranges, we show that the optimal exchanger consists of densely packed pipes which can span a thin sheet of large area (an "active layer"), which may be crumpled into a fractal surface and supplied with a fractal network of pipes. We derive the efficiencies of such exchangers, showing the potential for significant gains compared to regular exchangers (where the active layer is flat), using parameters relevant to biological systems.
authors.affiliation: The London Institute for Mathematical Sciences, 35a South Street, Mayfair, London W1K 2XF, United Kingdom and Unilever R&D, Colworth Science Park, Bedford MK44 1LQ, United Kingdom.
authors.forename: Robert S
authors.initials: RS
authors.lastname: Farr
authors.affiliation: School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
authors.forename: Yong
authors.initials: Y
authors.lastname: Mao
mesh_terms: D055592:Biophysical Phenomena; D017709:Fractals; D008954:Models, Biological; D016571:Neural Networks, Computer