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Treelike networks accelerating capillary flow

Dahua Shou1,*, Lin Ye1,†, and Jintu Fan2,‡

  • 1Centre for Advanced Materials Technology (CAMT), School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
  • 2Department of Fiber Science & Apparel Design, College of Human Ecology, Cornell University, Ithaca, New York 14853, USA

  • *dhshou@gmail.com
  • †Corresponding author: lin.ye@sydney.edu.au
  • ‡jf456@cornell.edu
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Phys. Rev. E 89, 053007 – Published 12 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.053007

Abstract

Transport in treelike networks has received wide attention in natural systems, oil recovery, microelectronic cooling systems, and textiles. Existing studies are focused on transport behaviors under a constant potential difference (including pressure, temperature, and voltage) in a steady state [B. Yu and B. Li, Phys. Rev. E 73, 066302 (2006); J. Chen, B. Yu, P. Xu, and Y. Li, Phys. Rev. E 75, 056301 (2007)]. However, dynamic (time-dependent) transport in such systems has rarely been concerned. In this work, we theoretically investigate the dynamics of capillary flow in treelike networks and design the distribution of radius and length of local branches for the fastest capillary flow. It is demonstrated that capillary flow in the optimized tree networks is faster than in traditional parallel tube nets under fixed constraints. As well, the flow time of the liquid is found to increase approximately linearly with penetration distance, which differs from Washburn's classic description that flow time increases as the square of penetration distance in a uniform tube.

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Phys. Rev. E 89, 053007– Published 12 May, 2014
  • Received 13 November 2013

©2014 American Physical Society

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