Optimal fractal tree-like microchannel networks with slip for laminar-flow-modified Murray’s law

• Dalei Jing,
• Shiyu Song,
• Yunlu Pan and
• Xiaoming Wang

Beilstein J. Nanotechnol. 2018, 9, 482–489, doi:10.3762/bjnano.9.46

• Institute of Technology, Harbin, 150001, P. R. China, School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, 150001, P. R. China 10.3762/bjnano.9.46 Abstract The fractal tree-like branched network is an effective channel design structure to reduce the hydraulic resistance

• as compared with the conventional parallel channel network. In order for a laminar flow to achieve minimum hydraulic resistance, it is believed that the optimal fractal tree-like channel network obeys the well-accepted Murray’s law of βm = N−1/3 (βm is the optimal diameter ratio between the daughter

• the fractal tree-like microchannel network to achieve the minimum hydraulic resistance. The optimal diameter ratio to achieve minimum hydraulic resistance is not only dependent on the branching number, as stated by Murray’s law, but also dependent on the slip length, the level number, the length ratio