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

• 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

• some solid–liquid interfaces for the optimal design of the fractal tree-like channel network. The present work reinvestigates Murray’s law for laminar flow in a fractal tree-like microchannel network considering slip condition. It is found that the slip increases the complexity of the optimal design of

• 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