Journal
BEILSTEIN JOURNAL OF NANOTECHNOLOGY
Volume 9, Issue -, Pages 482-489Publisher
BEILSTEIN-INSTITUT
DOI: 10.3762/bjnano.9.46
Keywords
fractal tree-like microchannel networks; hydraulic resistance; Murray's law; slip
Funding
- National Natural Science Foundation of China [51505292]
- Shanghai Aerospace Science and Technology Innovation Fund Project [SAST2017-038]
Ask authors/readers for more resources
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 beta(m) = N-1/3 (beta(m) is the optimal diameter ratio between the daughter channel and the parent channel and N is the branching number at every level), which is obtained under the assumption of no-slip conditions at the channel wall-liquid interface. However, at the microscale, the no-slip condition is not always reasonable; the slip condition should indeed be considered at 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 between the daughter channel and the parent channel, and the diameter of the channel. The optimal diameter ratio decreases with the increasing slip length, the increasing level number and the increasing length ratio between the daughter channel and the parent channel, and decreases with decreasing channel diameter. These complicated relations were found to become relaxed and simplified to Murray's law when the ratio between the slip length and the diameter of the channel is small enough.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available