Fluid flow in a porous tree-shaped network: Optimal design and extension of Hess–Murray’s law

2015 ◽  
Vol 423 ◽  
pp. 61-71 ◽  
Author(s):  
Antonio F. Miguel
Keyword(s):  
Fluid Flow ◽  
Optimal Design ◽  
Murray's Law ◽  
Murray’S Law

scholarly journals Optimal Branching Structure of Fluidic Networks with Permeable Walls

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Vinicius R. Pepe ◽  
Luiz A. O. Rocha ◽  
Antonio F. Miguel
Keyword(s):  
Fluid Flow ◽  
Flow Distribution ◽  
Asymmetric Flow ◽  
Murray's Law ◽  
Engineering Studies ◽  
Murray’S Law ◽  
Permeable Walls ◽  
Wall Permeability ◽  
Branching Flow ◽  
Optimum Relationship

Biological and engineering studies of Hess-Murray’s law are focused on assemblies of tubes with impermeable walls. Blood vessels and airways have permeable walls to allow the exchange of fluid and other dissolved substances with tissues. Should Hess-Murray’s law hold for bifurcating systems in which the walls of the vessels are permeable to fluid? This paper investigates the fluid flow in a porous-walled T-shaped assembly of vessels. Fluid flow in this branching flow structure is studied numerically to predict the configuration that provides greater access to the flow. Our findings indicate, among other results, that an asymmetric flow (i.e., breaking the symmetry of the flow distribution) may occur in this symmetrical dichotomous system. To derive expressions for the optimum branching sizes, the hydraulic resistance of the branched system is computed. Here we show the T-shaped assembly of vessels is only conforming to Hess-Murray’s law optimum as long as they have impervious walls. Findings also indicate that the optimum relationship between the sizes of parent and daughter tubes depends on the wall permeability of the assembled tubes. Our results agree with analytical results obtained from a variety of sources and provide new insights into the dynamics within the assembly of vessels.

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

scholarly journals Seeking minimum entropy production for a tree-like flow-field in a fuel cell

2020 ◽  
Vol 22 (13) ◽  
pp. 6993-7003 ◽  
Author(s):  
Marco Sauermoser ◽  
Signe Kjelstrup ◽  
Natalya Kizilova ◽  
Bruno G. Pollet ◽  
Eirik G. Flekkøy
Keyword(s):  
Fuel Cell ◽  
Flow Field ◽  
Entropy Production ◽  
Minimum Entropy ◽  
Murray's Law ◽  
Field Patterns ◽  
Murray’S Law ◽  
Minimum Entropy Production

We show how we can improve bio-inspired flow field patterns for use in PEMFCs by deviating from Murray's law.

Deviation from Murray's law is associated with a higher degree of calcification in coronary bifurcations

2012 ◽  
Vol 221 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Andreas W. Schoenenberger ◽  
Nadja Urbanek ◽  
Stefan Toggweiler ◽  
Robert Seelos ◽  
Peiman Jamshidi ◽  
...  
Keyword(s):  
Murray's Law ◽  
Murray’S Law

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

2018 ◽  
Vol 9 ◽  
pp. 482-489 ◽  
Author(s):  
Dalei Jing ◽  
Shiyu Song ◽  
Yunlu Pan ◽  
Xiaoming Wang
Keyword(s):  
Laminar Flow ◽  
Hydraulic Resistance ◽  
Slip Length ◽  
Diameter Ratio ◽  
Slip Condition ◽  
Channel Network ◽  
Murray's Law ◽  
Murray’S Law ◽  
Level Number ◽  
Optimal Diameter

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 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.

Murray's law, the ‘Yarrum’ optimum, and the hydraulic architecture of compound leaves

2009 ◽  
Vol 184 (1) ◽  
pp. 234-244 ◽  
Author(s):  
Katherine A. McCulloh ◽  
John S. Sperry ◽  
Frederick C. Meinzer ◽  
Barbara Lachenbruch ◽  
Cristian Atala
Keyword(s):  
Hydraulic Architecture ◽  
Murray's Law ◽  
Murray’S Law
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