Accessing the Influence of Hess-Murray Law on Suspension Flow through Ramified Structures

Serrenho, Ana; Miguel, António F.

doi:10.4028/www.scientific.net/ddf.334-335.322

Cited by 10 publications

(6 citation statements)

References 22 publications

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“…It is obvious that branching networks are not limited to those with cylindrically shaped tubes and hence they include other flow duct geometries, such as ducts with square cross sectional shape [26], and even free surface open channel networks [21].…”

mentioning

confidence: 99%

Fluid Flow at Branching Junctions

Sochi

2015

Inter J Fluid Mech Res

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mentioning

confidence: 99%

Fluid Flow at Branching Junctions

Sochi

2015

Inter J Fluid Mech Res

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“…This is a major simplification, and both experimental [12,20,21,34,45] and numerical [2,13,22,23,24,33,34,40] studies demonstrated that the inherent unsteadiness in blood vessels has a major impact on the exponent of the allometric correlation. c) Independence on the type of fluid Both sap and blood are non-Newtonian fluids, and experimental and numerical studies demonstrate that releasing the newtonianity condition results in a different value of the exponent n in Eq.…”

Section: B) Validity Of the Steady State Flow Conditionsmentioning

confidence: 99%

Predictive Models for the “Optimal” Radius Ratios in Natural Bi- And Trifurcated Vessels: Beyond the Hess-Murray Law

Sciubba

2023

36th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 20

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Bifurcated structures are ubiquitous in nature, both in living and non-living systems. The modern approach to their physical modelling starts from the recognition that in plants and animals the substitution of (a portion of) a straight vessel length with a branched one serves a biological "goal" that requires some energy and material "expenditure". Such expenditure must be justified by a compensating gain for the resulting evolved structure. A great number of studies addressed this topic, mainly from a biomedical science perspective, but since all of them indicate a weak agreement with experimental data, it is useful to explore the matter in some more detail. The purpose of the vessels considered in this study is to "transport" material flows like sap, blood or air, and the striking geometrical similarity of the forked structures found in plants, circulatory systems, bronchial alveoli and river deltas suggests indeed the presence of a single underlying physical principle. Experimental evidence indicates that the topology of bifurcated blood, air and sap vessels (e.g., their "shape") is amazingly similar under quite different external constraints, and this might imply that the shape of a bifurcation is at least to some extent independent of the boundary conditions. Furthermore, it is unclear if and to what measure the functional advantage obtained by repeated bifurcations decreases with the number of splitting levels. This paper presents a critical review of the most popular physical model formulated for the description of bifurcated structures, the so-called Hess-Murray law ("H-M" in the following). It is first shown that, under a very restrictive set of assumptions, the H-M law can be obtained by the assumption of constant wall stress in the parent and daughter branches. Then both Hess' and Murray's original derivations are discussed from a physical point of view, and the extension of the rule to the case of non-symmetrical bi-and trifurcations is presented. It is then argued that in real branched networks the actual optimality criteria (i.e., in an evolutionary sense the "driving force") may be quite different from the assumptions posited in the H-M law literature, which explains the weak predictive value of the law. Some adjustments to the model that include a resource-based cost/benefit of the formation of a bifurcation are presented and discussed.

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“…This model is based on counting bifurcations inwards from the periphery. Other approaches, focused on change in size of consecutive vessels generation, are provided by Reis [50], Serrenho and Miguel [51], Miguel [52]. Based on the constructal law, a comprehensive generalized scaling equations are presented for the vessels diameters and lengths of non-symmetric flow structures [51]…”

Section: Laws Of Branched Vessel Network To Fluid Flowmentioning

confidence: 99%

Dendritic design as an archetype for growth patterns in nature: fractal and constructal views

Miguel

2014

Front. Physics

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The occurrence of configuration (design, shape, structure, rhythm) is a universal phenomenon that occurs in every flow system. Dendritic configuration (or tree-shaped configurations) is ubiquitous in nature and likely to arise in both animate and inanimate flow systems (e.g., lungs and river basins). Why is it so important? Is there a principle from which this configuration can be deduced? In this review paper, we show that these systems own two of the most important properties of fractals that are self-similarity and scaling. Their configuration do not develop by chance. It's occurrence is a universal phenomenon of physics covered by a principle. Here we also show that the emergence of dendritic configuration in flow systems constitutes a basic supportive flow path along which "order" need to persist is propagated.

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Accessing the Influence of Hess-Murray Law on Suspension Flow through Ramified Structures

Cited by 10 publications

References 22 publications

Fluid Flow at Branching Junctions

Fluid Flow at Branching Junctions

Predictive Models for the “Optimal” Radius Ratios in Natural Bi- And Trifurcated Vessels: Beyond the Hess-Murray Law

Dendritic design as an archetype for growth patterns in nature: fractal and constructal views

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