Consequences of forced convection for the constraints on size and shape in embryos

S. Kranenbarg, J.H.G. Verhagen, M. Muller, J.L. van Leeuwen

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocity around the object. In reality, however, water velocity is always intermediate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assumed oxygen inside the object to be transported by diffusion and outside the object by diffusion and convection. Fick's first law of diffusion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and flow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and flattened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10-4ms-1for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10-4ms-1, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated
Original languageEnglish
Pages (from-to)521-533
JournalJournal of Theoretical Biology
Volume212
Issue number4
DOIs
Publication statusPublished - 2001

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Convection
Forced Convection
Forced convection
Embryo
Embryonic Structures
Water
Oxygen
oxygen
water
Fick's laws
Gas Exchange
Eggs
Optimal Shape
Cross-flow
Mass Transport
mass flow
Flow velocity
Zero
Gases
convection

Cite this

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title = "Consequences of forced convection for the constraints on size and shape in embryos",
abstract = "Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocity around the object. In reality, however, water velocity is always intermediate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assumed oxygen inside the object to be transported by diffusion and outside the object by diffusion and convection. Fick's first law of diffusion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and flow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and flattened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10-4ms-1for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10-4ms-1, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated",
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journal = "Journal of Theoretical Biology",
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Consequences of forced convection for the constraints on size and shape in embryos. / Kranenbarg, S.; Verhagen, J.H.G.; Muller, M.; van Leeuwen, J.L.

In: Journal of Theoretical Biology, Vol. 212, No. 4, 2001, p. 521-533.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

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AU - Verhagen, J.H.G.

AU - Muller, M.

AU - van Leeuwen, J.L.

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AB - Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocity around the object. In reality, however, water velocity is always intermediate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assumed oxygen inside the object to be transported by diffusion and outside the object by diffusion and convection. Fick's first law of diffusion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and flow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and flattened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10-4ms-1for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10-4ms-1, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated

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