Consequences of Forced Convection for the Constraints on Size and Shape in Embryos

✍ Scribed by S KRANENBARG; J.H.G VERHAGEN; M MULLER; J.L VAN LEEUWEN

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 325 KB
• Volume: 212
• Category: Article
• ISSN: 0022-5193
• DOI: 10.1006/jtbi.2001.2391

✦ Synopsis

Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and in"nite water velocity around the object. In reality, however, water velocity is always intermediate between zero and in"nity. 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 di!usion and outside the object by di!usion and convection. Fick's "rst law of di!usion describes the inner transport. For the outer transport, we relied on semi-empirical relations between mass transport and #ow conditions (Friedlander's equations). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross #ow. If water velocity is low, a spherical shape is most favourable for gas exchange. If water velocity is high, an elongated and #attened shape is more favourable. A size-dependent intermediate velocity exists where shape does not matter (10\ m s\ for teleost embryos). Teleost embryos are typically exposed to #ow velocities equal to or larger than 10\ m s, making an elongated shape more favourable than a spherical one. Although teleost eggs are typically spherical, the oxygen-consuming embryos inside are indeed elongated.