Consequences of forced convection for the constraints on size and shape inembryos

Previously, predictions of the maximum size of biological objects based on oxygen availability have been made for both zero and infinite water velocit y around the object. In reality, however, water velocity is always intermed iate between zero and infinity. We predicted maximum size and optimal shape of biological objects, pending the velocity of water around them. We assum ed 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 equatio ns). To keep mathematical complexity acceptable, we restricted ourselves to the analysis of a sphere and a cylinder in cross flow. If water velocity i s low, a spherical shape is most favourable for gas exchange. If water velo city is high, an elongated and flattened shape is more favourable. A size-d ependent intermediate velocity exists where shape does not matter (10(-4) i n s(-1) for teleost embryos). Teleost embryos are typically exposed to flow velocities equal to or larger than 10(-4) m s(-1), making an elongated sha pe more favourable than a spherical one. Although teleost eggs are typicall y spherical, the oxygen-consuming embryos inside are indeed elongated. (C), 2001 Academic Press.