Adding Convection

Now imagine a bee's heart pumping hemolymph as she subjects her body to the pitching, yawing and impacts of walking and flying. Consider also that her hemocoel contains only a small volume of hemolymph, a volume just sufficient to coat the surfaces of her internal organs, the walls of the hemocoel and her diaphragms together with perhaps a small pool of hemolymph in a corner somewhere. Now her hemocoel is a connected two-dimensional surface within which our randomly diffusing particles move.

Somewhere in shrinking a larger volume of hemolymph to a smaller volume, a three-dimensional volume approaches a two-dimensional volume so that transport now depends more and more upon the moistened geometries of a connected, almost minimal, two-dimensional surface.

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