The TwoDimensional Hemocoel

We characterize our two-dimensional hemocoel in different ways. If it contains many randomly moving molecules engaged in Brownian motion, we might imagine our 'random walkers' to traverse fractal landscapes. We understand something of fractal elastic properties as well as phase transitions occurring on fractal structures, but we know very little of why fractals form in the first place. We don't even know which aspects of the evolution of a dynamical system give rise to fractals (Ref: Fractal Difficulties).

As hemolymph disperses over irregular surfaces, at the micro-scale we might see shallow pools around higher, dryer islands. Or our simple picture of diffusion as a sequence of random steps changes if our hemolymph resides in and percolates through a porous medium having a 'porosity' less than one. Under these conditions, our random walkers, now obstructed by 'islands' or pores, cannot occupy all positions of space. If the porous matrix is homogenous and isotropic, an effective diffusion coefficient involves a formation factor that now is no longer purely geometric, like the porosity, but has become a transport coefficient (Ref: Percolation, Chapter 8).

On free surfaces in some systems, gradients in surface tension drive convection depending on the Marangoni number, an equation relating the fluid density, its kinematic viscosity, the interfacial energy per unit area of surface or the surface tension and a characteristic measure of the size of the container, which in our case might be a hemocoel (Ref: Meakin, 1998).

We shall continue this discussion after again considering the three-dimensional hemocoel of Deuterostomes.

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