As you know, I've been looking at fractal networks -- e.g., bifurcating trees like the air pathways in the lung, the arterial & venous systems for the blood. Ever since I was a kid, I always wondered why we had red blood cells flowing through our arteries & veins instead of having hemoglobin as just another component of blood plasma. I think I finally found the answer. The human arterial system is a fractal binary tree approximately 30 levels deep, with the aorta at the root, and the capillaries at the leaves. At every level there are arterioles where the blood flow is governed by the "Poiseuille" equation Q = pi*R^4*dP/(8*mu*L) where Q is the quantity of flow, R is the radius of the arteriole, dP is the pressure differential, L is the length of the arteriole, and mu is the "effective" viscosity. https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation That Q is proportional to R^4 has been tested experimentally by putting blood through glass pipes of varying sizes, and holds experimentally over 4 orders of magnitude in radius. Here's the problem: Poiseuille tells us that the flow through the capillaries should be too small to support our body's requirements for oxygen. The solution (!) is that *mu* -- the "effective" viscosity -- varies quite a bit over the size range from aorta-sized (cross sectional area of ~ 2.5cm^2) to capillary-sized (cross sectional area of ~5-7 micrometers), due to the "Fåhræus–Lindqvist" effect. In particular, the situation at the capillary level is considerably different from the situation at the aortic level of the arterial tree. At the aortic level, blood is quite viscous, and flows at 40-50 cm/sec (~ 1 mph), while at the capillary level, the red blood cells (RBC's) travel in *single file* (ballistically?) at ~1 mm/sec (~ 1/500 mph), as the capillaries are too small for the RBC's to pass one another within the capillary. As a result of this orderly flow through the capillaries, the resistance of the capillaries is smaller than one would expect from Poiseuille, and we have the paradoxical effect that the RBC's travel through the capillaries *faster* than the plasma itself travels through the capillaries. At least at scales approaching those of the capillaries (where the Fåhræus–Lindqvist effect operates), the plasma becomes essentially a *lubricant* to enable the quicker passage of the RBC's. (Perhaps the Fåhræus–Lindqvist effect should be called a kind of "superconducting" effect for RBC's through capillaries?) The net result is that the oxygen is carried through the capillaries faster via RBC's then it could have been carried by the plasma itself. This is a cool evolutionary hack: similar in coolness to that of a high jumper or pole vaulter whose *center of gravity* NEVER gets over the bar, even though the athlete himself/herself does. https://en.wikipedia.org/wiki/F%C3%A5hr%C3%A6us%E2%80%93Lindqvist_effect "The Fåhræus–Lindqvist effect ... is an effect where the viscosity of a fluid, in this case blood, changes with the diameter of the tube it travels through; in particular there's a decrease of viscosity as the tube's diameter decreases (only if the vessel diameter is between 10 and 300 micrometers). This is because erythrocytes [RBC's] move over the center of the vessel, leaving plasma at the wall of the vessel." "First, mu decreased with decreasing capillary radius, R. This decrease was most pronounced for capillary diameters < 0.5mm." "These initially confusing results can be explained by the concept of a plasma cell-free layer, a thin layer adjacent to the capillary wall that is depleted of red blood cells. Because the cell-free layer is red cell-poor, its effective viscosity is lower than that of whole blood. This layer therefore acts to reduce flow resistance within the capillary, with the net effect that the effective viscosity is less than that for whole blood. Because the cell-free layer is very thin (approximately 3 micrometers) this effect is insignificant in capillaries whose diameter is large." Lipowsky, Herbert H. "Microvascular Rheology and Hemodynamics", Microcirculation 12 (2005), 5-15.