A fluorescently labeled molecule (with a diffusion coefficient of 1 × 10−6 cm2/s) is released into the upstream end of a small blood vessel of diameter 100 μm and length 2 mm. The flow rate of blood passing through this vessel is 0.3 μl/min. Roughly estimate how long it should take before the molecule can be detected at the downstream end of the blood vessel.

Transport of nutrients, growth factors, and other molecules to tissues frequently takes place through the capillary wall. In many capillaries, there are tiny gaps between endothelial cells that allow both diffusion and convection of solutes across the vessel wall. Consider a particular endothelium in which the gaps between the cells are characterized by the following dimensions: L = 1 μm long, h = 200 nm high, and W = 10 nm in width (the last dimension is the distance between the two cells; see the figure below). The fluid in this gap is at 37 °C, and has the same properties as physiologic saline.