K. Park et al., Optimal lamellar arrangement in fish gills, PNAS 111, 8067 (2014)
Is there an optimum size of fish gills lamella ?
K. Park et al., Optimal lamellar arrangement in fish gills, PNAS 111, 8067 (2014)
Scaling laws for lamella spacing and length
d ~ l1/2 d ~ M1/6
Typical sizes d ~ 50 μm H ~ 400 μm
l ~ 1 mm
D02 ~10-9 m2/s
U ~1 cm/s
What is the order of magnitude of the Reynolds and Peclet number ? Flow field within the channels ?
Write the transport equation for O2
Boundary conditions on O2 concentration ?
ν02 ~10-6 m2/s
Re ~ 0.5 Pe ~ 500
Laminar Poiseuille Flow (parabolic velocity profile)
Model experiment
Channel length L = 70 mm Channel width W = 2 mm
Central channel height d 70 to 190 μm Top and bottom channels height 200 μm
U=(d2/12 η) Δp/L
Oxygen transfer rate
Channel height