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Is there an optimum size of fish gills lamella ?

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(1)

K. Park et al., Optimal lamellar arrangement in fish gills, PNAS 111, 8067 (2014)

Is there an optimum size of fish gills lamella ?

(2)

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

(3)

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)

(4)

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

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