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Re: QYNGA: CO2, water movement, Prandtl layer & turbulence

Steve Dixon <stdixon at bechtel_com> asks:
> Next question:  Jeff Kropp and I were quite interested in dr. dave's
> note the other day about CO2 levels, water movement and photosynthesis.
> Jeff and I have been wondering about how much water movement is
> necessary to improve the CO2 diffusion rate.  Will gentle movement from
> say, a typical canister filter return, provide sufficient movement?
> Would we be likely to benefit from a powerhead "blowing" water in the
> lower portion of the tank? Any practical advise?

Why sure Steve! :-) As a matter of fact, this question was answered
before but you probably don't remember it. In an APD message dated Thu,
07 Aug 97 I answered a similar question as follows:

"Frank I. Reiter" <FIR at istar_ca> asks in the 8/7/97 Aquatic Plant Digest
what is an optimum current for plants?
If your plant leaves are moving slightly this is an indication of
turbulent flow which is what you want. Turbulent flow greatly increases
the mixing of the fluid (water) at the boundary layer of the leaf which
improves the transfer of water containing CO2 to the leaf surface where
it can be absorbed. If you have CO2 injection, high flow rates will also
increase the surface interaction of the water and result in a lower CO2
concentration at dynamic equilibrium. Again, this gas interchange is
greatly increased when there are turbulent flow regimes at the water
surface which are characterized by small disturbances in the water
surface e.g. ripples, eddies, any visible disturbance. If you have
bottled compressed CO2 and you are running trickle filters, box filters
or the like, the additional CO2 you need to inject may not be worth
worrying about. If you are using yeast CO2, you probably want to take
every precaution to minimize surface disturbances in your water."

To answer your specific question a powerhead filter or canister filter
should provide enough current to get your plant leaves wiggling around.
Just the slightest movement of the plant leaf indicates that a turbulent
(unstable) flow regime is occurring. There is a more precise analytical
method for predicting turbulent flow using Reynolds number which is the
ratio of inertial forces (velocity * length * density) to viscous forces
(viscosity). You can also determine this experimentally by injecting a
dye into the flow of the water over the surface of a leaf. Turbulent
flow is when the dye swirls and mixes; laminar flow is when the dye
streams off the leaf in a smooth thread. As you might imagine, the
amount of turbulence increases with velocity ranging from microscopic
eddies to very large vortexes (flow making the leaves wave madly).
Anyway, I could go on at length about other parameters affecting
turbulent mixing but you can do that for yourself by picking up a fluid
mechanics text.

As Dave pointed out, the lower CO2 concentration resulting from surface
motion of the water is more than compensated for by the increase in CO2
availability through the Prandtl layer.