X-Message-Number: 5038
From: Ralph Merkle <>
Subject: SCI.CRYONICS: Re: Comments to Ettinger (pt. I)
Date: Sun, 22 Oct 1995 20:52:03 PDT

I'd like to thank Steve Harris for pointing out an error in my
calculation of the Reynolds number.

The Reynolds numbers is approximately rdv/n where r is a characteristic
length, d is the density of the fluid, v is a characteristic speed, and
n the viscosity.  For cells, the characteristic length might be 1 micron
(10^-6 meters), the density is about 1,000 kilograms/cubic meter, the
speed is likely to be less than 1 meter/second, and the viscosity of
water is about 0.01 poise or 0.001 newton-second/meter^2.  A useful web
page is http://www.chemie.fu-berlin.de/chemistry/general/units.html,
which provides conversion facilities between units.  Entering
"0.01 poise" in the "from" field and "newton-second/meter2"
(note: "meter2" is a square meter in their syntax) in the "to" field
produces "0.01 poise = 0.001 newton-second/meter2".  Multiplying
gives a Reynolds number of ~1.

As the approximate criterion for the onset of turbulent flow is a
Reynolds number of a few thousand or more, this implies that
turbulent flow is implausible.  When we take into account the fact
that the viscosity of tissue is larger than the viscosity of water
(assuming that we can apply "viscosity," in an approximate way,
to a structure as heterogenous as tissue), that the tissue is
loaded with glycerol (which has a higher viscosity than water)
and that the whole system has been chilled to some low temperature
(which also increases viscosity) then we conclude that the actual
Reynolds number will be significantly smaller than 1.  This
reinforces the basic conclusion.

The "Encyclopedia of Physics" says "Blood flow in capillaries is laminar,
but water flow in household pipes is turbulent unless the flow is about
that allowed by a leaky faucet or less."

The conclusion that can reasonably be drawn is that turbulence in this
context is relatively implausible, and any proposal which presupposes
turbulent flow carries an extra burden of proof.  It does not address
other (non-turbulent) processes that might occur during freezing of
tissue.


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