From: Allen Minton <minton@helix.nih.gov>
  To  : rasmb@bbri.harvard.edu
  Date: Fri, 07 Sep 2001 16:07:04 -0400

Re: hydrodynamics of cylindrical rods

Thanks to all who replied to my question yesterday about estimating the 
frictional coefficient of a cylinder.

To summarize the most useful results:

Jose Garcia de la Torre directed me to his classic review (de la Torre & 
Bloomfield, Quart. Rev. Biophys. 14, 81-139; 1981) which describes two nice 
methods for estimating the translational frictional coefficient of a 
randomly oriented cylinder.  The first is a relation that compactly 
summarizes results obtained with a cylindrical shell bead model.

f = (3*pi*eta_o*L)/[ln p + gamma(p)]

where p = cylinder length/diameter, eta_0 is the solvent viscosity, L is 
the cylinder length, and

gamma(p) = 0.312 + 0.565/p + 0.10/p^2.

The second method is the use of the Perrin equation for prolate ellipsoids 
of revolution, with an effective ellipsoid whose long semi-axis is equal to 
the half-length of the cylinder, and whose short semi-axis is taken to be 
1.37 times the cylinder radius.  It is claimed that the result thereby 
obtained is accurate to within a few percent for all p>=2 (<1% error for p>5).