From: Walter Stafford <stafford@bbri.org>
  To  : Allen Minton , rasmb@bbri.harvard.edu
  Date: Thu, 6 Sep 2001 17:35:39 -0400

Re: hydrodynamic question

At 16:41 -0400 9/6/01, Allen Minton wrote:
>Hi gang -
>
>A question for the hydrodynamics experts:
>
>We can calculate the frictional coefficient for an ellipsoid of 
>rotation (prolate or oblate) using the well-known Perrin equation. 
>How can we calculate the frictional coefficient for a cylindrical 
>rod of arbitrary length/diameter ratio?

Tanford gives an equation for the diameter of a rod of the same 
volume and length as the hydrodynamically equivalent prolate 
ellipsoid if that helps. p.342  eq. (20-8). He considers this to be 
the best approximation. To approximate a rod <<as a simple linear 
array of beads with a diameter equal to a bead diameter and a length 
equal to the number of beads times the bead diameter>> one has to 
make the diameter of the beads slightly larger than the diameter of 
the rod. It might be best to use a whole lot of much smaller beads 
arranged as a doughnut of the right diameter and then stack them to 
give the right length.

just some thoughts....

>
>I am guessing that the bead model might work, but it's not clear how 
>one would best represent the rod as an array of beads.  I doubt that 
>one could realistically represent the rod as a simple linear array 
>of beads with a diameter equal to a bead diameter and a length equal 
>to the number of beads times the bead diameter, but perhaps some 
>experienced person could set me right on that point.
>
>Does anyone know of an analytical solution to the rod problem, along 
>the lines of the Perrin equation?
>
>Allen Minton

-- 
Walter Stafford
stafford@bbri.org">mailto:stafford@bbri.org