By Frederik W. Wiegel (auth.)
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Extra info for Fluid Flow Through Porous Macromolecular Systems
Example text
We calculate the v i s c o s i t y of the solution following the method of Burgers (1938). The macroscopic v e l o c i t y f i e l d should be distinguished from the local v e l o c i t y f i e l d in the v i c i n i t y of a macromolecule. The v e l o c i t y f i e l d which would be found at the position (~i) of a particular macromoiecule, when that molecule has f i r s t been removed, has a shear rate GO. 15-17), and these corrections have to be summed over a l l the coils in the f l u i d .
TRANSLATIONALDIFFUSION COEFFICIENT OF A UNIFORM SPHERE For the uniform sphere model of section 10 the derivative (k-i) ' of the inverse permeability vanishes both inside and outside the sphere. 2) : where E is a constant. 3) inside the sphere. 4) as can be verified by substitution. The boundary conditions at r=R have been discussed in section 10. 5), that ~(r) should be continuous in R. 7) that ~, ~' and ~" should be continuous in R. 13). I t is straightforward, but tedious, to solve the four constants C, D, E, F from these four equations.
19). The regime ~<< i is called the free draining regime for reasons which w i l l be obvious from this derivation. 15 of Abramowitz and Stegun (1970). Experimentally ~ is t y p i c a l l y of order unity and neither the free-draining l i m i t nor the impermeable sphere l i m i t can be used. Felderhof and Deutch (1975) also calculate the rotational f r i c t i o n c o e f f i c i e n t of a hollow spherical shell with a constant permeability at the surface. A biophysical application of these results can be found in a paper by McCammon, Deutch and Felderhof (1975).
