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By Frederik W. Wiegel (auth.)

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Example text

The pressure, velocity and the f i r s t should be continuous at r = R. 13) mOA re(r) = --3r (r> R). 7) transform the homogeneous equation into the equation d2f 2 df (1+ 2) f = O. 9) where B is a constant. Hence inside the coil the solution is given by k0 ~(r) = ~0 + B (--~ r cosh ~ r ko~-k0 r~--- sinh ~00). At r = R both m and m' must be continuous. 13) is a dimensionless quantity which measures the ratio between the radius R and the distance V~o by which the f l u i d e f f e c t i v e l y penetrates the porous medium (compare the discussion in section 5).

16) The values of the function T(m) have been calculated in t h i s way f o r m up to 17; the r e s u l t s , which were f i r s t published by Wiegel and M i j n l i e f f (1977a,b), are l i s t e d in table IV. The Gaussian model leads to values of DT which are in s a t i s f a c t o r y agreement with experimental data; t h i s w i l l be the subject of section 18. 219 Table IV. The functions T(m) and @(m) which determine the t r a n s l a t i o n a l d i f f u s i o n c o e f f i c i e n t and the i n t r i n s i c v i s c o s i t y of Gaussian c o i l s , according to eqs.

2) In this form, however, the equation is identical to the equation which would describe the movement of the same p a r t i c l e immersed in a f l u i d at rest, but subject to an external force equal to fT~O . 3) taken along a contour which ends in the point ~. According to s t a t i s t i c a l mechanics the local surface density p(~) of particles (the number of particles per unit area) is proportional to the Boltzmann factor p(~) ~ exp {-¢(~)/kBT}. 5) = 2mR 2 fT ~n (Sin½ e)+constant. 1) was used to express the f r i c t i o n c o e f f i c i e n t in terms of the diffusion c o e f f i c i e n t .

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