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Analysis of radiographic images
of papers yields estimates of
floc grammage and size distribution, from variance decay with
scale [5].
 
(42) 
The pdf b(r,x) for pairs of points in a square of side x,
is known analytically [4] and we obtain:
 
(43) 
For more details see Dodson [5] and Farnood et al. [16].
Kerekes and Schell [22] observed:
Long fibre fraction mm;
Short fibre fraction mm
Expect from above:
 
(44) 
Figure 10 shows how the two parameters and
were used to discriminate among the effectiveness of different refiner
geometries from the point of view of formation potential and tolerance
of the fibres for adverse forming conditions.
Figure 10:
Formation Diagram for potential
of a single pulp refined in three ways, from radiography of
sheets
made under four forming conditions. Same image analysis
procedure for optical transmission bitmaps of
shallow fibre suspensions. Spherical flocs
project grammage G proportional to diameter D.
Experimentally:
analogous to pore sizes.

Farnood et al. [17] provide graphical representations of a wide range
of simulated papers. They used lognormal disk diameter distributions parametrized
by the mean , which represents the scale of the variability in the
structure, and the mean disk areal density, which represents the
intensity or contrast in the areal density distribution. A tiling of such
structures for typical ranges of parameters found for commercial papers is
shown in Figure 11.
Figure 11:
Simulated structures from lognormal distributions of disks
with representing intensity and representing scale.

Next: Characterizing Anisotropy
Up: Paper Structure
Previous: Simulated Paper
C.T.J. Dodson
11/26/1998