WET SOLIDS FLOW ENHANCEMENT Page: 4 of 11
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1.1 is plotted in figure 6 for different filling angles and it shows that the value of the interparticle
force decreases monotonously with the particle separation a. This is not what the experiments
show, with the tensile stress going through a maximum. Several explanations were tried here. The
most obvious was to assume that the bridges are not aligned with the direction of displacement as
with a combination of vertical and horizontal bridges as is shown in Figure 7. As particle are
displaced orthogonal to the vertical bridges the horizontal component goes through a maximum as
shown in Figure 8. The maximum, however, takes place at shorter distances that those measured
and there is no obvious maximum when the combination of horizontal and vertical bridges is
considered. If it is assumed that this model applies to the region after the maximum has been
reached it can be seen in figure 9, the decay of the stress is too rapid to justify the model.
The deformation of the solid:
It is also possible that the elastic behavior of the solid is responsible for the elastic energy
accumulated. If the solids were elastic, the first part of the deformation would be the unloading of
the elastic forces mobilized by the capillary forces as shown in Figure 9. An attractive force F
between two elastic spheres, as is shown in Figure 10 will displace the centers toward each other
by a relative distance 2x/d given by [see reference 2]:
X_ 1_1 I_3F 1-v2
d 2 2 8d2 E
Where E and v are theYoung modulus and the Poisson coefficient, respectively. If we substitute
the capillary force given by equation 1.1 we can obtain the deformation of the material and the
distance traveled for the Parffit tester. The total distance is obtained by multiplying twice the
fractional distance by one half the diameter of the enlarged cell (inside diameter 81 mm, height 25
mm) described by Pierrat . Notice that to compute the displacement all of the particles should
be unloaded, while for the breakage only one bridge will participate.
Typical values of the parameters of the equations (a =0.72 N/m, 0 =30 , S =0 , v= 0.3
and E= 67,660 MPa). Unfortunately, the deformation predicted is very small compared with the
values measured in our experiments. A "fudge" factor of one thousand gives the "theoretical"
values shown in Figures 2 and 3. For the large number of experimental conditions, particle sizes
and fluids used the trends shown are correct but it is obvious that further work is needed to
explain the large deformations observed. Other tests were carried out with fine, cohesive particles
(such as starch) in a smaller Parfitt cell. For the instrument used the spatial resolution is estimated
to be slightly below one micron. Breakage occurs within that short distance and the very elastic
behavior observed in wet solids is not observed.
We plan to investigate the effect of the split pillbox size on the measured deformation and
compare the results with other methods used to measure the elastic parameters of a wet material.
To return to the practical applications we have, earlier in the project, quantified the effect of the
most important type of additives, the surfactants, in affecting the yield locus of the wet granular
materials. The most dramatic effects, however, were those caused by components, such as silanes,
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Caram, Hugo S. & Foster, Natalie. WET SOLIDS FLOW ENHANCEMENT, report, July 1, 1999; Morgantown, West Virginia. (https://digital.library.unt.edu/ark:/67531/metadc722847/m1/4/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.