Assuming soil detachment rate d and soil redeposition rate r can be expressed respectively as
d=
Zdexp (-
KdVmin),
r=Z
rexp (-
Kr
Vmax),
where
Vmin is the maximum potential energy between fiber and particulate soil;
Vmax is energy difference between
Vmax and the potential energy at the closest approach of 5 Å for two substrates ;
Zd,
Kd,
Zr and
Kr are constants respectively, then the following results are obtained : 1) The methods for obtaining constants,
Zd,
Kd, Z
r and
Kr respectively from
Vmax, V
min and the efficiency of detergency
D are clarified theoretically by using the relation among
d,
r and
D.
2) Assuming the experimental value of
D is 0.99 × the final value of
D, and applying the theory 1) above mentioned to the experimental values in which carbon black particles and cotton fabrics are used, we have
d=13.8×10
-3exp (-25.1×10
-3Vmin)
=3.02×10
-3exp (4.77×10
-3Vmax)
r=2.45×10
-3exp (-13.5×10
-3Vmax)
when
Vmax < 60
kT, and
d=4.46×10
-3exp (-2.14×10
-3Vmin)
=3.92×10
-3exp (0.41×10
-3Vmax)
r=1.25×10
-3exp (-1.82×10
-3Vmax)
when
Vmax > 60
kT.
3) The values
D calculated from equations 2) above mentioned agree well with the experimental results.
4) The above mentioned 2) and 3) show that the larger the
Vmax the larger the
d/
r on which the final value of
D depends.
5) The above mentioned 2) clarifies that
Zd>
Zr and K
d>
Kr.
6) The results of this article can be used to compare the potential energy with the dynamic energy given by liquid flow from the standpoint of their effects on detergency.
The authors thank Dr. M. Uno who gave many valuable suggestions.
View full abstract