Preparing for the subsequent analytical studies of soil removal, the fundamental relation between the soil detachment rate or the soil redeposition rate and the mass of soil on fabrics has been theoretically studied.
The study has shown that :
1) A fundamental model of washing and soiling is established by means of the block diagram theory with the Laplace transform. The model is a stable transfer element for the input which does not include direct current.
2) From the above mentioned model, the mass of soil on fabric at time t is expressed as {
b/(
d+
Ar/L)} [
Ar/L+
d exp {-(
d+
Ar/L)
t}], where
d is the soil detachment rate,
r the soil redeposition rate,
b the input mass of soil on unit area of fabric,
A the total surface area of fabrics and
L is the mass of aqueous detergent solution.
3) When the fabrics are soiled in the aqueous solution of soil, the mass of soil on fabric is, in the same way, {
Cr/(
d+
Ar/L)} [1-exp {-(
d+
Ar/L)
t}], where
C is the soil concentration. This result shows that the usual soiling degree is a function of
d/r approximately.
4) The soil concentration in aqueous detergent solution at time
t is also obtained.
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