where c is the remaining Cl− concentration in a slurry after the nth
washing, c0 is the starting concentration of the remaining Cl− in the
slurry, n is washing times, and r is ratio of concentrating–diluting.
For the present test r is 3. Fig. 9 shows that the Cl− concentration in
the titania slurry decreases with increasing washing times, which
could be well fitted with two linear functions, intersecting at washing
times between 5 and 6. In the first fitting, the concentration of
Cl− ions follows the formula ln C =
−1.08n + 11.11. The coefficient
before the n-value is very close to
−ln 3 (i.e., r = 3), which is in accord
with the prediction by the above formula. It suggested that the
reduction of Cl− concentration obeyed the concentrating–diluting
behavior during the initial-stage washing (≤5 washing times).