The ultrafiltration mechanism of the imidazoles from a caramel color through PM-10 and DDS-870 membrane was analyzed.
It was found that some imidazoles were bound irreversibly to impermeable matter in the caramel and thus these imidazoles could not be removed by ultrafiltration.
The following equations estimating the retained imidazoles concentration after various operations of ultra-filtration were obtained :
C= (
C0-
KM/
V0) (
V0/
V)
Ri +
KM/
V (for single batch operation)
Cn= (
C0-
KM/
V0) (
V/
V0)
n(1-Ri) +
KM/
V0 (for repeated batch operation)
C= (
C0-
KM/
V0) exp {- (1-
Ri)
Vp/
V0} +
KM/
V0 (for fixed-volume operation)
where C [mg/ml] is the concentration of imidazoles in sample,
C0 [mg/ml] is the initial concentration of imidazoles in sample,
Cn [mg/ml] is concentration of imidazoles in the sample after n operations of filtration (concentration factor
V0/
V) and dilution (
V0/
V-fold),
V [ml] is the volume of sample,
V0 [ml] is the initial volume of sample,
Vp [ml] is the volume of permeate,
n [-] is times of batch operation,
Ri [-] is the ideal rejection of imidazoles and
KM [mg] is the amount of impermeable imidazoles.
The amount of impermeable imidazoles through the membrane of
Ri=0 could be obtained from
KM=
Ra·
Cn ·
V0, where
Ra [-] is the apparent rejection of imidazoles.
It is expected that the equations obtained above are applicable to ultrafiltration of a solution in which a microsolute binds irreversibly to a high molecular weight solute.
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