1. The theoretical equations concerning the quantitative changes of constituents in the re-tentate and permeate on the process of ultrafiltration of whole milk were introduced. The quantity (APN (parts)) of membrane-permeable component A in the retentate at the concentra-tion factors (CF) of N is represented in the following equation.
APN=AP1••(MN/M1)CA
Ap1: the quantity of membrane-permeable component A in 100 parts of whole milk
M1: the quantity of water in 100 parts of whole milk
MN: the quantity of water in the retentate at CF N
CA: the permeability coefficient of membrane-permeable component A
The concentration (ARN (%)) of component A in the retentate at CF N is represented in the following equation.
ARN=N•(A1-AP1+APN)
A1: the quantity of component A in 100 parts of whole milk
The concentration (APPN'(%)) of component A in the permeate which permeates the mem-brane at CF N is represented in the following equation.
APPN'=100•CA•APN/(MN+CS•SPN)
Cs: the permeability coefficient of membrane-permable total solids
SPN: the quantity of membrane-permeable total solids in the retentate at CF N
2.Fresh whole milk was ultrafiltrated to CF about 3 at 10°C with the module UFP-10 equipped with the membrane IRIS 3038 of Rhone-Poulenc-Chimie Fine. The contents of permeable components in the milk were calculated by the equations using the analytical results of ARN and APPN'. The quantity of permeable and total components in 100g of the milk; total solids: 5.18, 11.73 (g), protein: 0.18, 3.05(g), lactose: 4.37, 4.26(g), ash: 0.46, 0.71(g), Na: 42.2, 46.2(mg), K: 144, 150(mg), Cl: 101, 101(mg), Ca: 35.9, 106(mg), Mg: 7.68, 10.7(mg), P: 39.8, 90.0(mg), and citric acid: 168, 188(mg). The permeability coefficient of each permeable component was 0.88, 0.83, 0.88, 0.95, 0.97, 0.94, 1.03, 0.88, 0.87, 0.93, and 0.92 respectively. The permeable fat was not detected, so the permeability coefficient could not be calculated.3. The theoretical equations mentioned above were proved to be appropriate to represent the quantitative changes of each component in retentate and permeate on the process of ultrafiltration of whole milk to CF 3. And MN is obtained by the following equation approximately. MN_??_M1-(100-SP1)(N-1)/N
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