An empirical mathematical model of retentate composition in ultrafiltration of dairy products

Summary

Analysis of retentates of milk or whey, ultrafiltered and diafiltered by a pilot batch process with DDS Lab module equipment or (whey only) ultrafiltered by an industrial continuous process showed that nitrogen and ionic contents could not be described mathematically by the use of any value of the retention coefficient K. Analytical data suggested a new concept called segregation for nitrogen and ions in which each of these components consists of a completely permeable fraction and a totally retained fraction that do not exchange. A segregation coefficient Y is then defined as the ratio of the totally retained fraction to the total concentration of the species in the product fed to the equipment. However, this concept does not apply to lactose, where the classic retention concept (K) is retained. The two models are equivalent when K = Y = 0 or K = Y = 1. A first mathematical expression of this model was elaborated for batch ultrafiltration and/or constant volume diafiltration. Another set of equations was established for industrial conditions. These empirical models predict the retentate and permeate composition at any time during processing as well as after drying. The fit of analytical data with computed values was generally fair, with K being 0·1–0·4 in the pilot plant, and 0·1 in the factory. The nitrogen Y value was ∼ 0·95 for milk, and 0·85 for whey. In whey, the calcium Y value varied greatly from 0·06–0·71 depending on the pH, citrate content and heat treatment; in milk it was fairly constant at 0·5 at pH 6·7–5·8.