On the direct osmotic concentration of liquid foods: Part II. Development of a generalized model

The performance of a pilot scale, direct osmotic (membrane) concentration unit was modeled in physical terms. Based on the fundamental equation for cross-flow mass transfer diffusion through membranes and an adequate set of experimental measurements, a generalized mathematical model for direct osmotic concentrators was successfully developed. The required number of independent equations was more than three times the number of the unknown parameters (constants) of the proposed model, in order to allow for modern non-linear problem solvers to converge to a satisfactory solution.A Non-Linear Regression software package was used to determine optimal values for coefficients and exponents appearing in the proposed model. The validity of the emerging physical model was properly verified. The defined model provided an insight on the relative importance of several experimental parameters and membrane compaction in controlling direct osmotic flux values.The proposed model and the described modeling approach could be used to develop physically meaningful models for other membrane processes.