Kinetic Modeling of Permeates Flux and Total Hydraulic Resistance of Camel Milk Ultrafiltration: Effect of Transmembrane Pressure and Temperature

Document Type : Research Paper


1 PhD student, Department of Food Science and Technology, Faculty of Agriculture, , Ferdowsi University of Mashhad, Mashhad, Iran

2 Academic member,, Department of Food Science and Technology, Ferdowsi University of Mashhad, Mashhad, Iran


ABSTRACT: In this study, kinetic modeling of permeates flux and total hydraulic resistance of camel milk ultrafiltration in different conditions of transmembrane pressure (TMP, 80-160 kPa) and temperature (T, 20-40 oC) was performed by six kinetic models and finally, the homographic kinetic model for modeling the permeate flux and exponential kinetic model for modeling the total hydraulic resistance considering R2 and RMSE values have been selected and their parameters were studied. The results of ANOVA of homographic kinetic model illustrated that the linear effect of transmembrane pressure on all model parameters (initial flux (J0), steady-state flux (J), flux decline time constant (I/b) and flux decline extent (a)) and the interaction effects of transmembrane pressure -temperature at a 95% level on the J0 and I/b were significant. The results of ANOVA of exponential kinetic model also showed that the linear effect of transmembrane pressure had a significant effect on all exponential kinetic model parameters (initial hydraulic resistance (R0), steady-state hydraulic resistance (R) and resistance increment rate (k)) at 95% level. Also, the linear effect of temperature and the interaction effects of transmembrane pressure -temperature at a 95% level on the k parameter were significant.


Alghooneh, A., Razavi, S. M. & Mousavi, S. M. (2016). Nanofiltration treatment of tomato paste processing wastewater: process modeling and optimization using response surface methodology. Desalination and Water Treatment, 57(21), 9609-9621.
Banks, H. T. & Tran, H. T. (2009). Mathematical and experimental modeling of physical and biological processes. Boca Raton: CRC Press.
Benmechernene, Z., Fernández-No, I., Quintela-Baluja, M., Böhme, K., Kihal, M., Calo-Mata, P. & Barros-Velázquez, J. (2014). Genomic and Proteomic Characterization of Bacteriocin-Producing Leuconostoc mesenteroides Strains Isolated from Raw Camel Milk in Two Southwest Algerian Arid Zones. BioMed research international, 20,14-24.
Eckner, K. & Zottola, E. (1992). Partitioning of skim milk components as a function of pH, acidulant, and temperature during membrane processing. Journal of dairy science, 75(8), 2092-2097.
Farah, Z. & Ruegg, M. W. (1989). The size distribution of casein micelles in camel milk. Food Microstructure, 8, 211-216.
Fenton-May, R., Hill Jr, C., Amundson, C., Lopez, M. & Auclair, P. (1972). Concentration and fractionation of skimmilk by reverse osmosis and ultrafiltration. Journal of dairy science, 55(11), 1561-1566.
Gautam, A. (1994). Ultrafiltration of salted acid whey. Department of Agricultural, Food and Nutritional Sciences, MSc thesis, University of Alberta, Canada.
Grandison, A. S., Youravong, W. & Lewis, M. J. (2000). Hydrodynamic factors affecting flux and fouling during ultrafiltration of skimmed milk. Le Lait, 80(1), 165-174.
Kautake, M., Nabetani, H. & Matsuno, I. (1986). Influence of operation parameters on permeate flux in ultrafiltration of milks, Technical Research Institute, Snow Brand Milk Products Co. Ltd., Report No. 83, 67-81.
Kaya, Y., Barlas, H. & Arayici, S. (2009). Nanofiltration of Cleaning-in-Place (CIP) wastewater in a detergent plant: effects of pH, temperature and transmembrane pressure on flux behavior. Separation and Purification Technology, 65(2), 117-129.
Luo, X., Ramchandran, L. & Vasiljevic, T. (2015). Lower ultrafiltration temperature improves membrane performance and emulsifying properties of milk protein concentrates. Dairy science & technology, 95(1), 15-31.
Ng, K. S., Haribabu, M., Harvie, D. J., Dunstan, D. E. & Martin, G. J. (2017). Mechanisms of flux decline in skim milk ultrafiltration: A review. Journal of Membrane Science, 523, 144-162.
Nourbakhsh, H., Emam‐Djomeh, Z., Mirsaeedghazi, H., Omid, M. & Moieni, S. (2014). Study of different fouling mechanisms during membrane clarification of red plum juice. International journal of food science & technology, 49(1), 58-64.
Rajca, M., Bodzek, M. & Konieczny, K. (2009). Application of mathematical models to the calculation of ultrafiltration flux in water treatment. Desalination, 239(1-3), 100-110.
Razavi, S. M., Alghooneh, A. & Behrouzian, F. (2017). Kinetic Modelling of Hydraulic Resistance in Colloidal System Ultrafltration: Effect of Physiochemical and Hydrodynamic Parameters. Journal of Membrane Science and Research, 3(4), 296-302.
Razavi, S. M., Alghooneh, A. & Behrouzian, F. (2018). Kinetic of permeate flux decline and fouling mechanism characterization of colloidal system ultrafiltration: Experimental and modeling study. Desalination and Water Treatment, 102, 38-48.
Razavi, S. M. A., Mousavi, S. M. & Mortazavi, S. A. (2003). Dynamic prediction of milk ultrafiltration performance: A neural network approach. Chemical Engineering Science, 58(18), 4185-4195.
Saltelli, A. (2002). Sensitivity analysis for importance assessment. Risk analysis, 22(3), 579-590.
St-Gelais, D., Haché, S. & Gros-Louis, M. (1992). Combined effects of temperature, acidification, and diafiltration on composition of skim milk retentate and permeate. Journal of dairy science, 75(5), 1167-1172.
Suki, A., Fane, A. & Fell, C. (1984). Flux decline in protein ultrafiltration. Journal of Membrane Science, 21(3), 269-283.
Thompson, S. J. & DeMan, J. (1975). Concentration and fractionation of milk by ultrafiltration. Canadian Institute of Food Science and Technology Journal, 8(2), 113-116.
Tong, P., Barbano, D. & Rudan, M. (1988). Characterization of proteinaceous membrane foulants and flux decline during the early stages of whole milk ultrafiltration. Journal of dairy science, 71(3), 604-612.
Vela, M. C. V., Blanco, S. Á., García, J. L. & Rodríguez, E. B. (2008). Analysis of membrane pore blocking models applied to the ultrafiltration of PEG. Separation and Purification Technology, 62(3), 489-498.
Wang, K. Y. & Chung, T.-S. (2005). The characterization of flat composite nanofiltration membranes and their applications in the separation of Cephalexin. Journal of Membrane Science, 247(1-2), 37-50.