Kinetic Modelling of Hydraulic Resistance in Colloidal System Ultrafltration: Effect of Physiochemical and Hydrodynamic Parameters

Document Type : Research Paper


1 Department of Food Science & Technology, Ferdowsi University of Mashhad (FUM), Iran

2 Division of Food Engineering, Department of Food Science and Technology, Ferdowsi University of Mashhad, Iran


In this work, different kinetic patterns (homographic, exponential-linear and exponential) of hydraulic resistance in ultrafltration process of a colloidal system have been investigated. Exponential kinetic model, as the best approach, was employed for description of dynamic hydraulic resistance of skim milk ultrafltration at different feed flow rates (FR) (10, 30 and 46 L/min), transmembrane pressures (TMP) (0.3, 0.6 and 1 atm), temperatures (30, 40 and 50°C), pH levels (5.6, 6, 6.6, 6.9 and 7.6) and NaCl concentrations (0, 0.03, 0.06 and 0.12 %w/w). Results indicated that the initial resistance (R0), steady-state resistance (R), resistance increment rate (k) and resistance increment extent (RE) increased with TMP and ionic strength increasing and FR decreasing. The most sensitive factor for prediction of RT (total hydraulic resistance), R0 and Rwas the NaCl concentration. Also, the highest sensitive factors for RE and k were temperature (0.77) and TMP (0.60), respectively.

Graphical Abstract

Kinetic Modelling of Hydraulic Resistance in Colloidal System Ultrafltration: Effect of Physiochemical and Hydrodynamic Parameters


• We developed three semi-empirical models on dynamic resistance modeling.
• Resistances altered by transmembrane pressures, pH, salt, flow rate and temperature.
• Extent, rate of rise, initial and semi-steady resistances, termed by kinetic model.
• Increasing applied variables enhanced the kinetic model terms except the flow rate.
•Transmembrane pressure was the main factor on the rate of resistance growth.


Main Subjects

[1] M. Cheryan, Ultrafiltration Handbook, Technomic Publishing Co., Lancaster, Basel, 1986.
[2] G. Brans, C.G.P.H. Schröen, R.G.M. van der Sman, R.M. Boom, Membrane fractionation of milk: state of the art and challenges,J. Membr. Sci. 243 (2004) 263–272.
[3] K. Dewettinck, T.T. Le, Membrane separations in food processing, in: A. Proctor (Eds.), Alternatives to conventional food processing. RSC Publishing, Cambridge, UK, 2011, pp. 184-253.
[4] J.L. Soler-Cabezas, M. Tora`-Grau, M.C. Vincent-Vela, J.A. Mendoza-Roca, F.J. Martı´nez Francisco, Ultrafiltration of municipal wastewater: study on fouling models and fouling mechanisms, Desalin. Water Treat. 56 (2015) 3, 3427-34.
[5] V.S. Mamtani, K.P. Bhattacharyya, S. Prabhakar, P.K. Tewari, Fouling studies of capillary ultrafiltration membrane, Desalin. Water Treat. 52 (2014) 542-551.
[6] K.L. Jones, C.R. O’Melia, Protein and humic acid adsorption onto hydrophilic membrane surfaces: effects of pH and ionic strength, J. Membr. Sci. 165 (2000) 31-46.
[7] A. Alghooneh, S.M.A. Razavi, S.M. Mousavi, Nanofiltration treatment of tomato paste processing wastewater: process modeling and optimization using response surface methodology, Desalin. Water Treat. 57 (2016) 9609-9621.
[8] C.Y. Ng, A.W. Mohammad, L.W. Ng, J.M.D. Jahim, Membrane fouling mechanisms during ultrafiltration of skimmed coconut milk, J. Food Eng. 142 (2014) 190-200.
[9] P. Rai, G.C. Majumdar, S. Dasgupta, S. De, Modeling the performance of batch ultrafiltration of synthetic fruit juice and mosambi juice using artificial neural network, J. Food Eng. 71 (2005) 273–281.
[10] C. Bhattacharjee, S. Datta, Analysis of polarized layer resistance during ultrafiltration of PEG-6000: an approach based on filtration theory,Sep. Purif. Technol. 33 (2003) 115-126.
[11] S.M.A. Razavi, S.A. Mortazavi, S.M. Mousavi, Dynamic modeling of milk ultrafiltration by artificial neural network, J. Membr. Sci. 220 (2003) 47-58.
[12] S.M.A. Razavi, S.M. Mousavi, S.A. Mortazavi, Dynamic prediction of milk ultrafiltration performance: A neural network approach, Chem. Eng. Sci. 58 (2003) 4185-4195.
[13] S.M.A. Razavi, S.M. Mousavi, S.A. Mortazavi, Application of neural networks for crossflow milk ultrafiltration simulation, Int. Dairy J. 14 (2004) 69-80.
[14] J. Malave-Lopez, M. Peleg, Linearization of the electrostatic charging and charge decay curves of powders, Powder Technol. 42 (1985) 217–223.
[15] M. Peleg, An empirical model for the description of moisture sorption curves, J. Food Sci. (1988) 1216-1219.
[16] M. Peleg, Linearization of relaxation and creep curves of solid biological materials, J. Rheol. 24 (1980) 451-463.
[17] K. Konieczny, Modelling of membrane filtration of natural water for potable purposes, Desalination 143 (2002) 123-139.
[18] M. Rajca, M. Bodzek, K. Konieczny, Application of mathematical models to the calculation of ultrafiltration flux in water treatment, Desalination239 (2009) 100-110.
[19] S.G. Yiantsios, A.J. Karabelas, The effect of colloid stability on membrane fouling, Desalination 118 (1998) 143-152.
[20] K.F. Eckner, E.A. Zottola, Modeling flux of skim milk as a function of pH, acidulant and temperature, J. Dairy Sci. 75 (1992) 2952-2958.
[21] W. Zhang, J. Luo, L. Ding, M.Y. Jaffrin, A review on flux decline control strategies in pressure-driven membrane processes, Ind. Eng. Chem. Res. 54 (2015) 2843-2861.
[22] A. Salahi, M. Abbasi, T. Mohammadi, Permeate flux decline during UF of oily wastewater: experimental and modeling, Desalination 251 (2010) 153-160.
[23] P. Bacchin, P. Aimar, R. Field, Critical and sustainable fluxes: theory, experiments and applications, J. Membr. Sci. 281 (2006) 42-69.
[24] C.L. Astudillo-Castro, Limiting flux and critical transmembrane pressure determination using an exponential model: the effect of concentration factor, temperature, and cross-flow velocity during casein micelle concentration by microfiltration, Ind. Eng. Chem. Res. 54 (2015) 414-425.
[25] P. Bacchin, P. Aimar, V. Sanchez, Model for colloidal fouling of membranes, AIChE. J. 41 (1995) 368-376.
[26] P. Bacchin, D. Si-Hassen, V. Starov, M.J. Clifton, P. Aimar, A unifying model for concentration polarization, gel-layer formation and particle deposition in crossflow membrane filtration of colloidal suspensions,Chem. Eng. Sci. 57 (2002) 77-91.
[27] A. Grandison, W. Youravong, M.J. Lewis, Hydrodynamic factors affecting flux and fouling during ultrafiltration of skimmed milk, Lait 80 (2000) 165-174.
[28] A.H. Bahnasawy, M.E. Shenana, Flux behavior and energy consumption of ultrafiltration (UF) process of milk, Australian J. Agr. Eng.1 (2010) 54-65.
[29] W. Zhang, Z. Zhu, M. Y. Jaffrin, L. Ding, Effects of hydraulic conditions on effluent quality, flux behavior, and energy consumption in a shear-enhanced membrane filtration using Box-Behnken response surface methodology, Ind. Eng. Chem. Res. 53 (2014) 7176-7185.
[30] A.L. Zydney, Module design and membrane configurations, in:  L.J. Zeman (Eds.), Microfiltration and Ultrafiltration: Principles and Applications, CRC Press, New York, 1996, PP. 333.
[31] V. Chen, A.G. Fane, S. Madaeni, I.G. Wenten, Particle deposition during membrane filtration of colloids: transition between concentration polarization and cake formation, J. Membr. Sci. 125 (1997) 109-122.
[32] M.Y. Jaffrin, L-H. Ding, O. Akoum, A. Brou, A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems, J. Membr. Sci. 242 (2004) 155-167.
[33] W. Youravong, A.S. Grandison, M.J. Lewis, The effect of physico-chemical changes on critical flux of skimmed milk ultrafiltration, SJST. 24 (2002) 929-939.
[34] M. Rabiller-Baudry, H. Bouzid, B. Chaufer, L. Paugam, D. Delaunay, O. Mekmene, S. Ahmad, F. Gaucheron, On the origin of flux dependence in pH modified skim milk filtration, Dairy Sci. Technol. 89 (2009) 363-385.
[35] P.R. Babu, V.G. Gaikar, Membrane characteristics as determinant in fouling of UF membranes, Sep. Purif. Technol. 24 (2001) 23-34.
[36] A. Saltelli, A. Tarantola, F. Campolongo, M. Ratto, Sensitivity analysis in practice, Wiley, New York, 2004.