Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions |
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| Institution: | 1. Chongqing Key Laboratory of Extraordinary Coordination Bonding and Advanced Materials Technology (EBEAM), Yangtze Normal University, Chongqing 108100, China;2. Institute of Coordination Bond Metrology and Engineering (CBME), College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China;3. Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education) and School of Materials, Science and Engineering, Xiangtan University, Hunan 411105, China;4. Institute of Nanosurface Science and Engineering, Shenzhen University, Shenzhen 518060, China;5. NOVITAS, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;1. Institute of General and Inorganic Chemistry, National Academy of Sciences of Belarus, Surganova 9/1, 220072 Minsk, Belarus;2. Laboratory of Green Chemistry, Lappeenranta University of Technology, Sammonkatu 12, 50130 Mikkeli, Finland;3. Department of Civil and Environmental Engineering, Florida International University, Miami, FL 33174, USA;1. Laboratory for Membrane Materials and Separation Technologies, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China;2. University of Chinese Academy of Sciences, Beijing 100049, China;3. ARC Research Hub for Nutrients in a Circular Economy, Center for Technology in Water and Wastewater, School of Civil and Environmental Engineering, University of Technology Sydney, Post Box 129, Broadway, Sydney, NSW 2007, Australia |
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| Abstract: | Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled. |
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