Exploring the Maximum Number of the Branch Pores in each Pore Tree Applied in an Optimized Tree-type Cylindrical-shaped Nanoporous Filtering Membrane

Background: An optimized tree-type cylindrical-shaped nanoporous filtering membrane has been proposed. The performance of this membrane needs to be investigated. Objective: The study aimed to investigate the maximum number of the branch pores in each pore tree practically applied in this proposed membrane. Methods: The analysis for the flow and transport of the filtered liquid in this membrane was derived based on the nanoscale flow equation. The flow resistance of this membrane was defined and its lowest value was found for the optimal condition. Results: The dimensionless lowest flow resistance I-f,I-min of the membrane in the optimal condition was calculated respectively for weak, medium-level and strong liquid-pore wall interactions, when both the radius R-b,R-1 of the branch pore and the number N of the branch pores in each pore tree were widely varied. It was shown that for any kind of liquid-pore wall interaction and any R-b,R-1 value, when N is over 10, the value of I-f,I-min becomes slowly reduced with the increase of N; Even for N=50, the value of I(f,min )is only modestly reduced compared to that for N=10 for the same operating condition. Conclusion: It is suggested that the value of the maximum number N-max, of the branch pores in each pore tree in this membrane should be taken as around 10 in spite of liquid-pore wall interactions, from the viewpoint of engineering application.