scholarly journals Runge–Kutta Numerical Method Followed by Richardson’s Extrapolation for Efficient Ion Rejection Reassessment of a Novel Defect-Free Synthesized Nanofiltration Membrane

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 130
Author(s):  
Chabi Noël Worou ◽  
Jing Kang ◽  
Jimin Shen ◽  
Pengwei Yan ◽  
Weiqiang Wang ◽  
...  

A defect-free, loose, and strong layer consisting of zirconium (Zr) nanoparticles (NPs) has been successfully established on a polyacrylonitrile (PAN) ultrafiltration substrate by an in-situ formation process. The resulting organic–inorganic nanofiltration (NF) membrane, NF-PANZr, has been accurately characterized not only with regard to its properties but also its structure by the atomic force microscopy, field emission scanning electron microscopy, and energy dispersive spectroscopy. A sophisticated computing model consisting of the Runge–Kutta method followed by Richardson extrapolation was applied in this investigation to solve the extended Nernst–Planck equations, which govern the solute particles’ transport across the active layer of NF-PANZr. A smart, adaptive step-size routine is chosen for this simple and robust method, also known as RK4 (fourth-order Runge–Kutta). The NF-PANZr membrane was less performant toward monovalent ions, and its rejection rate for multivalent ions reached 99.3%. The water flux of the NF-PANZr membrane was as high as 58 L · m−2 · h−1. Richardson’s extrapolation was then used to get a better approximation of Cl− and Mg2+ rejection, the relative errors were, respectively, 0.09% and 0.01% for Cl− and Mg2+. While waiting for the rise and expansion of machine learning in the prediction of rejection performance, we strongly recommend the development of better NF models and further validation of existing ones.

Author(s):  
B. L. Dixon Northern ◽  
Y. L. Chen ◽  
J.N. Israelachvili ◽  
J.A.N. Zasadzinski

Atomic Force Microscope (AFM), is the newest, and potentially most powerful of the scanning probe microscopes. The (AFM) is capable of resolutions approaching atomic dimensions on ideal surfaces. One of the favorite such surfaces is that of mica. Muscovite mica has a platelike structure consisting of an octahedral alumina sheet sandwiched by two tetrahedral silicate sheets. As a result of this structure, mica cleaves readily along a plane leaving a molecularly smooth surface. Because of the isomorphous substitution of the tetravalent silicon by trivalent aluminium, mica has an excess negative surface charge.This negative surface charge of 2.1-1014 charges per cm2 is neutralized by an equal number of positive monovalent ions, mainly potassium ions. The ion-exchangable surface ions of mica, in aqueous solution, can be readily replaced by other monovalent or multivalent ions. This ion exchange alters the surface of the mica. We then follow these changes by imaging with the AFM in air.


Author(s):  
Chabi Noël Worou ◽  
Jing Kang ◽  
Eric A. Alamou ◽  
Arcadius Degan ◽  
Pengwei Yan ◽  
...  

Abstract A flawless, extremely loose, and efficient for multivalent ions separation membrane has been successfully synthesized by the in-situ formation approach. The as-synthesized nanofiltration (NF) membrane, NF_PES-Zr, proceeded from a thin film layer of nanoparticles (NPs) zirconium coated the platform of polyethersulfone (PES) ultrafiltration (UF) membrane through a bio-glue made from dopamine hydrochloric and sodium bicarbonate buffer. The estimation of the average pore size of the novel organic-inorganic NF membrane NF_PES-Zr using the filtration velocity approach of GUEROUT-ELFORD-FERRY was close to 0.9 nm. NF_PES-Zr membrane holds a record in permeate water flux release of about 62.5 L.m–2.h–1 and was revealed to be effective for multivalent ions separation. A 5 days-test performed on NF_PES-Zr demonstrated its long-term stability and showed a rejection rate of 93.4% and 37.8% respectively for Ca2+ and Na+.


Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 184 ◽  
Author(s):  
Chabi Noël Worou ◽  
Jing Kang ◽  
Jimin Shen ◽  
Arcadius Degan ◽  
Pengwei Yan ◽  
...  

Titanium (Ti) nanoparticles (NPs) were successfully seeded on the platform of a polyacrylonitrile (PAN) ultrafiltration (UF) membrane previously coated with bio-glue (a co-deposition of dopamine hydrochloric bicarbonate buffer having undergone pyrocatechol deprotonation). The tools in vogue, especially field emission scanning electron microscopy (FESEM), energy dispersive spectroscopy (EDS), and atomic force microscopy (AFM), have made it possible to fully characterize the structure of the new organic-inorganic nanofiltration (NF) membrane, namely NF_PAN_Ti. A soft computing model has been applied to make commonplace the complex and implicit extended Nernst–Planck equations that govern the transport of ions through NF membranes. Euler’s numerical method was applied with a small step-size and the results obtained were very interesting. The filtration velocity approach of GUEROUT-ELFORD-FERRY helped to estimate the average pore size of NF_PAN_Ti to rp = 0.538 nm. A six-day test carried out on NF_PAN_Ti demonstrated its long-term stability and showed a steady-rejection rate of 89.3% of MgCl2 salt and permeate flux of 56 L·m−2·h−1. The Euler’ numerical method corroborated perfectly the experimental findings since the relative error was found to be very low at 0.33% for Cl− and 0.09% for Mg2+ (RE << 0.1). These practical prediction tools may henceforth help in the choice and calibration of next-generation NF membranes’ synthesis.


Membranes ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 156 ◽  
Author(s):  
Shailesh Dangwal ◽  
Ruochen Liu ◽  
Lyndon D. Bastatas ◽  
Elena Echeverria ◽  
Chengqian Huang ◽  
...  

ZnO was deposited on macroporous α-alumina membranes via atomic layer deposition (ALD) to improve water flux by increasing their hydrophilicity and reducing mass transfer resistance through membrane pore channels. The deposition of ZnO was systemically performed for 4–128 cycles of ALD at 170 °C. Analysis of membrane surface by contact angles (CA) measurements revealed that the hydrophilicity of the ZnO ALD membrane was enhanced with increasing the number of ALD cycles. It was observed that a vacuum-assisted ‘flow-through’ evaporation method had significantly higher efficacy in comparison to conventional desalination methods. By using the vacuum-assisted ‘flow-through’ technique, the water flux of the ZnO ALD membrane (~170 L m−2 h−1) was obtained, which is higher than uncoated pristine membranes (92 L m−2 h−1). It was also found that ZnO ALD membranes substantially improved water flux while keeping excellent salt rejection rate (>99.9%). Ultrasonic membrane cleaning had considerable effect on reducing the membrane fouling.


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