Geodesic
The Space Charge Model. A new analytical approximation solution of Poisson--Boltzmann equation: the extended homogeneous approximation
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 4, pp. 428-437.

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The validity of different analytical approximations solution is studied using the classical Poisson–Boltzmann (PB) equation based on a mean-field description of ions as ideal point charges in combination with the assumption of fully overlapped electrical double layers in the membrane pores. The electrical conductivity is calculated by numerical and approximate analytical methods in order to explain the process of ion transport. In this paper, a new analytical approximation named the extended homogeneous approximation (EH) is presented, which provides better results than the homogeneous approximation based on Donnan theory. Also, the results show that the electrical conductivity calculated by the EH, is coherent with the numerical method within specific limits.
Keywords: space charge model, Poisson–Boltzmann (PB) equation, electrical conductivity, extended homogeneous (EH) approximation. 
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     author = {Jalal Dweik and Hassan Farhat and Joumana Younis},
     title = {The {Space} {Charge} {Model.} {A} new analytical approximation solution of {Poisson--Boltzmann} equation: the extended homogeneous approximation},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {428--437},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_4_a4/}
}
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Jalal Dweik; Hassan Farhat; Joumana Younis. The Space Charge Model. A new analytical approximation solution of Poisson--Boltzmann equation: the extended homogeneous approximation. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 4, pp. 428-437. http://geodesic.mathdoc.fr/item/NANO_2023_14_4_a4/