The Space Charge Model. A new analytical approximation solution of PoissonBoltzmann equation: the extended homogeneous approximation

被引:1
|
作者
Dweika, Jalal [1 ]
Farhat, Hassan [1 ]
Younise, Joumana [1 ]
机构
[1] Jinan Univ, Main Campus Zaytoun Abi Samra,POB 818, Tripoli, Lebanon
来源
NANOSYSTEMS-PHYSICS CHEMISTRY MATHEMATICS | 2023年 / 14卷 / 04期
关键词
space charge model; Poisson-Boltzmann (PB) equation; electrical conductivity; extended homogeneous (EH) approximation; NANOFILTRATION THEORY; REVERSE-OSMOSIS; SEPARATION; TRANSPORT;
D O I
10.17586/2220-8054-2023-14-4-428-437
中图分类号
TB3 [工程材料学];
学科分类号
0805 ; 080502 ;
摘要
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.
引用
收藏
页码:428 / 437
页数:10
相关论文
共 50 条
  • [1] A new analytical approximation to the extended Brinkman equation
    Maussner, Johannes
    Pietschak, Alexander
    Freund, Hannsjoerg
    CHEMICAL ENGINEERING SCIENCE, 2017, 171 : 495 - 499
  • [2] A new solution approach via analytical approximation of the elliptic Kepler equation
    Wu, Baisheng
    Zhou, Yixin
    Lim, C. W.
    Zhong, Huixiang
    ACTA ASTRONAUTICA, 2023, 202 : 303 - 310
  • [3] Analytical approximation solution for logistic delay differential equation
    Talib, Nurul Atiqah
    Mean, Normah
    Barde, Aminu
    MALAYSIAN JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES, 2020, 16 (03): : 368 - 373
  • [4] POINT APPROXIMATION OF A SPACE-HOMOGENEOUS TRANSPORT-EQUATION
    MOTTA, S
    RUSSO, G
    MOOCK, H
    WICK, J
    NUMERISCHE MATHEMATIK, 1990, 56 (08) : 763 - 774
  • [6] Equivalent acoustic impedance model. Part 2: analytical approximation
    Faverjon, B
    Soize, C
    JOURNAL OF SOUND AND VIBRATION, 2004, 276 (3-5) : 593 - 613
  • [7] The stochastical model of approximation of the solution of subdiffusion equation
    Selezneva, LV
    KORUS 2005, PROCEEDINGS, 2005, : 100 - 103
  • [8] A new method for the approximation to a solution for the differentiation equation
    Fischer, A
    PHYSIKALISCHE ZEITSCHRIFT, 1921, 22 : 26 - 28
  • [9] AN APPROXIMATION OF THE ANALYTICAL SOLUTION OF THE FRACTIONAL EULER-LAGRANGE EQUATION
    Ciesielski, Mariusz
    Blaszczyk, Tomasz
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2013, 12 (04) : 23 - 30
  • [10] An analytical solution to Kepler's equation using Chebyshev approximation
    Barker, L
    ASTRODYNAMICS 2003, PTS 1-3, 2003, 116 : 1105 - 1118