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

Abstract

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 FOR CITATION Dweik

Mixed problem for a linear differential equation of parabolic type with nonlinear impulsive conditions

“…Differential equations of mathematical physics have direct applications in the theory of nanosystems (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13], and [14]). Partial differential and integro-differential equations of parabolic type with initial and boundary conditions are investigated widely by large number of scientists and have different applications in sciences and technology (see, for example, [15][16][17][18][19][20][21][22][23][24][25][26][27][28]).…”