scholarly journals Asymptotic solution of the cylindrical nonlinear Poisson-Boltzmann equation at low salt concentration: Analytic expressions for surface potential and preferential interaction coefficient

2002 ◽  
Vol 99 (5) ◽  
pp. 2597-2602 ◽  
Author(s):  
I. A. Shkel ◽  
O. V. Tsodikov ◽  
M. T. Record
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Solution ◽  
Surface Potential ◽  
Salt Concentration ◽  
Interaction Coefficient ◽  
Preferential Interaction ◽  
Low Salt ◽  
Analytic Expressions ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

On an Asymptotic Solution of the Poisson—Boltzmann Equation—The Moderately Charged Cylinder

1966 ◽  
Vol 45 (6) ◽  
pp. 2184-2188 ◽  
Author(s):  
A. D. MacGillivray ◽  
J. J. Winkleman
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Charged Cylinder

scholarly journals Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

2009 ◽  
Vol 6 (1) ◽  
pp. 300-314 ◽  
Author(s):  
Marcia O. Fenley ◽  
Michael Mascagni ◽  
James McClain ◽  
Alexander R. J. Silalahi ◽  
Nikolai A. Simonov
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Salt Concentration ◽  
Monte Carlo Sampling ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

scholarly journals The zeta potential calculation for fluid saturated porous media using linearized and nonlinear solutions of Poisson–Boltzmann equation

2018 ◽  
Vol 34 (3) ◽  
Author(s):  
Luong Duy Thanh
Keyword(s):  
Experimental Data ◽  
Boltzmann Equation ◽  
Zeta Potential ◽  
Surface Potential ◽  
Electric Potential ◽  
Small Magnitude ◽  
Nonlinear Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Nonlinear Solutions

Theoretical models have been developed to calculate the zeta potential based on the solution of the linearized approximation of the Poisson-Boltzmann equation (PB). The approximation is only valid for the small magnitude of the surface potential. However, the surface potential available in published experimental data normally does not satisfy that condition. Therefore, the complete analytical solution to the PB equation (nonlinear equation) needs to be considered. In this work, the comparison between the linearized and nonlinear solutions has been performed. The results show that the linearized solution always overestimates the absolute value of the electric potential in the electric double layer as well as the zeta potential. For a small magnitude of the surface potential, the electric potential distribution predicted from the linearized solution is almost the same as that predicted from the nonlinear solution. It is also shown that the zeta potential computed from the linearized PB solution closely matches with that computed from the nonlinear solution for the fluid pH = 5 - 8 and the shear plane distance of 2.4×10−10 m. Therefore, the solution of the linearized PB equation can be used to calculate the zeta potential under that condition. This is validated by comparing the linearized and nonlinear solutions with experimental data in literature.

scholarly journals Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

2015 ◽  
Vol 48 ◽  
pp. 420-446 ◽  
Author(s):  
Mireille Bossy ◽  
Nicolas Champagnat ◽  
Hélène Leman ◽  
Sylvain Maire ◽  
Laurent Violeau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Methods ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation
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