Estimation of electric double layer thickness from linearized and nonlinear solutions of Poisson–Boltzman equation for single type of ions

The electric double layer (EDL) plays an important role in the sodification and desodification processes. The Gouy (1910) and Chapman (1913) solution to the linearized Poisson–Boltzman equation is mostly used for quantification of the EDL. In this paper, a simplified analytical solution to the nonlinear Poisson–Boltzman equation is derived. The solution of the nonlinear Poisson–Boltzman equation given by Appelo and Postma (2005) is supplemented with a method for determining the EDL thickness, β. It is found that the solution to the linearized equation overestimates β. However, at higher bulk concentrations, β computed from the solution of linearized Poisson–Boltzman equation closely matches with that computed from the solution to the nonlinear equation. The difference in β computed using the two solutions being significant for lower Cb, solution given by Appelo and Postma should be used for finding true value of β.

Graphical abstractThe nonlinear Poisson–Boltzman equation is solved in a simplified way. A method is suggested for computing the exact electric double layer thickness, β. The β computed through the solution to the linearized Poisson–Boltzman equation given by Gouy (1910) and Chapman (1913) is higher than the exact β.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A simplified solution to the nonlinear Poisson–Boltzman equation derived. ► A method is suggested for computation of exact β. ► The solution given by Gouy (1910) and Chapman (1913) gives higher β. ► β computed by the above two solutions differ much for lower bulk concentrations.