Estimation of the electric double layer thickness in the presence of two types of ions in soil water

• Analytical solution to the Poisson–Boltzman equation derived for two types of ions.
• Voyutsky's approximate solution overestimates electric double layer thickness, β.
• The results for the approximate and analytical solutions are compared.
• Due to addition of gypsum to the sodic soil, β decreases exponentially.
• Analytical solution should be used for computing the β exactly.

The deficit of charges on the clay surface is balanced by the cations in soil water forming the electric double layer (EDL). In sodic soil monovalent Na+ ions are dominant and hence, thickness of the EDL (β) is more than in the nonsodic soil where bivalent Ca2 + ions are dominant. For reclaiming the sodic soil, gypsum is added as a source of Ca2 + ions to replace the Na+ ions from the EDL as well as for reducing β. In this paper, an analytical solution is derived to the nonlinear Poisson–Boltzman equation and the solution is used for computing β exactly. A comparison is made between β computed from the solutions of linearized and nonlinear Poisson–Boltzman equation. The solution to the linearized Poisson–Boltzman equation overestimates β. Therefore, it is appropriate to adopt the solution of the nonlinear Poisson–Boltzman equation for computing β.

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