The Zeta Potential Calculation for Fluid Saturated Porous Media Using Linearized and Nonlinear Solutions of Poisson–Boltzmann Equation

Abstract

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.