Applicability of the Linearized Poisson-Boltzmann Theory to Contact Angle problems and Application to the Carbon Dioxide-Brine-Solid Systems

Abstract

In colloidal science and bioelectrostatics, the linear Poisson Boltzmann Equation (LPBE) has been used extensively for the calculation of potential and surface charge density. Its fundamental assumption rests on the premises of low surface potential. In the geological sequestration of carbon dioxide in saline aquifers, very low pH conditions coupled with adsorption induced reduction of surface charge density result in low pH conditions that fit into the LPB theory. In this work, the Gouy-Chapman model of the electrical double layer has been employed in addition to the LPBE theory to develop a contact angle model that is a second-degree polynomial in pH. Our model contains the point of zero charge pH of solid surface. To render the model applicable to heterogeneous surfaces, we have further developed a model for the effective value of the point of zero charge pH. The point of zero charge pH model when integrated into our model enabled us to determine the point of zero charge pH of sandstone, quartz and mica using literature based experimental data. In this regard, a literature based thermodynamic model was used to calculate carbon dioxide solubility and pH of aqueous solution. Values of point of zero charge pH determined in this paper agree with reported ones. The novelty of our work stems from the fact that we have used the LPB theory in the context of interfacial science completely different from the classical approach, where the focus is on interparticle electrostatics involving colloidal stabilization.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson–Boltzmann Framework: An Analytical Treatment

“…6,9 Interestingly, only the energy components depending on potential coefficients subjected to further changes need to be recalculated; see 7a and 8. To this end, we propose and then numerically benchmark (section 5) the approximation methodology, the simpler "azimuthally symmetric" version of which for m = 0 was proposed in ref 36) if n max ≥ n is taken; however, this is not the case, e.g., for the coefficient b nml (r, R ̃) with general triplet (n, m, l) of indices (an illustrative example of the convergence of the re-expansion coefficients, approximated by the methodology just described, is given in Appendix B.3).…”