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.

Interrelationship of Electric Double Layer Theory and Microfluidic Microbial Fuel Cells: A Review of Theoretical Foundations and Implications for Performance

“…Consequently, bacterial cell surfaces carry a net negative charge under most physiological conditions, with a few notable exceptions [101,102], implying the existence of an electric double layer on microbial cells. Accordingly, Table 1 summarizes the information on the ionization of ionizable functional groups, as well as their molecular relationships.…”

Spontaneous Imbibition and an Interface-Electrostatics-Based Model of the Transition Zone Thickness of Hydrocarbon Reservoirs and Their Theoretical Interpretations

“…For a cylindrical surface, the solution to the PBE in cylindrical geometry [56,57] permits calculation of the surface charge density as [58]:…”

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

“…This, however, does not diminish the importance of studying the behavior of the LPBE also in the case of highly charged objects: their electrostatics may still be correctly described at sufficiently long distances (as compared to the Debye length) by the usual DH approximation provided that the sources of the electric field are properly renormalized. − (See also the recent ref for additional comments concerning the ranges of applicability of the DH theory.) This once again emphasizes the importance of a thorough study of the DH approximations, both theoretically and numerically, and justifies the constant stream of works related to the LPBE (see recent refs , , and − , and references therein).…”