Equação de Poisson-Boltzmann e teoria do funcional da densidade clássica aplicadas a sistemas eletrolíticos: desde sistemas biológicos até recuperação avançada de petróleo

Abstract

Electrostatic interactions play an indispensable role in physical, biological, and chemical processes. Therefore, the study of such interactions provides a better understanding of counterintuitive phenomena, as well as guiding the development of new solutions and strategies at the industrial level. The techniques used for modeling electrolyte systems can be classified as implicit methods, integral equations and classical density functional theory, explicit methods, and hybrid methods. In this thesis, the Poisson-Boltzmann equation (PBE) and the classical density functional theory (DFT) were used. At PBE level, (i) the transmembrane ion partition of an erythrocyte was evaluated through the inclusion of the non-electrostatic interactions and Bohr term, being possible to take into account the effects of the change in the dielectric constant between intra and extracellular environments; (ii) the electrical behavior of the Bacillus brevis cell wall was investigated with the charge-regulated volume bounded-charge density approach; and (iii) the contact angle and wetting of a three-phase system (two liquids and a solid surface) was determined. Unlike the former two systems, which have biological appeal, the latter was investigated aiming at the application in the enhanced oil recovery through the injection of an aqueous electrolyte solution. Furthermore, the DFT was developed in three-dimensional coordinates with convolutions calculated by the fast Fourier transform, and applied to the analysis of the wettability and contact angle of a system characterized by brine/ hydrocarbon/ rock. Understanding the effects of engineered water injection is of paramount importance to the oil recovery as it allows the rational selection of the composition of this water. It is worth mentioning that the application of DFT to study liquid/liquid/solid substrate system as well as the inclusion of the Bohr term in the PBE and the volumetric charge-regulated approach, as far as we could track, have not been performed in the literature. Finally, the balancing of the intrinsic approximations of the PBE might cancel them out, promoting an excellent reproduction of experimental data, depending on the system to be studied, as demonstrated in the prediction of the ionic partition of the Cl‒ ion that occurs passively in the erythrocyte and zeta potential of B. brevis cell wall. On the other hand, the DFT is important to study complex systems, such as confined systems with high ionic concentrations, since it has a higher level of detail.