Chromatographic Cycle Solution for Two Solute Adsorption Considering pH-Dependent Langmuir Isotherm Coefficients

T. Rodrigues () and A. P. Pires ()
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T. Rodrigues: Universidade Estadual do Norte Fluminense Darcy Ribeiro
A. P. Pires: Universidade Estadual do Norte Fluminense Darcy Ribeiro

Chapter Chapter 23 in Integral Methods in Science and Engineering, 2026, pp 351-371 from Springer

Abstract: Abstract The mathematical model of pH-dependent chromatography is a powerful tool to understand the influence of the ions concentration and adsorption for several chemical and petroleum processes. This technique can be applied in different fields, ranging from cancer treatment to the production of pharmaceutical drugs in the chemical industry, and also in oil industry, in the case of smart water injection. The mathematical problem is composed by a system of hyperbolic partial differential equations which represents the conservation of the dissolved chemical components, hydrogen proton, and water. The analytical development of the solution for the non-linear system of equations follows the method of characteristics. First, the pH equation is solved and the solution is used for the two-solute chromatography problem. The boundary conditions consider the case of multiple changes in water pH and ions concentration, therefore a series of waves interactions may occur, such as confluence of shocks, cancellation of simple waves and shocks, and wave transmission. Finally, multiple cases subject to different initial and boundary conditions are discussed, as well as their respective pH, solute concentrations, and water saturation profiles.

Date: 2026
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DOI: 10.1007/978-3-032-04458-7_23

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