Mathematical analysis of some diffusion problems associated to the modeling of surfactant compounds at the air-water interface

Abstract

Surfactants are chemical compounds with a particular structure, that is the responsible of their behavior in a water solution. When a new surface is formed in a surfactant solution, surfactant molecules tend to migrate from the bulk of the solution to the surface, consequently varying its surface tension. The dynamic surface tension is a very important property since it plays a major role in several biochemical, biological and industrial processes. All the huge applications of the dynamic surface tension make it a subject of study for a long period of time. There are several publications in the chemical literature dealing with the numerical solutions of the models that describe the surfactant behavior. However, none of them deal with their mathematical analysis. In this thesis, we introduce the mathematical treatment of those models, that consist of the diffusion equation coupled with an adsorption model.