Mathematical Modeling of Microemulsification Processes, Numerical Simulations and Applications to Drug Delivery
Abstract
Microemulsion systems are a great pharmaceutical tool for the delivery of formulations containing multiple hydrophilic and hydrophobic ingredients of varying physicochemical properties. These systems are gaining popularity because of its long shelf life, improved drug solubilisation capacity, easy preparation and improvement of bioavailability. Despite the advantages associated with the use of microemulsion systems in pharmaceutical industries, the major challenge impeding their use has been and continues to be the lack of understanding of these systems. Microemulsions can be mathematically modeled by an initial boundary value problem involving a sixth order nonlinear time dependent equation. In this thesis, we present a numerical method simulating the process of microemulsions. Relying on the mathematical model proposed by Gommper et. al~\cite{GSM1990correlation}, we show that our numerical method successfully captures the microemulsification process and is uniquely and unconditionally solvable. While we use the C$^0$ Interior Penalty finite element method for the spatial discretization, the time discretizations are based on a modified convex splitting of the energy of the systems.
Subject Area
Mathematics|Physics|Applied physics
Recommended Citation
Ifeacho, Ogochukwu Nneka, "Mathematical Modeling of Microemulsification Processes, Numerical Simulations and Applications to Drug Delivery" (2020). ETD Collection for University of Texas, El Paso. AAI28089763.
https://scholarworks.utep.edu/dissertations/AAI28089763