Many daily-life fluids behave in unexpected and interesting manners. While Newtonian fluids like water and air flow in a familiar and predictable way, non-Newtonian fluids often show more complex and unusual behavior under flow. Typical examples of non-Newtonian fluids are polymers, bread dough, peanut butter, and silly putty. Modeling the flow of such fluids during processing requires developing accurate mathematical models and numerical simulation techniques.
Professor Wapperom has recently worked on improving models for fiber composites and numerical techniques to simulate the flow of such fluids. Fibers will rotate in a solvent and the orientation that develops under flow highly influences material properties of the final product. Adding fibers to a polymeric solvent may create lightweight materials that are stronger than the original unfilled polymer if the fibers can be oriented in the direction of mechanical demand. Fiber orientation is modeled by partial differential equations at the macroscopic level and stochastic partial differential equations at the microscopic level.
To predict the time evolution of the orientation of fibers, one needs to obtain approximate solutions of a system of differential equations. For this, a numerical code has been developed that simulates numerically the time-dependent flow of fiber composites in three-dimensional injection molding geometries. The spatial discretization uses Galerkin and discontinuous-Galerkin finite element methods, while a pseudo-concentration method is used to track the moving flow front.