A Volume-Penalization Pseudo-Spectral method for Thermally Induced Phase Separation (TIPS
[ jeudi 04-07-2013 15:00
| français ]A Volume-Penalization Pseudo-Spectral method for Thermally Induced Phase Separation (TIPS
École Centrale de Nantes
The seminar presents a numerical method for the prediction of the morphology patterns at microscopic scale in composite materials. The work is motivated by the notion that the macroscopic properties of composites are determined by their structural morphology on a finer scale. Indeed, in many industrial applications a variety of brittle resins are modified by the addition of micro-metric sized fillers acting as tougheners. The overall mechanical properties enhancement is affected by the particle size and distribution. In systems where the dispersion of fillers is made difficult by the high viscosity of the matrix the desired morphology can be achieved through spontaneous phase separation of an initially homogeneous binary solution under specific conditions of temperature and composition. The class of systems that are investigated are denoted as Upper Critical Temperature Solutions (UCTS) since the separation occurs in reason of a temperature quenching. For highly viscous fluids this process is described by a modified Cahn-Hilliard equation taking into account for thermal effects. The governing equations are numerically solved in a representative elementary volume using a computationally efficient and accurate Fourier pseudo-spectral method and integrated in time by an unconditionally stable time stepping procedure allowing for time step adaptivity. To take into account the presence of longitudinal fibers immersed in the matrix a volume penalization techniques based on the phase-field formalism is developed. The method is originally introduced to simulate the thermal interaction between the fiber and the phase-separating solution but can be efficiently generalized as a method to solve the Cahn-Hilliard equation in confined domains, in a wider framework of applications.