Applied Math Seminar: Dr. Christel Hohenegger
Event Description:
Title: Simulation and diffusion of immersed particles in complex fluids
Abstract: Complex fluids, like polymer melts or cake batter, have prominent viscoelastic properties, which lead to the subdiffusive behavior of immersed particles, which is to say the variance of the particle displacement grows sublinearly with time. We propose a viscoelastic generalization of the Landau-Lifschitz Navier-Stokes fluid model for particles that are passively advected by such a medium and develop a simulation techniques based on the theory of stationary Gaussian processes. In contrast to the stochastic immersed boundary method for viscous fluids, which relies on step-by-step simulation techniques exploiting the Markov property, our method is based on the numerical evaluation of the covariance associated with individual fluid modes. Passive microrheology records displacement of such particles and extract mechanical properties of the bulk fluid. It is premised on the idea that statistics of particles trajectories can reveal fundamental information about the fluid environment. We use the produced simulated data to address the uncertainty in reconstructing loss and storage moduli which characterize the elastic and viscous properties of the fluid as an inverse problem.