Probing viscoelastic liquids as an inverse problem
Many biological fluids, like mucus or cytoplasm, have prominent viscoelastic properties. As a result, immersed and passive particles exhibit subdiffusive behavior, which is to say the variance of the particle displacement grows sublinearly with time. Passive microrheology, which records displacement of such particles and extract mechanical properties of the fluid environment, is premised on the idea that statistics of particles trajectories can reveal fundamental information about the fluid environment. First, I'll present a Landau-Lifshitz-Navier-Stokes model of a passive particle advected in a viscoelastic fluid and show how the mean square displacement and first step auto-correlation in the increment process are related to those of the fluid's modes. Second, I'll address the uncertainty in reconstructing loss and storage moduli which characterize the elastic and viscous properties of the fluid from simulated data as an inverse problem.
(Refreshments will be served.)