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A First step towards simulations of tracer motion in a thermally fluctuating viscoelastic fluid.

Banff International Research Station for Mathematical Innovation and Discovery

Many biological fluids, like mucus and cytoplasm, have prominent viscoelastic properties, which lead to the subdiffusive behavior of immersed particles. 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. The numerical method is spectral, meshless and uses results from the simulations of Generalized Langevin Equations.The implementation presents many practical problems, mostly stemming from the fact that the physical regime of interest corresponds to a situation where the memory kernel has a very slow (power law) decay.

Mathematics; Numerical analysis; Partial differential equations; Women and early careers in math

video/mp4

Author affiliation: University of Utah

2019-11-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72252

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/