Multiscale Methods for Hydrodynamics of Polymer Chains in Solution
Aleksandar Donev, Lawrence Postdoctoral Fellow, Lawrence Livermore National Laboratory


The hydrodynamics of complex fluids, such as polymer solutions and colloidal suspensions, has attracted great interest due to recent advances in fabrication of micro- and nano-fluidic devices. I will first review recent advances in mesoscopic numerical methods for simulating the interaction between complex fluid flow and suspended macro molecules and structures. Computational issues at play include coarse-graining to bridge the large gap in timescales and length scales, coupling between disparate methods such as molecular dynamics and Navier-Stokes solvers, the inclusion of thermal fluctuations.

I will then present my recent work at LLNL to develop novel particle methods for modeling polymer chains in flow. Typically, Molecular Dynamics (MD) is used for the polymer chains, and the solvent is modeled with a mesoscopic method. In our algorithm, termed Stochastic Event-Driven Molecular Dynamics (SEDMD) [A. Donev and A. L. Garcia and B. J. Alder, J. Comp. Phys., 227(4), 2644-2665, 2008], polymers are modeled as chains of hard spheres and the solvent is modeled using a dense-fluid generalization of the Direct Simulation Monte Carlo (DSMC) method [Phys. Rev. Lett., 101, 075902, 2008]. Even with all of the speedup compared to brute-force MD the algorithm is still time-consuming due to the large number of solvent particles necessary to fill the computational domain. It is natural to restrict the particle model only to regions close to a polymer chain and use a lower-resolution continuum model elsewhere. I will present a hybrid method that couples an explicit fluctuating compressible Navier-Stokes solver with the particle method. The coupling is flux-based and generalizes previous work [J. B. Bell and A. L. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6, 1256-1280, 2008] to dense fluids as appropriate for polymer problems.

I will conclude with a look into the challenges of developing a simulation methodology capable of simulating macroscopic flows of complex fluids with atomistic fidelity.