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Multiscale Simulation of Micro- and Nano-Fluidics

Dr. Shiyi Chen

Mechanical Engineering at John Hopkins University

Abstract:   A continuum and molecular dynamics hybrid multiscale method is developed to simulate micro- and nano-fluid flows. The method uses the continuum Navier-Stokes equations for one flow region and atomistic molecular dynamics for another. The spatial coupling between continuum equations and molecular dynamics is achieved through constrained dynamics in an overlap region. To validate the numerical method, the proposed multiscale method is used to simulate sudden-start Couette flow and channel flow with nano-scale rough walls, showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations for different parameter regimes. The hybrid method is then used to study the two-dimensional driven cavity flow. Around the two corners, i.e., the intersections of the moving and the stationary walls, the continuum Newtonian shear stress approaches 1/r singularity with r the distance away from the corner. To remove the singularity induced by the continuum Navier-Stokes equations, we employ the hybrid method by simulating the corner flows using the molecular dynamics simulation and other flow regions using the Navier-Stokes equations. The bulk flow properties from the hybrid solution are found to be compared well with those from the full molecular dynamics and Navier-Stokes simulations regardless of how the corner singularity is treated. The differences of velocity and shear stress between the hybrid method and continuum Navier-Stokes solutions near two singular corners are obtained Our results indicate that the departure of the true stress from the 1/r law in nano-scale flows depends on the driven velocity and the characteristic time scale of the molecular interaction. The numerical algorithms pertinent to multiscale time and fast convergence to steady state flows will be presented. The applications of the proposed multiscale method for multiphase flows, polymeric flows and bio-fluid systems, will be discussed.