Multiscale simulation of electroosmotic flows

We develop an efficient hybrid multiscale method for simulating nano-scale electroosmotic flow based on spatial ``domain decomposition'' [1]. Molecular dynamics (MD) is used in the near wall region where atomistic details are important. A multigrid Particle-Particle Particle-Mesh (PPPM) method [2] is used to calculate the long-range Coulombic interaction between charged ions. Continuum (incompressible Navier-Stokes) equations for the solvent are solved in the bulk region, reducing the computational cost substantially. A discrete description of ions is retained in the continuum region because of the low density of ions and the long-range of electrostatic interactions. Langevin dynamics is used to model the Brownian motion of these ions in the implicit solvent. The fully atomistic and continuum descriptions are coupled through ``constrained dynamics'' [1] in an overlap region. Continuity of flux of both charged and solvent particles is ensured. The scheme is implemented in channel flow simulations with and without wall roughness. Results are compared with pure MD simulations. \\[4pt] [1] X. Nie, S. Chen, W. E, and M. O. Robbins, J. Fluid Mech., 500:55-64, 2004.\\[0pt] [2] J. Liu, M. Wang, S. Chen, and M. O. Robbins, J. Comput. Phys., 229:7834-7847, 2010.