A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM)[Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E {\bf 26}, 361(2008)], a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage $G'(\omega)$ and loss $G"(\omega)$ moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of $\Phi=0$, 0.41, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions

Multi-scale simulation method for electroosmotic flows

Electroosmotic transport in micro-and nano- channels has important applications in biological and engineering systems but is difficult to model because nanoscale structure near surfaces impacts flow throughout the channel. We develop an efficient multi-scale simulation method that treats near-wall and bulk subdomains with different physical descriptions and couples them through a finite overlap region. Molecular dynamics is used in the near-wall subdomain where the ion density is inconsistent with continuum models and the discrete structure of solvent molecules is important. In the bulk region the solvent is treated as a continuum fluid described by the incompressible Navier-Stokes equations with thermal fluctuations. A discrete description of ions is retained because of the low density of ions and the long range of electrostatic interactions. A stochastic Euler-Lagrangian method is used to simulate the dynamics of these ions in the implicit continuum solvent. The overlap region allows free exchange of solvent and ions between the two subdomains. The hybrid approach is validated against full molecular dynamics simulations for different geometries and types of flows