Boundary Conditions and Multi-Scale Modeling for Micro-and Nano-flows

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Johns Hopkins University
The development of micro- and nanofluidic devices requires detailed knowledge of interfacial phenomena. This thesis addresses two important effects at wall-fluid interfaces, boundary slip and electroosmosis, through numerical simulations. The first study uses molecular dynamics (MD) simulations to probe the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries. As wall curvature increases, the slip length decreases dramatically for close-packed surfaces and increases slightly for sparse ones. The magnitude of the variation depends on the crystallographic orientation and the flow direction. The different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response. The second study performs MD simulations to explore the effective slip boundary conditions over surfaces with one-dimensional sinusoidal roughness for two different flow orientations: transverse and longitudinal to the corrugations, and different atomic geometries of the wall: smoothly bent and stepped. The results for the sparse bent surfaces quantitatively agree with the continuum predictions with a constant local boundary condition. The effective slip length decreases with increasing corrugation amplitude, and the reduction is larger for the transverse direction. Atomic effects become significant for the close-packed bent and for the stepped surfaces, which may even enhance the effective slip along the longitudinal direction. In the third study, an efficient multi-scale method is developed to simulate electroosmotic flows. MD is used in the near wall region where the atomistic details are important, while continuum incompressible fluctuating hydrodynamics is applied in the bulk region. The two descriptions are coupled in an overlap region. Because of the low ion density and the long-range of electrostatic interactions, discrete ions are retained in the bulk region and simulated by a stochastic Euler-Lagrangian method (SELM). The MD and SELM descriptions seamlessly exchange ions in the overlap region. This hybrid approach is validated against full MD simulations for different geometries and types of flows.
slip boundary condition, electroosmotic flow, multi-scale modeling