Abstract

A deeper understanding of fluid-wall interactions in microfluidic devices is crucial to many emerging applications in modern science and engineering. To date, the numerical investigation of these interfacial phenomena is conducted mostly by means of molecular dynamics (MD) simulations. MD is credited for offering the highest degree of physical realism, but suffers from severe limitations in reaching the spatial and temporal scales of direct experimental relevance. The standard alternative is to resort to continuum formulations of fluid mechanics in the bulk flow, supplemented with ad-hoc boundary conditions at the solid walls. The continuum approach is computationally efficient, but its predictive capability is severely constrained by the empirical nature of the boundary conditions. In the recent years, an alternative, mesoscopic, approach has emerged in the form of suitably stylized lattice kinetic equations. By its very mesoscopic nature, naturally placed inbetween the continuum and atomistic levels, the lattice-kinetic approach holds great promise of combining the best features of the atomistic and continuum descriptions, while doing away with their major limitations. In this talk we shall illustrate the basic ideas and mathematical tools behind lattice kinetic theory, and discuss its successful application to some outstanding problems in microfluidics, such as the onset of slip-flow at solid interfaces and super-hydrophobic effects on micro-corrugated surfaces.