Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics

The framework of the heterogeneous multiscale method (HMM) is used to develop numerical methods for the study of macroscale dynamics of fluids in situations, where either the constitutive relation or the boundary conditions are not explicitly available and have to be inferred from microscopic models such as molecular dynamics. Continuum hydrodynamics is used as the macroscopic model, while molecular dynamics serves as the microscopic model and is used to supply the necessary data, e.g., the stress or the boundary condition, for the macroscopic model. Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains. This naturally decouples the micro and macrospatial and temporal scales whenever possible. Applications are presented for models of complex fluids, contact line dynamics, and a simple model of non-trivial fluid–solid interactions.