Numerical Approaches for Multiphase Microfluids

In this contribution strength and limitations of two modern and reliable numerical models for computing multiphase flows in the microcirculation regimens are reviewed and critically analyzed. Specifically, algebraic Volume of Fluid approach for fluid/fluid interaction problems is considered, as well as the dynamic-Immersed Boundary for fluid/structure interaction problems with a special accent on bio-inspired systems. On one hand, the one-fluid approach for computing multi species mixtures is adopted. The Navier-Stokes system for the mixture evolution is considered and the interface between the different species is tracked through a convenient discretization of the Heaviside function. On the other hand, the dynamic Immersed Boundary method combined with a BGK Lattice–Boltzmann technique is presented, in which the body surface is modeled as a collection of points responding to an elastic potential and a bending resistance. A moving least squares reconstruction is used to accurately interpolate flow quantities and the forcing field needed to enforce the boundary condition on immersed bodies. Validations against well known benchmark data for both models are discussed.