The front-tracking method for multiphase flows in microsystems: fundamentals

Abstract

The aim of this paper is to formulate and apply the front-tracking method to model multiphase/multifluid flows in confined geometries. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties. The effects of the surface tension are treated as body forces and added to the momentum equations as functions at the phase boundaries so that the flow equations can be solved using a conventional finite-difference or a finite-volume method on a fixed Eulerian grid. The interface, or front, is tracked explicitly by connected Lagrangian marker points. Interfacial source terms such as surface tension forces are computed at the interface using the marker points and are then transferred to the Eulerian grid in a conservative manner. Advection of fluid properties such as density and viscosity is achieved by following the motion of the interface. The method has been implemented for two (planar and axisymmetric) and fully three dimensional interfacial flows in simple and complex geometries confined by solid walls. The front-tracking method has many advantages including its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary, electric field, soluble surfactants and moving contact lines. In this chapter, the fundamentals of the front-tracking method including the formulation and details of the numerical algorithm are presented.