The different aspects of hybrid three-phase flow systems containing suspended solid parts and two immiscible fluids has recently been the subject of particular numerical studies. This subject is important from the polymer processing point of view; since the assessment of the rigid body (e.g., the filler) distribution in each phase, which determines the final mechanical properties, could be evaluated via rigorous analysis of the hybrid three-phase flow fields. In this research, a new mathematical scheme (the moving least-squares aided finite element method or MLS-FEM) is employed to evaluate the tendency of a solid particle to the migration from one phase to other. The MLS-FEM considers each phase as independent flow domains, which have communal boundaries. Employing this method, the effects of the surface tension and viscosity on the particle migration in a stationary flow field has been studied.