Abstract:

A novel numerical approach based on Eshelby''s equivalent inclusion method is presented to simulate the Stokes flow of many particles moving in a viscous fluid at a small Reynolds number. For each particle, an eigenstrain rate, which is given by a polynomial function, is introduced to represent the mismatch between the particle and the rest fluid. Based on Eshelby’s equivalent condition, the eigenstrain rate of each particle can be solved and the sedimentation process of a many-particle system can be simulated. Because the Stokes’ flow is obtained by the integral of eigenstrain in all particles, which can be analytically derived for spherical particles, therefore, no mesh is needed for each particle. This approach creates a possibility to simulate a large-scale particle system. Using a mix of aluminum and high-density polyethylene spherical powders in sedimentation, one can simulate the microstructural evolution during the sedimentation process, which will lead to a manufacturing method for functionally graded materials.