Phase Field Simulation of Viscous Sintering

The presence of a liquid phase, which provides capillary force during viscous sintering, can accelerate the evolution of sintered particles. Due to the difficulty of coupling about the Navier-Stokes equations, however, it is quite challenging to obtain simulation results that meet the laws of physics. In the present study, a phase field model of the viscous sintering process is established, and the morphology, velocity field, and pressure field evolutions of the sintered particles are analyzed. First, the Cahn-Hilliard and Navier-Stokes equations are solved using the finite difference method and the predictor-corrector method. In the finite difference method, the upwind and central difference schemes are combined. The simulation results show that under the drive of surface tension, two circular particles gradually merge into one. The velocity field is divided into a pure straining region and a rigid body motion region inside the particle; the pressure difference between the inside and outside of the particles is proportional to the curvature of the particles. Then, the contact radius and shrinkage of the two circular particles are calculated, and then a curve over time is drawn. The results show that they vary drastically at the beginning stage of evolution and satisfy the law of viscoelastic contact. In the later stage of evolution, the change becomes slower when the contact radius and shrinkage of the two circular particles are close to the values of the equilibrium state. With the increase in mobility, the evolution rate accelerates, but the morphology of the stable state is almost unchanged. The evolution of multiparticles and pores is also simulated. The results show that the pores in the viscous sintering process are initially spheroidized and then slowly disappear, resulting in densification. Under the same simulation conditions, the smaller pores evolve faster.