Phenomena related to a liquid droplet impacting on a smooth or rough solid substrate, spreading, recoiling and/or solidification exist in many industrial applications such as soldering, inkjet printing and thermal spray coating. There are strong interactions among surface wetting, droplet free surface, and solidification. It is very difficult for a traditional meshed method to solve the problems with both free surface and solidification movements. A meshless method, Smoothed particle hydrodynamics (SPH), is therefore developed in this thesis to investigate the materials processing involving droplet spreading and solidification.In this thesis, the SPH method will be further developed and applied to new applications.

First, the vdW model is applied to simulate the effect of surface tension. However, there is tensile instability in the simulation. Then XSPH is included into the vdW model to remove tensile instability. Also, the SPH model is applied to a droplet impacting on a substrate with different roughness. Spreading, solidification, oxide redistribution, and droplet pinch-off are presented in two and three dimensions. Numerical results demonstrate that the SPH model is a powerful tool to study fluid flow and heat transfer problems with moving boundaries.

The SPH method is further applied to simulate the impact of YSZ droplet on a cold inclined substrate. Heat transfer during droplet impacting and spreading is studied by using an improved artificial heat model. Temperature distribution of the droplet during impact is provided. A solidification model is proposed to simulate the movement of the solidification interface. The effect of the impact angle on droplet splashing has been investigated.

Finally, the droplet impacting on various porous substrates is investigated by using the SPH method. Droplet impacting, spreading and penetrating are investigated for substrate with different shapes, line or sphere, different sizes, and different distribution, homogeneous or random. The porosity of the porous substrate has a great effect on the fluid flow in the porous media. The fluid only can penetrate the large gap. From this study, we will understand the role of porous structure on droplet impacting. The SPH method is further improved to handle the fluid flow in porous media with different structure.