Experimental and numerical experiments were carried out to study the coffee rings or coffee splats formed by droplet evaporation with micro or nano polystyrene sphere particles (Dp = 10 μm or 100 nm). Particle image velocimetry (PIV) and a high-resolution camera were used in this experiment, along with a temperature-controlled heater and a data-acquisition computer. The results showed that a nano particle could form a homogeneous coffee splat, instead of the common coffee ring formed when using micro particles. In order to account for this phenomenon, this paper developed a complex multiphase model, one which included the smooth particle hydrodynamics (SPH) fluid model coupled with the van der Waals equation of state for droplet evaporation, the rigid particle model of finite-size micro particles, and the point-particle model of the nanometer particles. The numerical simulation was operated on a GPU-based algorithm and tested by four validation cases. A GPU could calculate 533 times the speed of a single-core CPU for about 300,000 particles. The results showed that, for rigid solid particles, the forms emerged spontaneously on the wall, and their structure was mainly affected by the boundary wettability, and less affected by the fluid flow and thermal condition. When the wall temperature was low, it was easier for the particles to be deposited on the contact line. At high wall temperature, the coffee ring effect would be weakened, and the particles were more likely to be deposited in the droplet center. The hydrophilic surface produced a larger coffee ring compared to the hydrophobic surface. The experimental and numerical results proved that particle size could play a significant role during the particle deposition, which may be a possible route for producing uniform-distributed and nano-structure coatings.
Keywords: additive manufacturing; coffee ring effect; diffuse interface model; droplet evaporation; particle deposition; phase field.