The transition mechanism of the nanoparticle deposition patterns after a nanofluid droplet dried naturally on a hydrophilic substrate

Nanoparticle deposition induced by the natural evaporation of droplets plays a significant role in printing and device fabrication. However, the transition mechanisms among typical nanoparticle deposition patterns remain insufficiently understood. In this paper, the deposition front evolution and the droplet's three-phase contact line dynamics during the evaporation of nanofluid droplets with different droplet sizes, nanoparticle diffusion coefficients, and environmental humidities have been simulated by a lattice Boltzmann model that incorporates nanoparticle deposition dynamics. The simulation results are in qualitative agreement with previous experimental results. The coupling effects of the droplet's three-phase contact line dynamics, nanoparticles' non-uniform concentration distribution, and nanoparticles' deposition dynamics on the deposition front evolution have been fully uncovered. The dimensionless Peclet number that characterizes the intensity of the nanoparticle enrichment effect at the droplet edge and another dimensionless number that characterizes the time-integral effect on the nanoparticle deposition dynamics at the droplet edge are found to determine the final deposition pattern. A phase diagram of the four typical deposition patterns after nanofluid droplet drying has been given based on the two dimensionless parameters. Importantly, it is found that in addition to the traditional local nanoparticle enrichment effect at the droplet edge, the time-integral effect of nanoparticle deposition dynamics at the deposition front edge is also the key factor determining the final deposition pattern. The final deposition pattern is a competitive or cooperative result of these two effects. The critical transitional conditions among different nanoparticle deposition patterns are revealed, thus a low-cost control path for the deposition pattern is provided.