Monte Carlo modeling of nanofluid drying patterns
Date of Issue2013
School of Mechanical and Aerospace Engineering
Nanofluids are a new kind of fluids engineered by dispersing nanoparticles in base fluids. After full drying of nanofluid, nanoparticles are left on a substrate and can self-organize into different structures. This process can be employed as a convenient way to generate useful micro-devices or new materials. Better understanding of nanofluid drying patterns will lead to cost-saving optimizations in applications such as printing, coating, medical research, etc. Two different modeling approaches are combined together to investigate drying nanofluid patterns and qualitatively predict the shape and structure of the resulting particle aggregates. The first model is based on the Kinetic Monte Carlo (KMC) simulation and is developed to predict the drying patterns in an open two-dimensional (2D) domain, in which the dewetting front shrinks from the edge towards the center. The model behavior is investigated independently in open domains of two shapes: square and circle. The simulation in the open square domain reveals that the dispersed particles can be deposited into an isotropic branched structure which remains frozen after full evaporation of the base fluids. The prediction of fractal particle aggregation in the square domain is confirmed in the experiments with drying water-based nanofluids under the Scanning Electron Microscope. The KMC approach in the open circular domain simulates the formation of fractal-like structures during evaporation of the water-based nanofluid sessile droplets in the experiments. We found that the lattice-gas based Monte Carlo model can theoretically predict the nanoparticle self-assembly into a solid fractal-like aggregate after a sessile droplet is fully dried. The simulated patterns show an agreement with the experimental counterparts. Furthermore, if the chemical potential function is coupled with the solvent thickness profile of a sessile droplet, the results reveal that fingering contact line instabilities can emerge under a given condition and lead to the formation of branched nanoparticle structure. The second model, based on Diffusion Limited Aggregation (DLA) approach, accounts for particle pre-aggregation in the bulk of drying nanofluids. We mathematically extend a classical DLA by developing a stochastic model of drying the pinned sessile droplet which includes cluster-cluster aggregation (DLCA) as well. The dried pattern has been shown to change from coffee-ring-like configuration to uniform-like one if the particle sticking probability substantially increases. In addition, the model is upgraded to include the different drying conditions, such as sole outward capillary flow (1 flow model), inward and outward flows (2-flow model), and particles' interactions.The KMC and DLCA models are then combined to describe the full process of sessile droplet drying: the DLCA model is used to simulate the initial stage of droplet evaporation, capillary flows and particle pre-aggregation, while KMC is used to simulate the final stage of the thin-film dewetting. The cases of broken coffee rings, fractals inside the rings and drying holes have been studied. The three-dimensional (3D) DLCA model is consequently developed. The 3D simulation provides a realistic view of drying of nanofluid droplets and also includes the cluster-cluster aggregation and the capillary flow. The influence of droplet base diameter, contact angle, particle sticking probability and volumetric concentration on the final 3D pattern has been investigated in the presented study. Finally, the simulation results are supported by experimental work with drying nanofluid droplets, and quantitative comparisons of results are provided. The future work aims to model more complicated conditions, such as non-uniform local evaporation, shrinking three-phase line in the three-dimensional domain, etc. More detailed experiments are planned, including the study of 3D patterns.