Effects of insoluble nano-particles on nanofluid droplet evaporation

A model is presented for predicting the evaporation behavior of liquid droplets containing nano-sized insoluble particles. The model is constructed based on, and supported by, the existing experimental result. Of particular interest are the evolution of droplet size, and evaporation rate constant prior to the shell formation (also called the first drying or evaporation stage), when the particles forms a compact shell at the droplet surface. As the droplet evaporation proceeds, increasingly more particles are “included” on its surface, reducing the effective liquid surface area for evaporation causing deviation from the classical d2-law for pure fluid droplet evaporation. Peclet number (Pe), a non-dimensional ratio of particle diffusion time to the droplet lifetime, and initial particle concentration (Yvo) are shown to play a role in the evaporation behavior prior to shell formation. The model predicts that: (1) the deviation from the classical d2-law is increasingly significant with increased Pe and Yvo; (2) the time to shell formation decreases, and shell diameter increases, with increased Pe and initial particle concentration (Yvo). As a consequence, Yvo·Pe<1.8 is necessary for the first stage to exist at all. Within the limiting value, the combination of larger Pe and smaller Yvo produces larger hollow shells with low densities. For Yvo·Pe>1.8 the shell forms instantly and evaporation occurs after liquid diffuses through, and wet, the shell. The effect of contact angle (θ) on the effective liquid surface area for evaporation is also discussed.