Numerical study on the dispersion and deposition of particles in evaporating sessile droplets
Evaporating sessile droplets including dispersed particles are utilized in the coating, printing, and biomedical applications. Modeling this problem is a challenging process, therefore diﬀerent assumptions are used in the literature. It is important to have a model which covers both pinned and moving contact line regimes for the droplet, thus whole evaporation process and deposition proﬁle can be understood. Therefore, in this work, a numerical and mathematical model is derived to simulate two-dimensional symmetric thin evaporating sessile droplets whose contact line is ﬁrstly pinned and then moving. This model is derived by combining diﬀerent models in literature with the help of lubrication theory and rapid vertical diﬀusion assumption. This model includes a temporal change in the droplet’s surface height, contact line dynamics, particle dispersion, and deposition. The ﬁnite diﬀerence method is used in the numerical solution. Cases including pinned and moving contact lines in the literature are solved separately by diﬀerent numerical algorithms developed in this work and these algorithms were combined. This new algorithm ﬁrst solves a mathematical model in the pinned contact line regime. When the contact angle goes below the deﬁned limit, the second part of the algorithm solves the mathematical model in the moving contact line regime until 95 percent of the total particle mass is deposited. A parametric study has been done with the developed algorithm. A set of parameters is deﬁned and chosen parameters are changed to see their eﬀects. It is observed that increasing the Marangoni number and Capillary number, increased particle accumulation near the center. Decreasing evaporation number and increasing Damkohler number result in more uniform particle deposition.