Evaporation of thin droplets of colloidal suspensions in shallow cavities

The drying of droplets of colloidal suspensions in cavities is of importance for applications such as inkjet printing, pattern analysis of dried blood, and fabrication of printed electronics. Nonuniformity of particle deposition can lead to a pinch point, a sharp local minimum of particle number density that is detrimental for some applications. In contrast to prior work that assumes the droplet contact line is pinned, here we focus on how cavity shape, solvent evaporation rate, and thermal Marangoni flow affect particle deposition when the contact line is free to move. A lubrication-theory-based model is developed to derive nonlinear evolution equations for the droplet height and vertically averaged particle concentration. Contact-line motion is accounted for by using a precursor film and disjoining pressure and solvent evaporation is described using the one-sided model. Finite-difference solutions for trapezoidal-like cavities show that a pressure maximum appears at the droplet edge as the evaporation rate or thermal Marangoni flows increase, or as the cavity depth decreases. The resulting inward flow causes the contact line to depin, which leads to an increase in the uniformity of particle deposition but also to the occurrence of a pinch point near the droplet edge.