Evaporation of a sessile droplet of water containing nonvolatile colloidal particles is not only a problem of fundamental interest to scientists but also has real life practical applications. The applications are as ancient as writing on papyrus paper using ink invented by Egyptians and Chinese around 4500 years ago. Modern day applications include inkjet printing, forensic analysis of patterns left behind by dried blood drops, manufacture of DNA microarrays, and enhancing agricultural produce by spraying micronutrient with nanofluids onto plant leaves. The canonical example of this phenomena is the “coffee stain” deposit formed by colloid-containing water droplets. This problem was first tackled from a physical chemistry viewpoint by Deegan et al. (1997).
Since this pioneering work, there has been an exponential growth in the number of literature on the topic. Several experiments exploring different aspects of this problem have been performed in the last decade or so. From a fluid mechanics perspective, evaporating drops with suspended particles is a rich problem. With some simplifying assumptions, the evaporation of a sessile liquid droplet and the colloidal deposition pattern can be described analytically. However, the problem can be made more complicated by incorporating various phenomena like heat conduction and convection, natural convection, viscous and inertial flows, or surface-tension-driven flows. It also includes thermal-hydrodynamic instabilities, buoyancy effects, liquid spreading, contact-line pinning and depinning, and adhesion. In order to fully explore the nonlinear effects of these phenomena, we needs to perform numerical simulations. Hence, the problem of evaporating drops has intrigued scientists from various disciplines, including experimentalists, theorists and numerical simulations experts.
In particular, the problem of evaporating drops on inclined and vertical planes is of great significance in many industrial settings. Inclining the plane allows gravitational forces to take a central role in the final deposit patterns. This problem has been solved numerically by Du and Deegan JFM (2015) and Timm et al. Sci Rep. (2019) recently in two- and three-dimensions, respectively. However, the natural choice for simulations, boundary element method (BEM), has not been employed to study this problem so far and transient drop dynamics remains unaddressed. Having reproduced previous results by a novel numerical method based on BEM, we will tackle the practical situation where a pair drops on an inclined plane are interacting with each other through the vapour field. Furthermore, building on the very successful paper of Dr.Wray on evaporation of multiple droplets, we will extend the theoretical results to include the effect of gravity.