The drying of liquid droplets

The drying of liquid droplets is a daily life phenomenon, yet is actually a complicated scientific problem, which has long held a special interest in scientific research. Droplets made of Propylene glycol (PG) and water placed on glass show complex motions; various deposition patterns have been found in the drying of liquid droplets that contain nonvolatile solute. How to control the final deposition patterns and the direction of the droplet motion is an important technique in various industry manufacturing processes, and also is an interesting multi-disciplinary problem in physics, chemistry, materials and so on. The study of this problem has wide applications in the fabrication of micro-fluid devices, self-cleaning, inject printing, and heat conduction, etc. Although tremendous experimental studies have been reported, the theoretical studies are very few resulting in the fact that the understanding of this problem is still at a preliminary stage.

We proposed a theoretical model for the drying of liquid droplets, which is based on the Onsager variational principle. We gave mechanisms behind the formation of various deposition patterns and for controlling the direction of the droplet motion. The advantage of this model is that we obtained a first order evolution equation that is much simpler to be solved than the convention Navier-Stokes equation. Our work about the drying of liquid droplets has been published in Phys. Rev. Lett.

Results show that the droplet moves from high evaporation side to low evaporation side, and from high surface tension side to low surface tension side. When droplets subject to asymmetrical surface tension and evaporation rate, evaporating droplets show attraction-repulsion-chasing behaviors. When two droplets are close to each other, the vapor density is higher in the middle region than the outside area, resulting in asymmetrical evaporation rate that actuates the droplet motion. The mechanism of droplet motion induced by an asymmetrical evaporation rate is new, and gives a new way of controlling the droplet motion.

We also investigated the deposition pattern of drying liquid droplets. We predicted that the deposition patterns can be controlled by the evaporation rate and the moving ability of the droplet contact line. For a single droplet, we showed a continuous transition of the deposition pattern from “coffee-ring” to “volcano-like” and to “mountain-like” patterns. When the contact line is pinned, the inner fluid flow induced by evaporation convects solutes to the contact line, forming the coffee-ring pattern. Oppositely, when the contact line moves freely, the inner fluid flow moves inward and convects solutes to the center of the droplet. When the contact line moving ability is in between pinned and freely moving, the solute deposits in a place between the original contact line and the center, forming the volcano-like pattern.

We further studied asymmetrical ring patterns of two neighboring drying droplets. We demonstrated that the gradient of evaporation rate along droplets is the main reason of forming asymmetrical deposition patterns for two neighboring droplets. Our model predicts that by controlling the evaporation rate combined with varying the contact line friction, fan-like and eclipse-like deposition patterns are obtained.




Fig 1. Evaporation effect droplet moving from high evaporation side to low evaporation side




Fig 2. The deposition pattern changes continuously from a coffee ring to volcano-like and to mountain-like depending on the mobility of the contact line and the evaporation rate.




Fig 3. The asymmetrical ring patterns of the drying of two neighboring droplets



Xingkun Man, associate professor, school of physics and nuclear engineering, Center of Soft Matter Physics and Its Applications, Beihang University, E-mail:

Masao Doi, professor, school of physics and nuclear engineering, Center of Soft Matter Physics and Its Applications, Beihang University, E-mail:



[1]Xingkun Man, Masao Doi, Vapor-Induced Motion of Liquid Droplets on an Inert Substrate, Phys. Rev. Lett. 119, 044502 (2017).

[2]Shiyuan Hu, Yuhan Wang, Xingkun Man*, Masao Doi, Deposition Patterns of Two Neighboring Droplets: Onsager Variational Principle Studies, Langmuir 33, 5965 (2017).

[3]Xingkun Man, Masao Doi, Ring to Mountain Transition in Deposition Pattern of Drying Droplets, Phys. Rev. Lett. 116, 066101 (2016).