Interfacial flows in sessile evaporating droplets of mineral water

Liquid flow in sessile evaporating droplets of ultrapure water typically results from two main contributions: a capillary flow pushing the liquid toward the contact line from the bulk and a thermal Marangoni flow pulling the drop free surface toward the summit. Current analytical and numerical models are in good qualitative agreement with experimental observations; however, they overestimate the interfacial velocity values by two to three orders of magnitude. This discrepancy is generally ascribed to contamination of the water samples with nonsoluble surfactants; however, an experimental confirmation of this assumption has not yet been provided. In this work, we show that a small “ionic contamination” can cause a significant effect in the flow pattern inside the droplet. To provide the proof, we compare the flow in evaporating droplets of ultrapure water with commercially available bottled water of different mineralization levels. Mineral waters are bottled at natural springs, are microbiologically pure, and contain only traces of minerals (as well as traces of other possible contaminants), and therefore one would expect a slower interfacial flow as the amount of “contaminants” increase. Surprisingly, our results show that the magnitude of the interfacial flow is practically the same for mineral waters with low content of minerals as that of ultrapure water. However, for waters with larger content of minerals, the interfacial flow tends to slow down due to the presence of ionic concentration gradients. Our results show a much more complex scenario than it has been typically suspected and therefore a deeper and more comprehensive analysis of the huge differences between numerical models and experiments is necessary.

Figure 1

Schematic of the experimental setup. The water droplet is deposited on a glass coverslip under constant temperature and humidity. A side-view camera is used to measure the droplet shape. An epifluorescent microscope in combination with a cylindrical lens is used to image the tracer particles inside the droplets for the 3D-PTV method.

Figure 2

Evolution in time of droplets volume for all the experiments in real (a) and normalized (b) units. Time is set to 0 when the contact angle is ${45}^{\circ }$. The difference in evaporation rate is given by the different radius of droplets.

Figure 3

Internal flows for different contact angles. The colormap represent the radial velocity: positive velocity are directed outward toward the contact line. For UPW, two contribution are present: a bulk flow toward the contact line and a interfacial flow toward the drop summit. For mineral water, a third contribution due to concentration gradient pushing the fluid in the bottom toward the drop center start to build up as the mineral content is increased (i.e., moving from ViO to Gerolsteiner).

Figure 4

Interfacial flow velocity ($v_s$) as a function of the radial position and the contact angle. Negative velocities indicate flow directed toward the droplet center.

Figure 5

Final stain obtained after evaporation of the droplet for the four different types of water. The stain is formed by 1-$\mu \mathrm{m}$-diameter spheres dispersed in the water. In all cases the typical ring-shaped stain at the contact line can be observed. Going toward the center there is a region without particles corresponding to the portion of surface where the inward interfacial flow is stronger. Before reaching the droplet's summit, the interfacial flow weakens, a stagnation region appears (see Fig. 4), where particles tend to accumulate, specially in the case of ViO and Vittel.

Figure 6

(a) Vector plots of the PTV measurements of six individual experiments, reported in cylindrical normalized coordinates and corresponding to a contact angle of ${38}^{\circ }$. (b) Average velocity components inside the area indicated by the black box in the vector plots, as a function of the contact angle. (c) Final values of the velocity components in the central point of the box after combining the six measurements. The red line indicate a time-averaged value used to estimate the random error.

Figure 7

Evolution in time of droplets volume for droplets with and without LED illumination (no particles) and with two type of particles (1-$\mu \mathrm{m}$-diameter particles from Thermofisher and 2-$\mu \mathrm{m}$-diameter particles from Microparticles GmbH). (a) Plot in in real units and (b) plot in normalized units. Time is set to 0 when the contact angle is ${45}^{\circ }$.

Figure 8

Stain patterns obtained from different drying experiments carried out at the same conditions. The first and second rows correspond to experiments performed with the water Vio and Gerolsteiner, respectively. The dashed line in the first row indicates the center of the stagnation region with low velocities, which coincides with a particle accumulation region.

Figure 9

Comparison of flow velocities measured with 1-$\mu \mathrm{m}$-diameter particles and 2-$\mu \mathrm{m}$-diameter particles. (a) Internal flows in cylindrical coordinates for different contact angles. (b) Interfacial flow velocity as a function of the radial position and the contact angle.