Solutal Marangoni flow as the cause of ring stains from drying salty colloidal drops

Evaporating salty droplets are ubiquitous in nature, in our home and in the laboratory. Interestingly, the transport processes in such apparently simple systems differ strongly from evaporating “freshwater” droplets since convection is partly inverted due to Marangoni stresses. Such an effect has crucial consequences to the salt crystallization process and to the deposits left behind. In this work we show unprecedented measurements that, not only confirm clearly the flow inversion, but also elucidate their impact on the distribution of nonvolatile solutes. Contrary to what has been often reported in the literature, such a flow reversal does not prevent the formation of ring-shaped stains: particles accumulate at the contact line driven solely by the interfacial flow. We can therefore conclude that the classical “coffee-stain effect” is not the only mechanism that can generate ring-shaped stains in evaporating droplets.

Figure 1

(a) Sketch of a sessile droplet containing a nonsaturated aqueous saline solution and a dilute dispersion of polymer microparticles. The blue lines illustrate the direction of the flow within the droplet. Note that a large portion of the liquid (close to the substrate) flows in opposite direction as in the classical “coffee-stain effect.” (b) Particles reach the contact line along the liquid-gas interface, forming a ring-shaped stain. Here the contact line is defined as $r/R=1$, where $R$ is the droplet radius and $r$ the radial distance from the center. (c) The inverted vortical flow profile is shown through the computed streamlines, which is also measured experimentally via particle tracking velocimetry [see Fig. 3].

Figure 2

(a) Images close to the contact line (black line) depicting the particle accumulation in the final stage of drop evaporation for increasing NaCl concentrations. The droplet radius $R$ for all experiments is 1 mm and the total evaporation time about 1000 s. All images are taken using a confocal microscope in a $z$ position close to the glass slide. Filled red circles are fluorescent particles accumulated at the bottom substrate; dimmer ones are located in higher layers. (b) Number of particles near the contact line per unit of wet area against the time for different solute concentration. The dashed lines show the binned data. Circles depict the instants in which images from Fig. 2 were taken. Inset: Final values of normalized particle increment in terms of NaCl concentration. Black continuous line corresponds to the stain growth $N\propto t^{1.33}$, reported by Deegan et al. [2] for comparison.

Figure 3

(a) Experimentally obtained flow profile in an evaporating droplet obtained by a 3D particle tracking (APTV [18, 19]). (b) Velocity profile and (c) flow streamlines in an evaporating droplet with an initial NaCl concentration of 100 mM obtained by solving the Stokes flow inside the droplet in the lubrication approximation. The instant shown corresponds to 50% of the total evaporation time. The experimental conditions are identical as those in the simulations shown in (b) and (c). Note that in both simulations and experiments the interfacial flow toward the contact line dominates the flow in the droplet.

Figure 4

Results from the numerical simulations on the evaporating salty droplets. The plots correspond to different stages in the evaporation of a droplet containing NaCl at a concentration of 100 mM, initial contact angle of ${20}^{\circ }$, and radius of 1 mm. The different lines correspond to 0, 20, 40, 60, and 80% of the total evaporation time: (a) droplet interface h(r) in time, (b) salt concentration $c$ in mol/l (c), and normalized evaporative flux $j/j_{\text{max}}$, which becomes singular as the contact line is approached ($r/R\to 1$) [2].