Figure 1

Typical results providing evidence for the reverse motion of particles. Sequential optical micrographs [18] were superimposed to reveal the motion of microspheres. We observe an inward migration of $20\text{−}\mu \text{m}$-diameter polystyrene microspheres suspended in a drying water droplet on a solid substrate (Petri dish). This reverse motion phase was preceded by the formation of ringlike stains at the perimeter by the normal coffee-ring effect.Reuse & Permissions

Figure 2

(Color online) Real-time optical and x-ray micrographs. (a) Top-view optical micrographs show the normal and reverse motions of 2- and $20\text{−}\mu \text{m}$-diameter particles in an evaporating water droplet of 1.5 mm diameter. (b) Side-view x-ray micrographs show the gradual reduction in the contact angle with the evaporation time for a water droplet suspension under the same conditions as (a). The reverse motion distance $L$ from the edge increases with time, depending on the particle size and the contact angle.Reuse & Permissions

Figure 3

(Color online) Capillary force leading to reverse motion. (a) High-resolution x-ray micrographs in the vicinity of the droplet edge. No protrusion of particles indicates the presence of capillary force during evaporation. (b) A schematic view of the capillary force explaining the reverse motion. (c) Geometric model of the reverse motion. A relation $\text{tan}\left(\theta /2\right)=r/L$ links the particle radius $r$, the reverse moving distance $L$, and the contact angle $\theta$. The increase in $L$ is caused by the net capillary force $F$ and is directly related to the contact angle evolution.Reuse & Permissions

Figure 4

(Color online) Correlation of the moving distance and the contact angle. The distance $L\left(t\right)$ (open squares) and the angle $\theta \left(t\right)$ (solid circles) were measured from the real-time optical [Fig. 2a] and x-ray [Fig. 2b] micrographs, respectively. The capillary force is predicted to lead to an inverse power-law increase in the moving distance $L\left(t\right)$ from the edge. The measured contact angle $\theta \left(t\right)$ that decreases with time $\left(t\to t_0\right)$ follows a power-law dependence as $\theta \left(t\right)\approx {\theta }_0{\left(t_0-t\right)}^{\beta }$ (dotted line). The measured moving distance in fact follows the inverse power law $L\left(t\right)\approx L_0{\left(t_0-t\right)}^{-\alpha }\approx \left(2r/{\theta }_0\right){\left(t_0-t\right)}^{-\beta }$ (solid line). The inverse power law $L\left(t\right)$ applies even for different droplet sizes, as shown by the dashed lines in the left inset, reporting results for (from left to right) 1.5-, 2.0-, 2.5-, and 4.0-mm-diameter drops. The power law $L\left(t\right){\theta }_0\approx 2r{\left(t_0-t\right)}^{-1}$ is rescaled for different drop sizes with different ${\theta }_0$ values in the right inset.Reuse & Permissions

Figure 5

(Color online) Confocal micrographs of multiple-ring formation. Multiple rings were formed from a mixture of 3.6- and $0.2\text{−}\mu \text{m}$-diameter fluorescently labeled PMMA particles in decalin on a clean cover glass. Sequential confocal images [18] taken for an evaporating droplet of the suspension show that the reverse motion (marked by the arrow and revealed by the bright ring of large particles) sweeps the particles toward the center and stops by rupture. The repeated events result in the multiple-ring formation.Reuse & Permissions