Dewetting-mediated pattern formation inside the coffee ring

The rearrangement of particles in the final stage of droplet evaporation has been investigated by utilizing differential interference contrast microscopy and the formation mechanism of a network pattern inside a coffee ring has been revealed. A tailored substrate with a circular hydrophilic domain is prepared to obtain thin liquid film containing monolayer particles. Real-time bottom-view images show that the evolution of a dry patch could be divided into three stages: rupture initiation, dry patch expansion, and drying of the residual liquid. A growing number of dry patches will repeat these stages to form the network patterns inside the ringlike stain. It can be shown that the suction effect promotes the rupture of the liquid film and the formation of the dry patch. The particle-assembling process is totally controlled by the liquid film dewetting and dominated by the surface tension of the liquid film, which eventually determine the ultimate deposition patterns.

Figure 1

(a) The tailored substrate is comprised of a circular hydrophilic domain surrounded by superhydrophobic coating. The white part is the hydrophobic domain while the black part is the hydrophilic domain. (b) The inset shows SEM image of the cross section of the substrate. (c) A large droplet could be confined in the hydrophilic domain of the substrate. (d) As with evaporation of the colloidal droplet, the self-assembly process of particles is controlled by three kinds of dynamic behavior: Marangoni flow, outward capillary flow, and capillary forces. (e) The network pattern formed inside the ringlike stain, the dry patch in the red rectangle, is a typical case that will be thoroughly analyzed.

Figure 2

Sequence of optical micrographs showing the onset and evolution of the rupture of the liquid film and aggregation of particles in the final stage of a drying droplet. (a) Rupture initiation at the particle-poor region of the substrate, (b) formation and expansion of the first dry patch, and (c)–(f) an increasing number of dry patches appear in the same way as the first one.

Figure 3

(a1)–(a8) Successive stages of the formation and evolution of a typical dry patch $\left(S_1\right)$ and particle-free region $\left(S_2\right)$. The dry patch is surrounded by the three-phase contact line (boundary of $S_1$), while the particle-free region is the area surrounded by particles (boundary of $S_2$). (a1) and (a2) In stage I the particle-free region expands due to the deformation of liquid film and film rupture initiates at the particle-poor region as shown in the red circle. (a3)–(a6) In stage II the dry patch forms and expands and particles aggregate by dewetting of the liquid film. (a7)–(a8) In stage III a close-packed structure forms and the residual liquid dries (see movie S4 in the Supplemental Material [33]). (b) Plot of the measured area of the dry patch $\left(S_1\right)$ and the particle-free region $\left(S_2\right)$ versus time. (c) Schematic presentation of the formation and evolution of a dry patch.

Figure 4

(a) Schematic of the liquid flow caused by the uneven distribution of particles. The pressure in the large pore is larger than that in the small pore, which induces liquid flow from the large pore to the small pore and eventually makes the film rupture in the large pore. (b) The minimum thickness of the liquid film changes with particle spacing under a certain pressure difference. The various values of the pressure difference are estimated from the Laplace equation base of experimental data.

Figure 5

Analysis diagram of the influence of the liquid film dewetting on the particles assembling. (a) Microscopic image of the particle aggregation process captured by an interference microscope. The frictional force $F_f$ increases to resist the surface tension force $F_s$ along the radial direction of the dry patch. (b) Image of the local structure of the dry patch in Fig. 3. The structure in the yellow rectangular is enlarged and presents a close-packed hexagonal array. The structure in the red rectangular is chosen to estimate the equivalent number of particles $\overline{n}$ in the experiment. (c) Lateral and normal capillary forces generated by the menisci formed around two particles. (d) Schematic of forces acting on particles adjacent to the dry patch.

Figure 6

(a) Calculated particle migration rate and dry patch expansion rate as a function of time. (b) Estimated surface tension force $F_s$ and the DRCA variance with time. The RCA of the hydrophilic domain of the tailored substrate is about ${22}^{\circ }$.