Evaporation and Deposition of Colloidal Binary Droplets

Droplet evaporation is a versatile process to deposit solute materials on a substrate unless it induces solute accumulation at droplet perimeter because of outward capillary flows. Despite many efforts to generate inward Marangoni flows to suppress outward capillary flows, it is challenging to control Marangoni flows in colloidal droplets that include binary solvents. To understand and manipulate Marangoni flows in colloidal binary droplets, we investigate droplet evaporation and deposition dynamics by changing the mass ratio of binary solvents. We show that island deposits emerge when Marangoni flows overwhelm capillary flows during most evaporation. The formation of island deposits in colloidal binary droplets would be a helpful route to achieve uniform deposits of colloidal particles or nanoparticles.

Figure 1

Deposition of the island (core) and coffee ring (edge) from colloidal binary droplets. (a) Top-view image of the final deposits of the PS colloidal particles with the diameter $d=1.0\mu \mathrm{m}$ and the concentration $\varphi =2.0$ wt% dispersed into the binary droplets of water and 2ME with the mass fraction of water ($x_w=1/2$). The initial droplet volume is $v_0=0.7\mu \mathrm{l}$. (b) Measurement of the mass changes of the water droplet and the binary ($x_w=1/2$) droplet including the PS colloidal particles with $v_0=2.5\mu \mathrm{l}$ at $H_r=60\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$. The bold lines taken from the simulations (Supplemental Material [47]) show good agreements with the experimental data (the thin lines).

Figure 2

Evaporation dynamics of colloidal binary droplets. (a) The time sequential top-view images of the evaporating colloidal binary droplets ($v_0=0.7\mu \mathrm{l}$, $d=1\mu \mathrm{m}$, $\varphi =2.5$ wt%, and $x_w=1/3$) with time ($t$) normalized by the complete evaporation time ($t_f$) at $H_r=20\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$ (see Movie S1 within the Supplemental Material [47]). (b) The corresponding illustration of (a) shows the Marangoni flows (moving toward the center) along with the air-liquid interface associated with the island growth and the phase segregation, where two solvents are separate near the edge, preventing the island formation.

Figure 3

Phase diagram for colloidal binary droplets. The time-sequential top-view images of the colloidal binary droplets ($v_0=0.7\mu \mathrm{l}$, $d=1\mu \mathrm{m}$, and $\varphi =2.5$ wt%) with respect to the water-to-2ME mass ratio and the normalized time ($t/t_f$) at $H_r=20\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$. Here, the island deposits appear at lower water mass fractions than a half ($x_w=1/2,1/3,1/5,1/6$), as marked by the arrows (the yellow lines are the boundaries of the edge and the center deposits).

Figure 4

Evaporation dynamics of colloidal binary droplets with respect to the water mass fraction ($x_w$) of the whole binary solvent ($v_0=0.7\mu \mathrm{l}$, $d=1\mu \mathrm{m}$, and $\varphi =2.5$ wt% at $H_r=20\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$). (a) The mass changes with time for the binary droplets from the initial mass of 0.7 mg, taken by Raoult’s law simulation (Supplemental Material [47]). (b) The evaporation times $t_f$, taken from the experimental data (black squares) and the simulation data [green line, from (a)]. (c) The coefficient product, $D_b{c}_{v,b}$, in the diffusion-limited evaporation equation for the binary droplets, taken from the experimental data (black squares) and the simulation data [green line, from (a)]. (d) The droplet geometry (contact radius and contact angle) by the water mass fraction.

Figure 5

Island formation under the predominance of the Marangoni flows ($v_0=0.7\mu \mathrm{l}$, $d=1\mu \mathrm{m}$, and $\varphi =2.5$ wt% at $H_r=20\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$). (a) The flow constraints, the geometric term ($q_g$) and the material property term ($q_m$), as a function of the water-to-2ME mass fraction ($x_w$) at $t/t_f=0$. (b) The flow ratio $Q_{\mathrm{Ma}}/Q_{\mathrm{Ca}}$ as a function of time ($t/t_f$). (c) The Marangoni force component $Q_{\mathrm{Ma}}\times \eta$ derived from Eq. (6) as a function of time ($t/t_f)$. (d) The segregation time $t_s$ normalized by the complete time ($t_f$) as a function of $x_w$ (the inset image taken from Fig. 2 shows the phase segregation for $x_w=1/3$ at $t/t_f=0.8$).

Figure 6

Particle size and initial concentration effects (for $v_0=0.7\mu \mathrm{l}$ at $H_r=20\mathrm{\%}$ and $T=25{}^{\circ }\mathrm{C}$). The scanning electron microscope images for (a) 1-$\mu \mathrm{m}$-diameter 2.5 wt% PS colloids and (b) 10-$\mu \mathrm{m}$-diameter 2.5 wt% PS colloids in 0.7-$\mu \mathrm{l}$-volume droplets, showing the occurrence of crystallization in smaller colloids. The digital microscope top-view image of (c) shows the uniform coating at the higher initial concentration (e.g., 40 wt%) for 1-$\mu \mathrm{m}$-diameter PS colloids in 0.7-$\mu \mathrm{l}$-volume droplets.

Figure 7

Secondary solvent effects. (a) The inward Marangoni flow induces the island formation by $Q_{\mathrm{Ma}}/Q_{\mathrm{Ca}}>0$ for the water-2ME system, while (b) the outward Marangoni flow induces the dispersed deposition by $Q_{\mathrm{Ma}}/Q_{\mathrm{Ca}}<0$ from the water-ethanol system.