Particle monolayer assembly in evaporating salty colloidal droplets

Ring-shaped deposits can be often found after a droplet evaporates on a substrate. If the fluid in the droplet is a pure liquid and its contact line remains pinned during the process, then the mechanism behind such ring-shaped deposition is the well-known coffee-stain effect. However, adding small amounts of salt to such a droplet can change the internal flow dramatically and consequently change the deposition mechanism. Due to an increase of surface tension in the contact line region, a Marangoni flow arises which is directed from the apex of the droplet toward the contact line. As a result, particles arrive at the contact line following the liquid-air interface of the droplet. Interestingly, the deposit is also ring shaped, as in the classical coffee-stain effect, but with a radically different morphology: Particles form a monolayer along the liquid-air interface of the droplet, instead of a compact three-dimensional deposit. Using confocal microscopy, we study particle-per-particle how the assembly of the colloidal monolayer occurs during the evaporation of droplets for different initial concentration of sodium chloride and initial particle dilution. Our results are compared with classical diffusion-limited deposition models and open up an interesting scenario of deposits via interfacial particle assembly, which can easily yield homogeneous depositions by manipulating the initial salt and particle concentration in the droplet.

Figure 1

Laser scanning confocal microscopy is employed to obtain three-dimensional information on the particle assembly. Panel (a) shows sketches of the top-view (glass-slide plane) and side-view projection of the scanned volume within the droplet, indicating length scales and axis definitions. The $s$ axis is defined along the droplet's interface. The boxes in (a) and (c) show the approximate location of the scanned volume respect to the droplet (not in scale). Panels (b) and (c) show projections of the scanned volume in the $(x,y)$ plane and the $(y,z)$ plane, respectively. Panel (d) shows an orthogonal projection of the full scanned volume as obtained from the fluorescent channel for $C_0=10\mathrm{mM}$ and $t/t_{\mathrm{evap}}=0.8$. The dimensions of the scanned volume are included.

Figure 2

Overview of the typical analysis results. Panel (a) shows the contact angle $\theta$ of the droplet as a function of time. A linear fit through these data is used to access the final evaporation time $t_F$, defined at $\theta =0^{\circ }$. Panel (b) shows an overview of the analysis results for the same confocal scan as shown in Fig. 1 ($C_0=10\mathrm{mM}$ NaCl and $\tilde{t}=0.8$). The found particle positions are shown as as black dots. These particles are plotted along $s$, which is the axis along the droplet's interface, for which the droplet contact angle $\theta$ is used. The contour of the droplet is given as the outer light blue line, and the typical detected Voronoi cells are presented. The definition of the height of the contour $h(x,t)$ is given as well.

Figure 3

Typical results of a Voronoi cell analysis performed in the particle monolayer for different salt concentrations: (a) 5 mM, (b) 10 mM, and (c) 50 mM. The colorbar represents the area of the cell $A_{\mathrm{cell}}$ in ${\mu \mathrm{m}}^2$.

Figure 4

The normalized average size of the Voronoi cell as a function of the distance from the contact line is shown for three different salt concentrations: (a) 5 mM, (b) 10 mM, and (c) 50 mM. For each concentration, the average cell size of five experiments is used, the shaded area displays the standard deviation. All structures are analyzed at $\tilde{t}=0.8$. The cell size is normalized with the area of a hexagonal cell, which is calculated using the particle diameter.

Figure 5

Contour height $h(x,t)$ of particle monolayers along the droplet surface as a function of dimensionless time $\tilde{t}$ for three different initial salt concentrations. Panel (a) shows 5 mM, (b) 10 mM, and both (c) and (d) show examples of 50 mM, as large heterogenities are observed for different positions along the droplet's contact line. For each experiment contours are shown for $\tilde{t}=0.35$, 0.5, 0.65, and 0.8.

Figure 6

The roughness of the monolayer contours $w$ as a function of the mean height $\overline{h}$. Panel (a) shows 5 mM, (b) 10 mM, and (c) 50 mM. Different markers indicate different experiments, the black dots represent the logarithmically binned data. In order to test if the data follows Family-Vicsek dynamic scalings [25] $w\sim {\overline{h}}^n$, we performed weighted linear regression fits of the binned data. The exponents $n$ found are (a) $n=0.41\pm 0.03$, in (b) $n=0.47\pm 0.05$, and in (c) $n=0.37\pm 0.04$.

Figure 7

The number of particles $N$ attaching to the monolayer as a function of dimensionless time $\tilde{t}$. Different markers indicate different experiments. Panel (a) shows the results for 5 mM, (c) 10 mM, and (d) 50 mM. This number $N$ is the total number of particles which arrive in one measurement section ($25\mu \mathrm{m}$ wide). The dashed gray line in these figures represents the classical coffee-stain flow where $N\sim {\tilde{t}}^{4/3}$ [1], using an arbitrary prefactor. The dotted light gray line in all figures shows the computed total number of particles which are captured by the droplet's surface $N_s\left(t\right)$ as a function of time. The results of the numerical solution for $N$ (using a constant surface velocity $u_s=1\mu \mathrm{m}$/s) are given with a solid black line. Panel (b) shows the same curves and experimental data as panel (a) in a linear representation and using real dimensional units.

Figure 8

(a) Final stains for different salt concentrations after the liquid phase has completely evaporated. The particle concentration is fixed at $0.1\%\mathrm{w}/\mathrm{v}$ and only the initial salt concentration $C_0$ increases from 0 to 50 mM. (b) Final stains for different particle concentrations after the liquid phase has completely evaporated. The initial salt concentration $C_0$ is fixed at 50 mM and the particle concentration changes from 0.01 to $0.1\%\mathrm{w}$, defined as the particle mass $m_p$ divided by the initial droplet mass $M_0$.

Figure 9

(a) The typical evolution of the mean height of the monolayer $\overline{h}$ for 4 different experiments with 3 different salt concentrations. Two curves are included for the 50 mM case to highlight the variability found for this salt concentration along the contact line. The dashed black line shows $\overline{h}\sim {\tilde{t}}^{2.5}$. [(b), (c), and (d)] The number of particles $N$ arriving at the contact line for 5, 10, and 50 mM respectively. In all three figures the solid black curve represents the outcome of the model constructed to account for the incoming particles to the monolayer as presented in the main manuscript. The dashed black line shows $N\sim {\tilde{t}}^{2.5}$, since it is expected from simulating deposition models that $\overline{h}$ and $N$ scale in the same way with time.

Figure 10

The interface roughness $w$ as a function of the mean height $\overline{h}$, obtained from 100 numerical simulations of the classical deposition models: (a) random or Poissonian deposition and (b) ballistic deposition. Both are 1D systems with size $L=5000$. The vertical shaded area represents the region of $\overline{h}$ captured experimentally. In (a) simulations are performed for a constant particle rate ($N=t$, to validate the algorithm) and for increasing particle influx as in the experiments ($N=0.1\times t^{2.5}$). (b) The ballistic deposition model shows larger variability in the larger values of $\overline{h}$ which is represented by the shaded region around the main curve showing the standard deviation of the 100 simulations. Interestingly, despite the variable particle rate ($N=0.1\times t^{2.5}$), the roughness follows the same scaling found by Family and Vicsek [37].

Figure 11

Alternative fitting procedure for the roughness of the monolayer contours $w$ as a function of the mean height $\overline{h}$: (a) 5 mM, (b) 10 mM, and (c) 50 mM. Different markers indicate different experiments. Curves for the best fit of $w\sim {\overline{h}}^n$ are obtain directly over the raw data (no binning) for each salt concentration: $n\left(5\mathrm{mM}\right)=0.40\pm 0.03$, $n\left(10\mathrm{mM}\right)=0.46\pm 0.05$, and $n\left(50\mathrm{mM}\right)=0.41\pm 0.04$.

Figure 12

A schematic representation is given to show how the change in local volume is implemented into the numerical code. In this schematic the number of grid points is 20. The two spherical caps represent $t=$ 0 s (blue) and $t$ is 100 s (orange), with respectively $\theta ={70}^{\circ }$ and ${65}^{\circ }$. The grid points at $t=100$ are equally spaced along the arc, and the corresponding points at the spherical cap of $t=0$ are shown.