Dynamic Stratification in Drying Films of Colloidal Mixtures

In simulations and experiments, we study the drying of films containing mixtures of large and small colloidal particles in water. During drying, the mixture stratifies into a layer of the larger particles at the bottom with a layer of the smaller particles on top. We developed a model to show that a gradient in osmotic pressure, which develops dynamically during drying, is responsible for the segregation mechanism behind stratification.

Figure 1

Sketch of a wet film containing a colloidal mixture of large particles with diameter $d_l$, and small particles with diameter $d_s$. The film is bounded at the bottom by a substrate and at the top by the air-water interface that falls with a velocity of $v_{\mathrm{ev}}$.

Figure 2

(a)–(f) Simulation snapshots of the top third of the simulation box, taken at the end of the run. The small particles are shown in yellow (light gray), the large particles in blue (dark gray), with size ratio $d_l/d_s$ of 7:1. In each case the system started at a total volume fraction ${\eta }_0=0.1$ and height $H=1500d_s$ and was run until a final height of $H_{\text{fin}}=303d_s$. The snapshots in (a),(b), and (c) are for systems with increasing amounts of the small particles, the number ratios are $N_r=5$, 29, and 151, respectively. The snapshots in (d),(e), and (f) are the top views of the systems in (a),(b), and (c), respectively. Due to the strong attraction between the surface and the large particles, even in (c) and (f), where stratification is strongest, we see some large particles trapped at the surface. Their presence does not affect stratification. (g)–(i) Volume fraction profiles of the small [yellow (light gray)] and large [blue (dark gray)] particles, for $N_r=5$, 29, and 151, respectively. The bin width used in the profiles is $0.25d_s$.

Figure 3

Experimental results for dried films formed of a binary mixture of colloidal particles of size ratio 7:1. (a)–(c) Height AFM images for films with number ratios $N_r=10$, 200, and 500, respectively. (d)–(f) Three-dimensional confocal images of the films for $N_r=10$, 200, and 500, respectively. The large particles are labeled with a red dye, while the small particles are unlabeled so the intensity of red indicates the concentration of the larger particles. To mark the position of the top surface, a drop of large (750 nm) green fluorescent particles was cast on the dry film. (g) Intensity of the red channel (large particles) as a distance from the top surface located at $z/H_{\text{fin}}=0$, for $N_r=10$ (blue circles), $N_r=200$ (green squares), and $N_r=500$ (red triangles). A correction was made for the depth dependence of the detected fluorescence intensity [15].

Figure 4

Density and pressure gradient profiles in the drying film at time $\mathrm{t}=4350{\tau }_B$ for ternary mixtures. The top surface is at $z/d_m=0$. The yellow (light gray) curves represent the majority species, the blue (dark gray) curves represent the larger species, $d_b/d_m=1.2$, and the black curves represent the smaller species, $d_s/d_m=0.8$. (a) Densities of particles as a function of the distance from the interface, plotted as $N^i(z)/N_0^i$, where $N^i(z)$ is the density of species $i=m$, $s$, $b$, and $N_0^i$ is the initial number density. (b) Vertical gradients of the osmotic pressure as a function of the distance from the top interface. The majority species makes the greatest pressure contribution. The vertical dotted lines indicate the position of the top interface.