Effects of Particle Shape on Growth Dynamics at Edges of Evaporating Drops of Colloidal Suspensions

We study the influence of particle shape on growth processes at the edges of evaporating drops. Aqueous suspensions of colloidal particles evaporate on glass slides, and convective flows during evaporation carry particles from drop center to drop edge, where they accumulate. The resulting particle deposits grow inhomogeneously from the edge in two dimensions, and the deposition front, or growth line, varies spatiotemporally. Measurements of the fluctuations of the deposition front during evaporation enable us to identify distinct growth processes that depend strongly on particle shape. Sphere deposition exhibits a classic Poisson-like growth process; deposition of slightly anisotropic particles, however, belongs to the Kardar-Parisi-Zhang universality class, and deposition of highly anisotropic ellipsoids appears to belong to a third universality class, characterized by Kardar-Parisi-Zhang fluctuations in the presence of quenched disorder.

Figure 1

(a) Illustration depicting deposition mechanism. Radially outward flows carry particles from drop center to drop edge, where they are deposited on the air-water interface. (b)–(d) Binarized experimental images of deposits of spheres ($\epsilon =1.0$) (b), slightly stretched particles ($\epsilon =1.2$) (c), and ellipsoids ($\epsilon =2.5$) (d), along with images of single particles. A label in (b) demonstrates our definition of height ($h$), i.e., distance from drop edge. The drop edges and the direction of the coffee-ring driving flow are indicated. The probed window size $L$ is defined for $L=100\mu \mathrm{m}$ (b) and $L=25\mu \mathrm{m}$ (d). These scale bars also hold for (c). (e)–(g) The deposit height profile (growth line) $h$ plotted as a function lateral position $x$ at three different times, for $\epsilon =1.0$, 1.2, and 2.5 [(e)–(g), respectively].

Figure 2

Deposit width ($w$), i.e., standard deviation of deposit height ($h$), plotted versus $\overline{h}$ for spheres ($\epsilon =1.0$, squares), slightly anisotropic particles ($\epsilon =1.2$, circles), and ellipsoids ($\epsilon =2.5$, 3.5, triangles). Different colored dots indicate data derived from different experiments. The data collapse onto three trend lines based on $\epsilon$.

Figure 3

(a) Width $w$ plotted versus probed length scale $L$ for a drop containing slightly anisotropic particles $\epsilon =1.2$ with height $\overline{h}=13\mu \mathrm{m}$. The dashed line represents the best power-law fit for $L<15\mu \mathrm{m}$. The observed power-law scaling is consistent with the KPZ universality class. (b) Skewness (${\gamma }_1$) and kurtosis (${\gamma }_2$) of the $h$ distribution for particles with $\epsilon =1.2$ are plotted versus $h$. Solid lines represent values of ${\gamma }_1$ and ${\gamma }_2$ for Gaussian unitary ensemble matrices. Thus, the skewness and kurtosis imply that the height distribution is consistent with the KPZ universality class.

Figure 4

(a) Skewness ${\gamma }_1$ multiplied by width $w$ plotted versus $\overline{h}$ for $\epsilon =1.0$, 1.2, 3.5 (solid, dashed, and dotted lines, respectively). The line with dashes and dots is ${\gamma }_{1}w=1$, the prediction for a Poisson process; i.e., the skewness grows linearly with width. Error bars represent standard deviation. (b) $w$ plotted versus probed length scale $L$ for a drop containing ellipsoids $\alpha =2.5$ with height $h=17\mu \mathrm{m}$. (c) Example of the colloidal “Matthew effect.” The trajectory of an ellipsoid ($\epsilon =2.5$) during deposition is shown (red line). Initially, it flows towards a region that contains very few ellipsoids. However, when it adsorbs on the air-water interface, it is attracted to a particle-rich region and deposited there. (d) Dynamic scaling exponent $\beta$ plotted versus particle aspect ratio $\epsilon$. Three distinct regimes are identified (indicated by shading). Predictions for random deposition ($\beta =0.5$), KPZ processes ($\beta =1/3$), and KPZQ processes ($\beta =0.68$) are indicated by solid horizontal lines.