Dense Suspension Splat: Monolayer Spreading and Hole Formation after Impact

We use experiments and minimal numerical models to investigate the rapidly expanding monolayer formed by the impact of a dense suspension drop against a smooth solid surface. The expansion creates a lacelike pattern of particle clusters separated by particle-free regions. Both the expansion and the development of the spatial inhomogeneity are dominated by particle inertia and, therefore, are robust and insensitive to details of the surface wetting, capillarity, and viscous drag.

Figure 1

Dense suspension impact, splat, and instability. (a) Side view: A cylindrical plug impacts a smooth dry glass surface, splashes by ejecting particles upwards, and flattens into a monolayer. (b) Bottom view: The initial, nearly circular splat expands. Inhomogeneities appear as regions of particle clusters separated by particle-free regions (dark). (c) Close-up: Clusters drag streaks of liquid along as they move outwards, visible by the contrast in liquid color [10]. (d) Substrate area coverage as a function of time. Once the covered area approaches a constant value (shaded region), particles are spread out in a monolayer.

Figure 2

Splat expansion dynamics. (a) Expansion radius, defined as the difference between the splat’s outer edge $R(t)$ and the initial monolayer radius $R_0$. All data are for ${\mathrm{ZrO}}_2$ particles in water (filled triangle) and two silicone oils with viscosities 1.8 (filled circle) and 10 cSt (open square). Predictions from the leading-edge model (solid lines) and the chain model (dashed line) are shown. (b) Radial velocity profiles of the ${\mathrm{ZrO}}_2$-in-silicon-oil splat at the moment of formation $t=0$ and two instances afterwards. The dot-dashed line marks the velocity $U_r^{*}$, where ${\rho }_p{(U_r^{*})}^{2}d/\gamma =1$.

Figure 3

In the leading-edge model for splat expansion, the splat edge, initially ejected with horizontal speed $\dot{R}(t=0)$, slows over time due to resistance by surface tension $F_{\gamma }$ and drag force $F_{\mu }$ from a trailing liquid film. In the chain model for splat instability, particle-free regions emerge from variations in the initial radial velocity field. Beyond a critical separation $s_c$ between adjacent particles, bridgelike menisci transform into trailing liquid streaks, and the force switches from a bridging force $F_b$ to a trailing streak resistance $F_{\gamma }$ acting solely on the faster-moving particle in front.

Figure 4

Instability dynamics. (a) Average number of capillary-bridge bonds per particle, ${\overline{N}}_b$, as a function of $r/R(t)$, the radial distance normalized by current splat radius, for different values of radial strain $\epsilon$. Inset: Two-dimensional generalization of $F_b$ and $F_{\gamma }$. A cohesive capillary-bridge bond between neighboring particles becomes a trailing streak if the neighboring particle lies outside a wedge of opening angle $2\delta$ and radius $(d/2)+s_c$ (shaded region). (b) Area fraction of particle-free regions in circular annuli within the splat as a function of time. The boundary between the inner and outer annuli is chosen to lie at $\rho U_b^{2}d/\gamma =150$, where $U_b$ is the initial speed of the particle at the boundary. Experiments (filled circle, filled triangle), the one-dimensional chain model (solid and dashed lines), and the two-dimensional numerical model (open circle, open triangle) agree quantitatively. Inset: Snapshots from the simulation.