Drop impact of shear thickening liquids

The impact of drops of concentrated non-Brownian suspensions (cornstarch and polystyrene spheres) onto a solid surface is investigated experimentally. The spreading dynamics and maximal deformation of the droplet of such shear thickening liquids are found to be markedly different from the impact of Newtonian drops. A particularly striking observation is that the maximal deformation is independent of the drop velocity and that the deformation suddenly stops during the impact phase. Both observations are due to the shear thickening rheology of the suspensions, as is explained theoretically from a balance between the kinetic energy and the viscously dissipated energy, from which we establish a scaling relation between the maximal deformation of the drop and rheological parameters of concentrated suspensions.

Figure 1

(a) Image sequence of a drop of cornstarch suspension impacting a glass plate ($D_0=2.80$ mm, $U_0=1.04$ m/s, and ${\varphi }_0=35\%$). Part of the images consists of reflection of the drops on the glass surface. (b) Dimensionless drop height $h/D_0$ as a function of dimensionless time $U_{0}t/D$. The experiment can be divided into a kinematic stage (dashed black line) and the frozen stage (red dashed line) defining the plateau value ${\epsilon }_m$, which is shown in the inset as a function of the dimensionless crossover time $\tau$, also defined in the main plot. (c) Snapshots of frozen drops of cornstarch ($D_0=2.80$ mm and ${\varphi }_0=35\%$) and PS particle ($D_0=2.23$ mm and ${\varphi }_0=55\%$) suspensions, for different impact velocities. At later times, the drops will slowly spread and recover an axisymmetric shape. See Ref. [26].

Figure 2

Dimensionless height ${\varepsilon }_m$ as a function of drop diameter $D_0$ (logarithmic scale), for different cornstarch volume fractions 33% (red triangles), 35% (blue squares), and 38% (black circles) and for a 55% PS particle suspension (green circles).

Figure 3

Flow curves of cornstarch suspensions of different volume fractions: 33% (red squares), 35% (blue squares), and 38% (black squares). Dashed (solid) lines are the Newtonian (shear thickening) regimes.

Figure 4

Rescaled minimal height ${\varepsilon }_m{D}_0^{2/3}{[\rho /\kappa \left(\varphi \right)]}^{1/3}$ as a function of impact velocity $U_0$ for different cornstarch volume fractions: 33% (red triangles), 35% (blue squares), and 38% (black circles). The inset shows the rescaled minimal height ${\varepsilon }_m{D}_0^{2/3}$, with added data for PS droplets (green circles).

Figure 5

Prefactor $\kappa \left(\varphi \right)$ from the rheological law $\sigma =\kappa {\dot{\gamma }}^2$, estimated from the experimental data published by Fall et al. [24]. Our impact experiments were performed at $\varphi =55\%$; the corresponding value estimated from the impact experiment is reported as the open square.