Memory-induced alignment of colloidal dumbbells

Abstract

When a colloidal probe is forced through a viscoelastic fluid which is characterized by a long stress-relaxation time, the fluid is excited out of equilibrium. This is leading to a number of interesting effects including a non-trivial recoil of the probe when the driving force is removed. Here, we experimentally and theoretically investigate the transient recoil dynamics of non-spherical particles, i.e., colloidal dumbbells. In addition to a translational recoil of the dumbbells, we also find a pronounced angular reorientation which results from the relaxation of the surrounding fluid. Our findings are in good agreement with a Langevin description based on the symmetries of a director (dumbbell) as well as a microscopic bath-rod model. Remarkably, we find an instability with amplified fluctuations when the dumbbell is oriented perpendicular to the direction of driving. Our results demonstrate the complex behavior of non-spherical objects within a relaxing environment which are of immediate interest for the motion of externally but also self-driven asymmetric objects in viscoelastic fluids.

Figure 1

(a) Schematic drawing of the experimental setup. An oscillating mirror mounted onto a piezo-driven post is deflecting a laser beam through an objective into the sample cell where it creates an extended optical trap. (b) Snapshots of a dumbbell at the start $t=0$ and the end of a recoil experiment ($t\sim 20\text{s}$). The initial angle of the dumbbell’s long axis ${\theta }_0$ decreases during the recoil by $\delta \theta$. (c) Corresponding trajectories of the single particles forming the dumbbell particles demonstrate the complex particle motion during recoil. The horizontal dotted line is along the direction of shear.

Figure 2

Temporal evolution of angle $\theta$ made by the axis of the dumbbell with recoil direction for different recoil runs (colored lines) and the average curve (thick black line) for ${\theta }_0\sim {40}^{\circ }$, $v=0.3\mathrm{\mu }\text{m}/\text{s}$ and $t_{\text{sh}}=50\text{s}$. The angle made by the dumbbell after release ($t>0$) deviates significantly from the initial angle ${\theta }_0$ at $t<0$. The black dashed line denotes the standard deviation in the spread of the trajectories.

Figure 3

(a) Amplitudes of MIA for fixed shear time $t_{\text{sh}}=50\text{s}$ and two different shear velocities, $v=0.2\mathrm{\mu }\text{m}/\text{s}$ (dark blue) and $v=0.3\mathrm{\mu }\text{m}/\text{s}$ (light blue), as a function of initial angle ${\theta }_0$. Open symbols correspond to experimental data, the solid line shows simulation results of the model introduced in Fig. 4b. The curves show a maximum around ${\theta }_0={45}^{\circ }$ and decrease to 0 towards ${\theta }_0=0^{\circ }$ and ${90}^{\circ }$. (b) and (c) Show individual recoils (colored lines) and their mean (thick black curve) for ${\theta }_0=0^{\circ }$ and ${90}^{\circ }$, for fixed shear time $t_{\text{sh}}=50\text{s}$ and shear velocity $v=0.3\mathrm{\mu }\text{m}/\text{s}$. Even though the mean curve remains constant in both cases, the individual trajectories show a huge spread at ${\theta }_0={90}^{\circ }$ compared to ${\theta }_0=0^{\circ }$ signaling an instability when the dumbbell axis is perpendicular to the recoil axis. (d) Sketch of a director (top) and a vector (bottom). While driving left or right is equivalent for a director (green arrows), this is not the case for a vector (green and red arrows lead to different scenarios).

Figure 4

(a) Amplitudes of MIA and translational (inset) recoils as a function of shear velocity v for experiments (open symbols) and simulations (solid line) with fixed initial angle ${\theta }_0\sim {40}^{\circ }$ and shear time $t_{\text{sh}}=50\text{s}$. While MIA increases quadratically with v, translational recoil is linear in v. (b) Sketch of the microscopic model: The colloidal dumbbell is modeled as a rod of length l (gray), coupled to a bath rod (green) of length $l_b$ via a nonlinear spring.

Figure 5

Amplitudes of MIA and translational (inset) recoils for fixed initial angle ${\theta }_0\sim {40}^{\circ }$ and shear velocity $v=0.3\mathrm{\mu }\text{m}/\text{s}$ as a function of shear time $t_{\text{sh}}$. Open symbols correspond to experimental data and solid lines to simulations. For short times, the MIA amplitude scales $\propto t_{\text{sh}}^2$, while the translational recoil scales $\propto t_{\text{sh}}$.

Figure 6

(a) Variance of orientation angle during recoil ($t>0$) for experiments (dashed lines) and simulations (solid lines) for different initial angles (colors) and fixed shear velocity $v=0.2\mathrm{\mu }\text{m}/\text{s}$ and shear time $t_{\text{sh}}=50\text{s}$. The black curves correspond to a passive scenario, where dumbbells are released from a stationary trap. During recoil, the variance reveals a strong dependence on the initial angle ${\theta }_0$, with a monotonous increase of amplitude towards ${\theta }_0={90}^{\circ }$. Inset: variance of orientation before releasing the trap, obtained from our model, where the passive curve follows the equipartition theorem (black line). For initial angles ${\theta }_0\gtrsim {45}^{\circ }$ fluctuations are amplified while they are suppressed for angles ${\theta }_0\lesssim {45}^{\circ }$. (b) Experimental variance during recoil (colored lines) for a shear velocity $v=0.3\mathrm{\mu }\text{m}/\text{s}$. The black line gives the passive scenario.