Activity-driven changes in the mechanical properties of fire ant aggregations

Fire ant aggregations are active materials composed of individual constituents that are able to transform internal energy into work. We find using rheology and direct visualization that the aggregation undergoes activity cycles that affect the mechanical properties of the system. When the activity is high, the aggregation approximately equally stores and dissipates energy, it is more homogeneous, and exerts a high outward force. When the activity is low, the aggregation is predominantly elastic, it is more heterogeneous, and it exerts a small outward force. We rationalize our results using a simple kinetic model where the number of active ants within the aggregation is the essential quantity.

Figure 1

(a) Compressional test of hook Velcro. The closed symbols are descending and the open symbols are ascending. The black squares were first followed by the red circles and lastly by the green triangles. The inset is a side-view schematic of the experimental cell of the rheometer with parallel-plate geometry and Velcro. The distance between plates is $h_{\mathrm{plate}}$. The gap height is $h_{\mathrm{Velcro}}$. (b) Compressional test of loop Velcro. The closed symbols are descending and the open symbols are ascending. The black squares were first followed by the red circles and lastly by the green triangles.

Figure 2

Torque as a function of deflection angle for (dashed blue) $h_{\mathrm{Velcro}}=3$ mm and (solid black) $h_{\mathrm{Velcro}}=4.5$ mm. (a) Hook side of the Velcro. (b) Loop side of the Velcro.

Figure 3

(a) Magnitude of the complex modulus $G^{*}$, measured for ants with the loop side of the Velcro for (black squares) $h_{\mathrm{Velcro}}=3$ mm and (red circles) $h_{\mathrm{Velcro}}=4.5$ mm, and with the hook side of the Velcro for (green triangles) $h_{\mathrm{Velcro}}=4.5$ mm. The open symbols are the corresponding measurements with only Velcro. The hook side does not appear because the torque in these experiments was below the torque limit. (b) Magnitude of the complex modulus that results from subtracting the magnitude of the complex modulus of the Velcro by itself. The solid symbols are used for $|G_{\mathrm{ants}+\mathrm{Velcro}}^{*}|$, while the open symbols are used for $|G_{\mathrm{ants}+\mathrm{Velcro}}^{*}|-|G_{\mathrm{Velcro}}^{*}|$. The circles correspond to $h_{\mathrm{Velcro}}=4.5\mathrm{mm}$, while the square symbols correspond to $h_{\mathrm{Velcro}}=3\mathrm{mm}$.

Figure 4

(a, c) Creep experiment at 70 Pa. (a) Schematic based on results in Ref. [14] for the strain as a function of time. (c) Experimental data for the normal force in the experiment depicted in panel (a). (b, d) Creep experiment at 40 Pa. (b) Schematic based on results in Ref. [14] for the strain as a function of time. (d) Experimental data for the normal force in the experiment depicted in panel (b). The normal force dips in regions where the strain is constant; this is emphasized by the dashed vertical lines in the figure.

Figure 5

(a, b) Creep experiment at an applied stress of 0 Pa. (a) Strain as a function of time. (b) Normal force measurement corresponding to the creep test in panel (a). The normal force peaks at times where the strain changes. (c) Frequency sweep immediately after loading the ants in the rheometer and the normal force is high. (d) Three representative frequency sweeps taken when the normal force is low in between peaks.

Figure 6

A single normal force peak. Its standard deviation and skewness are 200 s and 0.2. The solid red line is a fit to Eq. (8b) with $R$ and $k_a$ as fitting parameters.

Figure 7

Visualization experiments using a two-dimensional apparatus constructed from three stacked sheets of acrylic with a hole cut in the center sheet for the ants. (a–d) Snapshots taken with a CCD camera at different times after loading the ants inside the cell. (e) Binarized version of image (c). Once each image in the time series is binarized, we find the fraction of black pixels, which we identify with an estimate of the area fraction occupied by the ants, ${\varphi }_s$. We plot the result as a function of time in panel (g). (f) Local ${\varphi }_s$ values obtained after averaging ${\varphi }_s$ in image (e) within boxes of size $30\times 30$ pixels. Note we have slightly squished the image horizontally. We perform this averaging for all images in the time series and use it to calculate the relative-mean-square fluctuations, $F_{\mathrm{RMS}}$ (see text), at different times. The result is plotted in panel (h). The snapshots (a)–(d) correspond to 50 min, 1 h 15 min, 1 h 45 min, and 2 h 15 min in panels (g) and (h). The scale bar in panels (a)–(e) corresponds to 10 mm.

Figure 8

Block diagram of the kinetic model for ant activation.

Figure 9

(a) Number of inactive ants, $N_I$, active ants, $N_a$, and postactive ants, $N_p$, as a function of dimensionless time in the fixed rate-constant model given by Eqs. (6), with $R=2$. (b) $N_I$, $N_a$, and $N_p$, as a function of dimensionless time in the time-dependent rate-constant model given by Eqs. (8), with $R=2$. In both plots, $N_I$ is the black dashed line, $N_a$ is the solid red line, and $N_p$ is the blue dotted line. The results are all normalized by the total number of ants, $N$.

Figure 10

Controlled shear rate experiment. (a) Schematic based on results in Ref. [14] for the viscosity as a function of strain rate illustrating the shear thinning behavior of fire ant aggregations. (b) Experimental data for the measured stress, $\sigma$, needed to maintain the imposed strain rate (blue circles) and normal force (blue circles) in the experiment depicted in panel (a).