Reconfigurable properties of fire ant aggregations

Michael Tennenbaum and Alberto Fernandez-Nieves

We are investigating the material properties of fire ant aggregations using rheology. Previosly we have seen evidence that ants are able to resist applied stresses[1] below a critical stress threshold. Here we fix the stress to zero, $$\sigma=0$$, and monitor the strain, $$\gamma$$, as a function of time. a representative strain curve is shown in figure 1a. The ants are able to self strain, at 2hrs the top plate of the rheomter is moving clockwise and at 4hrs counterclockwise. There are regions where the ants push and regions where they are static, this is also seen in the normal force, figure 1b. When the aggregation is moving the normal force is high.

Fig. 1: a) Strain vs time for an applied stress of 0PA. b) Corresponding normal force for the creep test in a).

To determine if there is a difference in the mechanical properties of the aggregation when it is moving vs static we use oscillatory rheology. We apply a sinusoidal strain, $$\gamma(t) = \gamma_0 sin(\omega t)$$ and measureing the resultant stress, $$\sigma(t)$$. In the linear regime this stress can be divided into an in-phase and out-of-phase components characterized by the storage modulus, G', and the loss modulus, G''.

If we preform a frequency sweep when the normal force is high we get what we have seen previously, that the storage and loss modulus are comparable and both scale with frequency, $$G' \approx G'' \sim \omega^{1/2}$$, fig. 2a. However, when we perform the same test when the normal force is low we see that the frequency dependence goes away and the storage modulus is always larger than the loss modulus. Both of these are indicative of elastic behavior, fig 2b.

Fig. 2: Frequency sweeps in the linear regime for a) high normal force and B) low normal force. The storage modulus is represented with solid symbols and the loss modulus with open symbols.

To see what is changing inside the aggregation we constuct system to confine the ants in 2D. We can then quantify the activity using the area fraction. When the ants are more active the ants fill space evenly and image is darker. When the ants are inactive there are clumps and dilute regions. There is a transition between these two states shown in video 1 and which can be seen in figure 3. From here we can see that it is the number of active ants in the system that is important.

Vid. 1: Ants in 2D. Sped up 32x.

Fig. 3: Area fraction of the ants in the 2D system. When the ants are active the area fractionn is high. When the ants are inactive and clumped the area fraction is low.

To better understand the peak shape in terms of number of active ants we construct a model with three populations of ants: inactive, active, and post active.Inactive ants become active with a rate of $$k_a$$ and active ants become inactive with a rate of $$RK_a$$, fig 4.

Fig. 4: Block diagram of the model of peak shape

This model can be represented in differential form: $$\frac{dN_I}{dt} = -k_a N_I$$ $$\frac{dN_a}{dt} = k_a N_I-R k_a N_a$$ $$\frac{dN_p}{dt} = R k_a N_a$$ This results in a peak shape that is asymetric, it has a fast turn on and slow turn off. Since this is not what we see in experiment we update the model to be more symetric by introducing a time dependence, $$k_a \rightarrow k_a t$$ $$\frac{dN_I}{dt} = -(k_a t) N_I$$ $$\frac{dN_a}{dt} = (k_a t) N_I-R (k_a t) N_a$$ $$\frac{dN_p}{dt} = R (k_a t) N_a$$ An example of this model is plotted in figure 5 along with normal force data. The model captures the shape of the peak in the normal force. From the fit we get a timescale of 400s. We also see that the turn on and turn off happen at the same rate, $$R\approx 1$$

Fig. 5: Normal force data (black square) and a fit to the time dependent model (red line). We see good agreement in the shape.

We find that the number of active ants is the critical parameter in determining the mechanics of fire ant aggregations. When the number of active ants is low: the normal force is low, the ants are clumpy, and the storage modulus is larger than the loss modulus and frequency independent. When the number of active ants is high: the normal force is high, the aggregation is more homogeneous, and the storage and loss modulus are comparable and frequency dependent.

References:
[1] M. Tennenbaum, Z. Liu, D. Hu, and A. Fernandez-Nieves, Nature materials 15, 54-59 (2016)

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
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alberto.fernandez [at] physics.gatech.edu