Material Properties of Fire Ant Aggregations
Authors: Michael Tennenbaum1, Zhongyang Liu2, David Hu2, Alberto Fernandez-Nieves1
1School of Physics, Georgia Institute of Technology, Atlanta, Georgia, USA,
2School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA.
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Fire ants are an impressive species. A remarkable property is that they are able to build rafts to survive flooding. These rafts are only made of ants; they contain no twigs or leaves. The raft is solely linked together with ants. This ability to link together means that we can think of ant aggregations as condensed states of matter, like the common fluid or solid states. In this work  we begin to characterize the properties of the ant aggregation as a material. However, in contrast to the particles in conventional materials, ants are alive; they are out of equilibrium and also are self-propelled. As a result, ant aggregations are particular examples of active materials.
In fact, the combination of being alive and being able to link together makes fire ants an excellent system to study active materials. Our work began with two simple experiments. The first is a penny that is dropped through a 2D column of fire ants, as shown in figure 1a-c. This behavior is reminiscent of what happens to a ball bearing falling through a viscous liquid. The second experiment in figure 1 shows what happens when an aggregation of fire ants is compressed by a Petri dish. Once compressed the ants spring back to their original shape. This is the classic behavior of elastic materials. We thus conclude that fire ant aggregations are both viscous and elastic. To more carefully study this viscoelastic behavior we employ rheology. We use a modified Anton Paar MCR 501 stress controlled rheometer to investigate the ants.
Figure 1: (a—c) A penny being dropped through a 2D column of ants. (d-f) Compression of an ant aggregation using Petri dishes. Videos are online at antphysics.gatech.edu .
In our recent paper we present the ant aggregation’s response to oscillations. This is called small amplitude oscillatory shear experiments. The premise is to apply a small sinusoidal strain and measure the stress necessary to maintain this strain. In elastic materials this stress is perfectly in phase with the strain. In contrast, for perfectly viscous materials it is completely out of phase. For viscoelastic materials, the response is in between. We can characterize how much energy is stored per cycle (Storage modulus) by the in phase component and how much energy is dissipated per cycle (Loss modulus) by the out of phase component.
Amazingly for ant aggregations these components are equal for the frequency range probed. This means that in each cycle the ants are dissipating energy and storing energy equally. The response is also power law with an exponent of ~0.5. This power law behavior implies that there is a lack of a unique timescale to relax. Polymer gels when they first percolate through the system show this same behavior . In polymer gels this is attributed to the fractal nature of the gel. However, fire ants are not fractal as far as we have seen. The power law exponent of 0.5 combined with the equality of the Storage and Loss moduli is consistent with the Kramers-Kronig relations [3,4], which apply to systems near equilibrium, in the so-called linear regime. However, fire ant aggregations are far from equilibrium and thus it is not obvious as to why linear response works. This is an interesting open question.
Figure 2: Storage modulus G' and Loss modulus G" as a function of frequency (a) Live ant frequency sweeps, (b) Dead ant frequency sweeps.
We are nevertheless sure that our observations are due to the active nature of the ants. When we performed similar measurements using dead ants the result was completely different. Dead ants are elastic. Their storage modulus is always higher than their loss modulus and are frequency independent.
Interestingly, when we increase the density of the live ant aggregation, the behavior approaches that of dead ants and eventually the system becomes predominantly elastic. Looking closer at this we see that there are two regimes. The first is at lower densities and here the storage modulus increases linearly with the fraction of space taken up by ants or volume fraction. In this regime the ants are crowding and the addition of ants decreases the available possibilities for them to rearrange. After a certain point in volume fraction though, the addition of ants causes them to pull their legs in a little. This progressive compression of the ants characterizes the second regime.
A very different response is obtained when the ant aggregation is forced to flow. In this case there is no difference between live and dead ants, and the aggregation behaves as a shear thinning liquid like ketchup, which manifests a smaller viscosity the harder it is pushed. Remarkably though, the amount of shear thinning in the ants is more pronounced relative to that observed in materials like ketchup. This result can ultimately be related to how the energy input is dissipated in the aggregation. For dead ants, this mainly happens at the ants joints, when these give way due to the imposed flow state of the aggregation . The similar behavior exhibited by live ants indicates that this mechanism is also at play for these aggregations.
In summary, we have found (i) that live ants at relatively “low” volume fractions are equally viscous and elastic, (ii) that they become predominantly elastic and approach dead-ant behavior as the volume fraction increases, and (iii) that when forced to flow, they do so with a viscosity that dramatically decreases as they are forced to flow faster. Our work opens the way to many more interesting studies where ants are used as model active particles. We thus hope to use them to address many more relevant problems.
 Michael Tennenbaum, Zhongyang Liu, David Hu, Alberto Fernandez-Nieves, "Mechanics of fire ant aggregations", Nature Materials, 15, 54-59, doi:10.1038/nmat4450 (2016). Abstract.
 Horst Henning Winter, Marian Mours, "Rheology of Polymers Near Liquid-Solid Transitions" in 'Neutron spin echo spectroscopy viscoelasticity rheology' (Volume 134 of the series 'Advances in Polymer Science', pp 165-234, Springer, 1997). Abstract.
 R. Byron Bird, Robert C. Armstrong, Ole Hassager, "Dynamics of polymeric liquids. Vol. 1: Fluid mechanics" (Wiley, 1987).
 Michael Stone, Paul Goldbart, "Mathematics for physics: a guided tour for graduate students" (Cambridge University Press, 2009).
 Sasha N. Zill, Sumaiya Chaudhry, Ansgar Büschges, Josef Schmitz, "Directional specificity and encoding of muscle forces and loads by stick insect tibial campaniform sensilla, including receptors with round cuticular caps", Arthropod structure & development, 42, 455-467 (2013). Abstract.