In order to properly model this system, we do not only need to look at the glue droplet properties but we must also quantify the layout of scales. These tiny structures are more complicated than they seem, though only about 60 microns in diameter (think the thickness of a strand of hair). Each scale has a microstructure complete with ridges that run along their length. Upon further inspection, we can see that the scales come in multiple lengths, thicknesses, and shapes. The macrostructure of these scales is how they lay over one another, creating a set of shingles. We hypothesize that the layout of the scales draws glue to neighboring scales, perpetuating glue flow.
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Numerical and Computational Modeling
The spreading behavior of Cyrtarachne glue droplets on moth scales shows acceleration and hyper-spreading relative to tests conducted on glass. We seek to determine the forces which govern this interaction in order to better understand the interaction between the material properties of aggregate glue and the topology of the moth wing. This work has applications towards synthetic adhesives aimed at adhering to contaminated or 'dirty' surfaces.
Numerical Modeling
Cyrtarachne glue appears to flow under the scales of the moth, where other spiders simply sit on top. The structure and chemical properties of the moth scales make them superhydrophobic, resisting the flow of water. The image to the left shows our model for Cyrtarachne glue flow on moth scales. Two fronts are created, a flow on top of the scales and one below. The flow beneath the scales is pulled in many directions; flowing left and right and even backward. We hope to discover the physic governing this relationship and explain this unique behavior. We can then verify and test hypotheses in computational models, combining our measured biomechanical properties to predict glue flow behavior.
To measure the spreading behavior of glue, we bring silk strands into contact with surfaces. The spreading front of the glue droplets is tracked over time. When Cyrtarachne and other spider glues are spread on glass, we see the behavior on the left. The spreading fronts are purely linear, except between glue droplets. The flow is always radially outward. The glue droplets only change direction when they come into contact with one another, and having nowhere to go, will begin to flow outward. Knowing the contact speed we can estimate the viscosity of the glue!
When we track the spreading behavior of Cyrtarachne glue on moth scales we find that the spreading behavior is much more dramatic and dynamic. As you can see on the right, the spreading fronts are no longer linear but instead change direction. The spreading speed is not only faster but also the ultimate spreading distance is further. There is a complicated and enhancing interaction between Cyrtarachne glue and the topology of the moth scales. We aim to discover if this is caused by chemical interactions or by specially evolved mechanical properties of the glue.
Surface tension is what causes water droplets to form. The internal forces of the liquid want to pull themselves together and this creates a droplet.
Viscosity is the resistance to flow. Think of it as liquid inertia. By tracking the glue droplets and their collision with glass we can estimate the viscosity of them. These values can and will be used in our computational modeling of the glues.
Tracking the flow of glues and comparing them to a known standard allows us to determine the important material properties of the glue. Often spreading interactions are dependent on the two factors below:
When we look at the base cuticle of the moth we can see that it's also much more complicated than we would assume. The scales are actually highly compacted. They grow in clusters that overlay one another, making them sporadically dense. In order to properly model this system, our models must take into account the overlay of scales and the area they will create between the scale and body of the moth. A perfect place for the glue to flow.
Looking at the spreading behavior from our videos we attempt to use established models to estimate the flow of glue droplets with the material properties we have measured. The first and most simple is Tanner's law of flow. We know this one doesn't work because it predicts linear flow! But it is a standard test case! So we begin there.
Our second basic model of interest is the Hagen-Poiseuille which talks about fluid flow within a pipe. We wonder if the ridges on the scales are acting like canals and we estimate their ability to drive flow along the surface of the scales.
Another base model is that of capillary flow, flow created by the adhesion of the glue to the moth scales, pulling the glue forward, throughout the complex matrix. This force can only occur in extremely small places. This is the force that occurs when you get your iron levels checked at the doctor. The small tube they put up to your finger to collect blood draws blood in passively through capillary forces!
Future Directions
At the present moment, we are still working diligently on this model, but we have hit a small snag. Looking at the flow predicted by each of our models to the left, you can see they do not explain the extremely fast-spreading of Cyrtrachne. We are working to combine multiple numerical models to explain this. As we do so, we also work on 3D models of the scale structure and layout, hoping to use fluid flow programs to estimate flow on moth scales. By creating an accurate model, we can change parameters and determine their individual importance and effect on spreading. This will even allow us to alter parameters and pit different spider glues against different moth scale types and layouts.