Multifunctionality of Butterfly Species via Scaling Law

Over the recent decades, the bright colors seen on the wings of butterflies are widely evaluated frequently due to the cause of nano-structures and are not supported by preferable pigments or any other dyes. This nature of bright and shiny appearance of various butterflies are caused by so-called ‘structural features of various response of colours’ which are originating from the smart combination of nano- and microstructures. For the discovery of the physical origin of these structural colors, the color-causing nano-structures are integrated into a complex structure of scales, which have densely covers the wings of butterflies. A research team has recently discussed about the structural analysis of the ridges of the cover scales in the species of butterflies and its height and distance from different families and its subsequent analysis reveals a linear scaling law [1].

Peter Kӧchling et al., have further reported that the color of the butterfly wings serves for several purposes with ranging from camouflage to mating along with thermoregulation, and the overall scale structures are believed to assist with self-cleaning, aerodynamics, and easy release of spider webs. The optical effective part needs to be integrated into a structure to serve for the purpose of including self-cleaning, aerodynamics, and thermoregulation, which has to fulfill the mechanical constraints. For the evolutionary design, this multi-functionality of butterfly scale ridges were caused via various constraints. Furthermore, the evolutionary constraints will prevent the butterfly scales from the development of fully arbitrary shape [1].

During 1920s, it can be interestingly noted that, the discovery of some principles of structural colours in butterflies on the high-resolution microscopy was scaled and limited only to the optical methods. However, in the recent decades, the simulation techniques on the imaging of nano-scale structures and the advent of advanced microscopy has become the standard procedure. As, it can be observed that, sometimes it is very tricky to identify the optical effective components of nanostructures, because it is hidden with a complex design, which is not only responsible for colour effects. Hence, these multi-dimensional constraints will prevent a nano-structure embedded in to the butterfly scales that can be identified for the colour production.

By analysing the geometry of ridges, one can observe that, the scaling law has caused via multifunctionality. Ten different butterfly species from 7 sub-families and 3 families of Lepidoptera were been analysed and they observe that the ridges in the scales of butterflies follows on the ‘scaling law’. Figure 1 depicts the examination/study of photos with dorsal sides of all examined butterflies arranged in the world map to indicate their natural habitat which have originate from all over the continents that are differ in colour appearance and habitat. The distance between two ridges is found to be roughly twice of its height, i.e., the ratio between these two parameters is roughly constant.

Figure 1. Photo examination study of butterflies arranged in a world map to indicate their natural habitat [1].

Distance between the height of the ridges

Analysis of all butterfly species (Ten species) are considered and the most prominent distinguishable parts of their wings are evaluated. For every butterfly species, they have measured for at least three different areas. And some of the butterflies were recorded for the data upto ten areas, which includes of dorsal and ventral sides. By this way, finally they obtained between one and ten averaged pairs of height and the distance data for each butterfly species. The distance between the ridges were plotted on the horizontal axis and its corresponding height were plotted on vertical axis. However, still there will be some scatter data that can be observed and some butterflies will have smaller ridge heights and distances. It is very important to be noteworthy that, they mention the ratio of the height and distance of ridges which can holds only for cover scales.

Various studies have shown that the butterfly scales are seen with specific colouring elements that have caused a tremendous effect with a variety of colours over 157000 species that are described in the order of Lepidoptera. These species (Lepidoptera) are found to be positive correlation between scale length and wing which is the best fit for a nonlinear power law [2].

It can be observed that the scaling law were preferred only for the cover scales and not for the ground scales. Further, their assumption was the simple morphogenesis, which is not for the cause of observation. On considering the fact, the butterfly scales are found with different shapes. Also, it seems that the scaling of the ridges observed over the cover scales is due to the result of genetic constraints with the typical geometry.

The scaling law have possess certain advantages on the cleaning of butterfly wings. Butterfly wings can also self-clean to remove the dirt particles when they are sprayed with liquids or water. The cleaning effect is mainly compared to the cleaning observed on several super hydrophobic plant leaves (e.g. famous lotus leaf) [3].

Our SNB team have emphasize this research article to enrich our viewer’s knowledge about the structural and featural analysis of the ridges over the cover scales in different butterflies species and its height and distance from different families. The subsequent analysis reveals a linear scaling law. Most likely, the scaling law is based upon the result of multifunctional optimization. The core fact is that the various butterflies will follow up on this presented scaling law for their cover scales and not for the ground scales. This suggests that this structural constraint is the most important at the surface of thin wings. Furthermore, most butterflies were live only for a short time or they might have live in a very dry environment, so that there is no any rain at all during in their full lifetime. Consequently, they have exclude the ridges of the scaling law, which is very important for a wet self cleaning effect. Hence, the structure of the upper lamina can potentially influence the drag for the improvement for dry self-cleaning properties, which have benefits from the scaling law of the ridges.

References

Peter Kӧchling, et al., Faraday Discuss., 223, 195 (2020).
T. J. Simonsen and N. P. Kristensen, J. Nat. Hist., 37, 673 (2003).
M. Raupp, What do butterflies do when it rains? https://www.scientificamerican.com/article/what-do-butterflies-do-wh/, accessed2020-04-05.

--- Dr. Y. Sasikumar

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