Invited Paper

The proboscis as a fiber-based, self-cleaning, micro- fluidic system

Kostantin G. Korneva*, Daria Monaenkovaa, Peter H. Adlerb, Charles E. Beardb, and Wah- Keat Leec

aDepartment of Materials Science and Engineering, Clemson University, Clemson, South Carolina, USA, 29634. E-mail: [email protected] bDepartment of Agricultural and Environmental Sciences, Clemson University, Clemson, South Carolina USA, 29634 cNational Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York, USA,11973.

ABSTRACT

The butterfly proboscis is a unique, naturally engineered device for acquiring liquid food, which also minimizes concerns for viscosity and stickiness of the fluids. With a few examples, we emphasize the importance of the scale-form- functionality triangle of this feeding device and the coupling through capillarity.

Keywords: Butterfly proboscis, capillarity, Laplace law, shaped fiber

1. INTRODUCTION

On our “buggy planet”[1], approximately 28% of all fluid-feeding are and moths constituting the mega-order [2]. The first Lepidoptera arose in the Permian period of Earth’s geological history [3-5]. Over a span of about 300 million years, the Lepidoptera diversified spectacularly and evolved a unique feeding device called a “proboscis”. Butterflies and moths use their proboscises to acquire food from a rich variety of sources. The diet of contemporary Lepidoptera includes plant sap, rotten fruits, , blood, tears, and organic wastes, to list but a few examples[6, 7]. Over evolutionary time, as the Lepidoptera came to inhabit nearly all terrestrial habitats over the globe, and while the Earth’s temperatures fluctuated widely, these insects encountered a wide range of food sources, which they became adapted to exploit. Many Lepidoptera are capable of acquiring any liquid food, whether a thick highly viscous liquid such as or a thin almost inviscid mineral water [6, 7]. Consequently, biologists refer to adult butterflies and moths as opportunistic feeders. Accordingly, the proboscis was honed by natural selection over millions of years into a multifunctional device capable of acquiring liquid from different sources of food. From the materials engineering standpoint, the lepidopteran proboscis is a unique engineering device. The proboscis (Fig. 1A) consists of a pair of C-type fibers, called galeae. Each galea carries muscles and trachea and is filled with blood called hemolymph. When two galeae come together, their C-shaped faces unite to form a food canal (Fig. 1B,C). In the first approximation, the food canal can be considered a circular cylinder; hence, each half has the same C-radius. The external part of the proboscis is not necessarily circular (Fig. 1B). For a long time, the proboscis was compared functionally to a pipe or a drinking straw[7-11], and was assumed to suck liquid in by a suction pump located in the ’s head [9, 12-14]. In this scenario of fluid uptake, the proboscis is viewed as a passive fluid conduit. However, materials organization, morphology, and surface properties of the proboscis are far from simple[15, 16]. Diverse food sources present butterflies and moths with the dual challenge of acquiring fluids while maintaining a clean proboscis[17]. The chemical composition of the proboscis includes

Bioinspiration, Biomimetics, and Bioreplication 2016, edited by Raúl J. Martín-Palma, Proc. of SPIE Vol. 9797, 979705 · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2218941

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hydrophobic chitin in its cuticle, coupled with surface lipids and waxes[18-21]. The roughness of the proboscis surface significantly changes the surface energy, decreasing it in the case of waxed hydrophobic patches and increasing it in the case of protein-rich hydrophilic patches [22-26]. These surface properties either facilitate proboscis cleaning or hinder its wettability. Thus, it is instructive to look back and revisit the drinking-straw model of the lepidopteran proboscis, with the intention of bringing together these materials features and unveiling their functionality and importance in food acquisition.

(C) 500µm

Figure 1. Photomicrographs of butterfly proboscises. (A) Coiled proboscis of the tiger swallowtail (Papilio glaucus). (B) Cross- section of the proboscis of the monarch butterfly (Danaus plexippus) with a circular hole, the food canal, formed by the two galeae, each filled with muscles and tracheae. The top and bottom fence-like structures link the two galeae together. (C) A single galea of the monarch butterfly taken separately resembles a C-type fiber.

2. IMPORTANCE OF SCALE

The lepidopteran proboscis is adapted for taking fluids from droplets and surface films; hence, its size and the sizes of its morphological features are evolutionarily tuned to deal with small amounts of fluids. When a proboscis is immersed in a liquid, the liquid surface deforms into a meniscus embracing the proboscis. Depending on the proboscis wettability, the contact line separating wet and dry parts of the proboscis surface can be located above (for wetting) or below (for non- wetting) the horizontal liquid surface. We know that the shape of a meniscus is determined by the Laplace[27] law of capillarity, which states that the pressure under meniscus Pl is different from the atmospheric pressure Pa and the pressure differential is determined by the surface tension σ and the mean curvature of the meniscus surface as

− =(1/ +1/) (1)

where and are the principal radii of curvatures of the liquid/air interface. Since the pressure in the liquid varies with the height, four physico-chemical parameters play important roles in shaping the meniscus: the surface tension of the liquid σ , its density ρ , contact angle θ that the meniscus makes with the proboscis surface, and acceleration due to gravity g . This set of parameters, plus the proboscis geometry, governs a huge variety of meniscus configurations, which, in turn, control the efficiency of food uptake by the insect. To understand the effect of the proboscis shape, we first assume that the proboscis is a blade with an infinitely large width. The vertically immersed blade-like proboscis forms the mirror-symmetrical menisci on each of its sides. Laplace[27] analytically solved the meniscus problem and found height h as

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hg=−21sin/()σ ()θρ. (2) As an upper estimate of the meniscus height, we assume that the wall is completely wettable by water, θ = 0 . Then the meniscus height is estimated as h ~ 4mm. This height is comparable to the size of a small moth! Thus, over evolutionary time, Lepidoptera gained an advantage by evolving something other than a blade, either by changing the proboscis shape or placing some hydrophobic barriers on its surface to stop the meniscus from rising. Otherwise it could be engulfed under the meniscus[28]. The blade model does not include any geometrical parameters of the proboscis, causing us to wonder how the proboscis size influences this scenario? And why did Lepidoptera develop a rich library of proboscis shapes [15, 16]? On the other hand, the blade model is quite informative as it gives us important scale, , called the capillary Lc = σ ()ρg length[29]. Using the capillary length, we can roughly estimate the distance from an obstacle where the liquid surface

levels off. This estimate is illustrated in Fig. 2. By approximating the meniscus with a circular cylinder of radius Lc , we

see that at the distance Lc from the blade, the liquid surface approaches the horizontal air/water interface. With this scale in hand, one can understand why butterflies aggregated at a mud puddle do not compete with one another [30, 31]:

if the neighbors are positioned a distance Lc apart, they would not influence the feeding process of others.

Figure 2. A schematic of a meniscus formed on a blade-like proboscis. Its height is proportional to the capillary length

Lgc = σ ()ρ and depends on the contact angle θ, see eq. (2). The horizontal water/air interface is perturbed only at the distance

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~ Lc from the blade. If two butterflies drink from the same mud puddle, they would not interfere with one another if their proboscises

are separated by the distance ~ 2Lc .

To see how the meniscus shape influences the meniscus height, it is natural to turn to a second proboscis model, a circular fiber of external radius R. The proboscis radius of Lepidoptera varies from a few microns to hundreds of

microns[6, 32]; that is, it is much smaller than the capillary length, R << Lc ~ 4mm. This inequality narrows the range of available meniscus configurations, and the meniscus height is estimated as[33-35]

hR=−cosθθ⎡⎤ ln 1 + sin + lneRLEE / 4 , = 0.577215 . (3) Cc⎣⎦()( )

There is a striking difference between eq. (2) and (3). One observes an almost linear dependence of the meniscus height on the proboscis radius; the smaller the proboscis radius, the smaller the height of the pulled meniscus! This result has far-reaching implications for the proboscis design and interpretation of lepidopteran diversity[2]. As long as the proboscis is not too short, any proboscis, either millimeter or sub-micrometer in thickness, can be used to pull up the liquid food, and the insect would not become wet. This scale does not influence the criterion for the distance when the feeding insect would not be disturbed by the presence of others. The deflection of the liquid surface by the proboscis

should not propagate farther than ~ Lc [36, 37].

3. IMPORTANCE OF SHAPE

The drinking-straw model of the lepidopteran proboscis does not adequately represent proboscis function[38]. Lepidoptera often drink from porous substrates, such as wet soil [30, 31, 39] or dung and carrion or rotting fruit[7, 40]. From these food sources, Lepidoptera are able to drink water that is enriched with nutrients while restricting debris[30, 31, 39]. Moreover, interaction of Lepidoptera with flowering plants is also quite complex. Insects visiting flowers are repeatedly removing nectar from the same flower by picking small droplets rather than drinking from a nectar pool [41- 44] . Under these circumstances, Lepidoptera capitalize on capillary action of the proboscis[16, 17, 45, 46]. To absorb liquid and restrict entry of debris, Lepidoptera developed different proboscis morphologies and shapes. One creative innovation deserving special attention is the linking mechanism holding the two galeae together, Fig. 1 (B). This mechanism is mechanically complex and its function is still not entirely clear. However, an important feature of this mechanism is the fence or zipper-looking structure with the teeth called legulae sitting tightly next to, or overlapping, each other. For more than 150 years, this fence structure of the proboscis was regarded as sealed. The English naturalist Philip Henry Gosse, while studying insects in Alabama, described the proboscis in 1838: “…it is composed of two parts perfectly separable, you see, each part being a cylinder, yet when placed side by side, meeting in such a manner as to form a tube quite air-tight between the two lateral ones.” [11]. The idea of a sealed tube persisted into the textbooks [6, 8, 10, 47] until recent experiments showed that water can enter the food canal through interlegular spaces [17, 45, 48, 49]. Experimental analysis of the wetting properties of proboscises reveals a hydrophobic-hydrophilic dichotomy of its surface17; in different butterflies and moths, only about 5%-20% of the proboscis length is hydrophilic, the remaining 95%-80% of each proboscis of the tested butterflies has a hydrophobic surface[16]. These observations allow us to subdivide the proboscis into two functional regions: a drinking region where water is attracted to the surface, and a non-drinking region where water is repelled from the surface. Using capillary rise experiments, we can quantitatively specify the demarcation as the position on the proboscis where the air/water interface remains horizontal. The bands of the linking mechanisms at the C-edges of the galeae are necessarily hydrophilic. And these two hydrophilic bands are important for butterflies and moths drinking from liquid films on substrates, such as soil, when the typically expose more than the drinking region of their proboscises to fluid[30]. Lepidoptera face the problem of keeping their proboscises clean and, at the same time, able to acquire liquid food. Drinking from floral corollas, animals encounter a range of nectar availability and its form; nectar is available as films adhering to the corolla surface, or as droplets. The level of insertion of the proboscis into the corolla influences the extent of the proboscis exposed to fluid,

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restricting it to the drinking region or presenting an amount sufficient to cover more than the drinking region46, 48. This suggests that nectar has to be collected at the hydrophilic bands of the linking mechanisms to get into the food canal through the gaps between the legulae. An ellipsoidal shape of the proboscis ensures that the liquid food will be collected at the bands of the linking mechanisms, as seen from the following analysis. Assume that the external surface of the proboscis is described by an ellipse x2 /a2 + y2 /b2 = 1 with the focal radii a and b 45 (Fig. 3). If the film covering the proboscis surface is thin, we can estimate the Laplace capillary pressure at the air/liquid interface by calculating the curvature of the proboscis surface. In Fig. 3, the liquid film is shown covering the entire surface of the proboscis, making the analysis simpler. However, the results are applicable to the cases when the film covers only a part of it. As soon as the film forms, the air/liquid interface is immediately subject to the action of capillary forces. / − = σ () +(/) () ) . (4)

As follows from eq. (4), the pressure differential at points ϕ=0 and ϕ = π is equal to − = σ while at points ϕ = π/2 and ϕ = 3π/2 it is equal to − = σ . Therefore, as the pressure at points ϕ=0 and ϕ = π is greater, a > b , the liquid will be forced to move from the sides towards the legulae bands situated at ϕ = π/2 and ϕ = 3π/2. This analysis may explain why the proboscis ellipticity is more noticeable in the non-flower visiting butterflies and moths, which probe animal wastes (e.g., dung) with bacteria and other sticky compounds: the insects move the liquid toward the parts which are subject to intensive rubbing during coiling and uncoiling of the proboscis such that the probability of shaking off the debris is greater.

Hydrophillic band, ventral

Figure 3. (A) Proboscis as an elliptical fiber with two hydrophilic dorsal and ventral bands of legulae shown in (B). (C) Liquid film on a wettable surface of a proboscis will move towards the legulae bands positioned around points ϕ = π/2 and ϕ = 3π/2, provided that a > b. (D) Liquid film on a non-wettable surface. The liquid is squeezed from points ϕ = 0 and ϕ = π where the pressure is high toward the linkage bands. On its way to these bands, the film may de-wet the surface to form solitary droplets shown as the dashed lines.(E) Pressure distribution in the water film, σ=72 mN/m, on proboscises with the major axis a =100μm and different ellipticity b/a.

4. IMPORTANCE OF FUNCTION: MANIPULATION OF LIQUID DROPLETS BY BENDING THE PROBOSCIS

Proboscis structure and function are indissolubly connected, as seen when a butterfly samples liquid from a porous sample such as rotting fruit or soil. Lepidoptera apply the proboscis to the substrate dorsally and keep drinking with a bent proboscis (Fig.. 4A). X-ray phase-contrast imaging reveals that the liquid penetrates the dorsal legular band and collects on the back of this band from inside, forming a drop (Fig. 3B).

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Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx The size of the drop is small, much smaller than the capillary length Lc; therefore, gravity should not be important. At the same time, one observes the droplets leaning towards the dorsal side of the proboscis from inside the food canal. These observations suggest that the proboscis bending during feeding is an important evolutionary development that needs to be explained. It is convenient to model the interior of the proboscis as a hollow torus, i.e., a tube with the internal radius Rp bent in a circular ring of radius R (Fig. 4 C, D). The torus surface is created by rotating the circle of radius Rp around the z - axis (Fig. 3 C, D). The center of the rotating circle describes another circle of radius R which is positioned in the plane perpendicular to the z-axis, i.e., the distance OO2 in Fig. 4 is equal to OO 2 = R. The position of any point on the torus surface can be specified by introducing an orthogonal system of coordinates, where the large circles are parallels formed by cutting the torus with planes perpendicular to the z-axis; the smaller circles are meridians formed by cutting the torus with planes containing the z-axis (Fig. 4C,D). The two principal radii of curvature for the torus surface coincide with radii of R1 and Rp for parallels and meridians, respectively. The center of curvature O1 of the parallels is sitting on the z-axis, external to the torus surface. The centers of curvature of meridians are sitting along the circle O2 O2'.

f

,,,,..... rr _7r/2

Figure 4. A) A monarch butterfly drinking liquid from a drop, keeping the proboscis curved in a bow, B) Series of X-ray phase- contrast images showing a curved proboscis touching a meniscus. The proboscis was pushed toward the meniscus by a needle. The liquid enters the food canal and forms an internal film and then forms a drop inside the food canal from the back side of the dorsal legular band. The inset shows a top view of the butterfly with a coiled proboscis and a needle threaded through the coil. C-D) Schematic helping to understand the definition of two principal radii of curvatures Rp and R1 of the torus for the cases −π/2 < ϕ < π/2 and π/2 < ϕ < 3π/2. E) Pressure distribution in the internal film for the different R1/ Rp ratios. The red dots on the rings show the ϕ coordinates of the four characteristic points on the cross-sectional circle. The inset illustrates the mechanism of drop formation by the capillary pressure that squeezes the liquid from the innermost circle = − , ϕ = 0 towards the outermost circle = + , ϕ = π of the curved proboscis.

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Using this proboscis model, we can explain formation of droplets as follows. When water penetrates the legular band, it is forced to wet the hydrophilic wall of the food canal [45]. The pressure in the outside droplet is greater than the atmospheric pressure (the drop is bulged under this pressure). According to the Laplace law, eq. (1), the pressure in the film inside the food canal that has just been formed is below the atmospheric pressure (the film wraps up the air bubble having the atmospheric pressure). Therefore, the liquid keeps flowing into the food canal (Fig. 4B). Once the film is formed, its free surface, which is exposed to the air, is subject to the Laplace capillary pressure. Eq. (1). Again, assuming that the film is thin, we can estimate the pressure distribution by looking at the curvature of the food canal.

The surface forces acting on the free surface of the film inside the food canal can be either positive or negative. The forces acting along the parallels are attempting to contract the film and have the same sign within the entire range 0 < ϕ < 2π. In contrast, the forces acting along the meridians may either pull the liquid toward the circle O2O2' or pull it toward the z-axis. As an illustration, consider a ZX cut of the proboscis as shown in Fig. 4 B. The z-projections of the surface tensions are balanced on both arcs −π/2 < ϕ < π/2 and π/2 < ϕ < 3π/2. However, the horizontal x-components of the surface forces are different. On the arc π/2 < ϕ < 3π/2, the x-component of surface tension acts to pull the film toward the z-axis while on the arc −π/2 < ϕ < π/2, it pulls the film toward point O2. These considerations help to understand the effect of concave/convex bends on the pressure distribution in the film. Using the Laplace law, the pressure distribution is written as (see the definition of the principal radii of curvature in Fig. 4 C, D)

− =−1/ +1/, −/2<</2 (5) − =−1/ −1/ , /2 < < 3/2 (6)

( −)/ = −(1 − 1/( tan − sin) + ( − cos) ), −/2<</2

( −)/ = −(1 + 1/tan(−) +(3/2 − ) ++sin (3/2 − ) ),

/2 < < 3/2

where = /. Since R1 > Rp the pressure in the liquid film is always below the atmospheric pressure. Note, that the radius depends on the position of the observer, =() = (ϕ) ; hence, the pressure distribution in the liquid film is not uniform. The film sitting farther from the z-axis along the band /2 < ϕ <3/2 experiences lower pressure than that sitting at the band −/2 < ϕ </2 . Therefore, one would expect the liquid accumulation on this part ( /2 < ϕ <3/2 ) of the proboscis (Fig.4B, E).

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Figure 4 E illustrates the effect of the proboscis bending on pressure distribution in the wetting film. Plotting the pressure dependence in the dimensionless form ( −)/ as a function of angle ϕ for different ratios =/, one can study this effect for different species having different radii of the food canal. The pressure reaches its lowest value at the farthest circle of the curved proboscis, = + , ϕ = π and its highest value at the circle closest to the z-axis, i.e., at = − , ϕ = 0. Thus, by bending the proboscis, Lepidoptera force the liquid food to accumulate at the back side of the dorsal legular band. The accumulated liquid is further transformed to a liquid bridge and is pulled by the animal using its suction pump[45]. Animals with finer proboscises may make the ratio / large, thus generating a stronger pressure difference across the wetting film. According to this simple model, by bending and unbending the proboscis, Lepidoptera can control the food collection and formation of liquid bridges during feeding from droplets or porous substrates. For example, an infinitesimally thin film of water in the food canal of a straight proboscis of a monarch butterfly having the radius of food canal Rp=48 µm generates the capillary pressure of about ( −)≅/ ≅1.5 KPa. Bending the proboscis in a bow of radius R = 660 µm (Fig 4 B) will make the ratio R/Rp ≅ 13 and generate the pressure difference across the film, − − + ≈ 0.23 KPa, which is of the same order of magnitude as the initial pressure drop ( −). The higher the pressure difference, the faster the liquid collection will occur.

5. CONCLUSION

Evolutionary development of the lepidopteran proboscis is a challenging and exciting story of the interactions of insects with plants and the environment in general [41, 42, 50-52]. In the “Lilliput World” that the Lepidoptera live in, the capillary forces are dominant; they can either enhance or prevent the development and diversification of particular species of insects at the evolutionary time scale. A complex shape of the proboscis together with the patterned external and internal surfaces of the galeae, and the presence of porous and fibrillar hierarchical structure used for fluid uptake, all suggest that the capillary action also has played a significant, yet unexplored, role in the diversification of the Lepidoptera feeding strategies. In the presented notes, we showed a few examples highlighting the importance of the scale, form, and functionality of lepidopteran feeding devices and their coupling through capillarity. Materials properties of the insect feeding devices evolved in at least two ways: to accommodate the narrow niche of the insect by specifically shaping the proboscis and elaborating it with a particular physico-chemical pattern. This is the purely materials side of the evolutionary development. In addition, the feeding device was honed by natural selection to enrich it with new materials functionalities. This is the systems biology side of the evolutionary development of the feeding device [53]. At both levels, the capillary forces seem to be accommodated to create a new robust structure which would suit the organismal function. The dual functionality of the proboscis at the compositional and organismal levels has enabled opportunistic feeding from a wide variety of food sources.

ACKNOWLEDGEMENTS

This work was supported by the National Science Foundation, Awards No. POL-S1305338 and IOS-1354956. We thank the Clemson University Electron Microscope Laboratory for assistance with the scanning electron microscopy. Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract no. DE-AC02- 06CH11357.

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