Paradox of the drinking-straw model of the butterfly proboscis

Butterflies and moths (Lepidoptera) use their slender proboscises to sip nectar, plant sap, animal tears, blood and other fluids, which are generally complex in composition (Krenn, 2010). The proboscis simultaneously is a multifunctional material and a fluidic device composed of two flexible strands, the maxillary galeae, with C-shaped medial faces joined by cuticular projections, the legulae (Monaenkova et al., 2012) (Fig. 1). The materials organization of the proboscis is unique, enabling it to perform multiple tasks, such as fluid acquisition, environmental sensing, coiling and uncoiling, and self-cleaning (Eastham and Eassa, 1955; Kingsolver and Daniel, 1995; Krenn, 2010).

The size of the dorsal legulae and their spacing significantly increase in the distal 5–20% of the proboscis (Krenn, 2010; Monaenkova et al., 2012). The distal region of the proboscis, which is called the ‘drinking region’, is hydrophilic, while the remaining portion has hydrophobic properties (Lehnert et al., 2013). The drinking region plays a critical role in fluid acquisition, especially for Lepidoptera that feed from porous materials such as rotten fruit. Submicrometer pores (interlegular spaces) in the proboscis, which is initially air filled, provide strong capillary action favoring the uptake of fluid droplets and films, and facilitating fluid withdrawal from substrate pores (Tsai et al., 2011; Monaenkova et al., 2012). The proboscises of Lepidoptera that feed on porous materials, such as rotten fruit, typically have a brush-like lateral series of chemosensilla that aid fluid uptake (Knopp and Krenn, 2003; Monaenkova et al., 2012; Lehnert et al., 2013). Extant members of ancient lepidopteran lineages also have brushy proboscises (Krenn and Kristensen, 2000), suggesting that capillarity had an early selective advantage, perhaps in exploiting limited moisture and sugary exudates (Kristensen, 1984; Grimaldi and Engel, 2005). To acquire fluid from porous materials and liquid films, butterflies rely on capillary instability in the food canal to partition the fluid into bubble trains and reduce the effective viscosity, relative to a continuous liquid column; the bubble train then facilitates the ability of the cibarial pump to draw fluid into the gut (Monaenkova et al., 2012). Lepidoptera, thus, use the dual action of capillarity and cibarial pumping to acquire fluids from porous materials and films. Evolutionary diversification of siphonate Lepidoptera, including those with comparatively smooth proboscises capable of reaching pools of nectar in floral tubes, was associated with the radiation of flowering plants (Barth, 1991; Grimaldi and Engel, 2005).

The mechanism by which Lepidoptera acquire fluid from a pool has been debated (Kingsolver and Daniel, 1995; Borrell, 2006; Borrell and Krenn, 2006). The drinking-straw model, based on the Hagen–Poiseuille equation (Vogel, 2003), was proposed to explain a relationship between the observed flow rate and the pressure differential required from the cibarial suction pump. This model assumes that the food canal is a straight tube, circular in cross-section (Kingsolver and Daniel, 1979; Kingsolver, 1985; Kingsolver and Daniel, 1995). The drinking-straw model is useful for crude estimates of the effects of food canal diameter and fluid viscosity on the feeding efficiency and energetic requirements (Kingsolver, 1985; Kingsolver and Daniel, 1995). The model faces problems, however, when attempting to interpret experimental observations of the uptake of thick fluids (Lehane, 2005). As revealed by X-ray tomography (Monaenkova et al., 2012), the food canal tapers apically to a microscopic slit-like opening. The complex geometry of the food canal draws into question whether the Hagen–Poiseuille model (Kingsolver and Daniel, 1995) of flow through a cylindrical tube can be applied directly to the butterfly proboscis. The distal taper of the food canal (Krenn and Muhlberger, 2002; Monaenkova et al., 2012) presents a structural problem for the drinking-straw model.

To test the hypothesis that the proboscis can function as a Hagen–Poiseuille straw, we examined permeability and flow in the drinking region of the monarch butterfly, Danaus plexippus (Linnaeus).

The ability of a conduit or porous material to transport fluid at the fixed pressure gradient is characterized by the materials parameter called ‘permeability’ (Scheidegger, 1974; Dullien, 1991), denoted

Permeability is a convenient metric for characterizing transport properties of the butterfly proboscis and interlegular pore structure (Monaenkova et al., 2012). Permeability of the interlegular pores in the non-drinking region can be determined by placing a droplet of water on the dorsal legulae and evaluating its uptake kinetics (Monaenkova et al., 2012). The distances between adjacent legulae of a monarch butterfly were estimated as 96±27 and 162±18 nm at 5 and 10 mm distal to the head, respectively (Monaenkova et al., 2012). This droplet method, however, is not reliable for determining the permeability of the drinking region; the spreading and intake rates of a droplet in the drinking region are comparable.

We therefore developed a new method to evaluate proboscis permeability in the drinking region. A proboscis was inserted into a glass capillary tube and immersed in deionized water (Fig. 2). The food canal of the proboscis was initially filled with air. As a result of capillary forces, water spontaneously invaded the proboscis pores (interlegular spaces) and food canal, moving farther into the capillary tube. When the proboscis was filled with water and a meniscus appeared in the capillary tube, the flow rate was measured directly with a Cahn DCA-322 Dynamic Contact Angle Analyzer. By monitoring incremental changes in the weight of a hanging capillary tube, we were able to evaluate flow rates. The flow rates through the capillary tube and the proboscis were the same, allowing us to specify the flow through the proboscis.

When a conduit has a fixed length and the pressure differential is applied to the ends of this conduit, the flow description is reduced to the Cohn–Rashevsky method of design of some parts of the cardiovascular system (Cohn, 1954; Cohn, 1955; Rashevsky, 1960). In the case of a moving meniscus, the length of the liquid column changes with time and the Cohn–Rashevsky model needs to be changed. A more realistic model of a tapered food canal was used and compared with the straight cylinder model. In each tube of the complex conduit, the flow was assumed to follow the Hagen–Poiseuille law, and the conservation of mass and the pressure continuity were used as the boundary conditions at the point where the proboscis met the capillary tube. With this model, the permeability of the capillary tube could be separated from the permeability of the proboscis.

As an illustration of our experimental protocol, we show the experimental L* versus t* curve for a single monarch proboscis (Fig. 4). The solid black line was plotted by adjusting the β-parameter to provide the best fit of the model to the experimental data. To determine other physical parameters of the model, we measured Jurin height Z_c=29 mm and parameter φ≈0.95 deg from representative scanning electron micrographs, and parameters L_p=4.9 mm and R_p=30 μm from optical images. These values were substituted into Eqns 9 and 10 to determine R₀=3.4 μm and H=1.61 mm.

Using this protocol, we analyzed the results of the wicking experiments on different proboscises and obtained their average characteristics (Table 1). Parameters φ≈0.95 deg, L_p=4.9 mm and R_p=30 μm were kept unchanged. The dimensionless parameter β, which depends on the geometrical structure of the butterfly proboscis, varied over a wide range, reflecting the different sizes of the tested proboscises (Table 1).

The following flow rates were obtained from the feeding experiments on droplets of aqueous sucrose solutions: =0.5×10⁻⁹ m³ s⁻¹ (N=8, concentration=25%), =0.3×10⁻⁹ m³ s⁻¹ (N=8, concentration=40%), =0.2×10⁻⁹ m³ s⁻¹ (N=8, concentration=56%). We theoretically analyzed the pressure that would be needed in the butterfly's suction pump to support these flow rates in feeding experiments (Fig. 5). In these calculations, the viscosities of sucrose solutions were measured by magnetic rotational spectroscopy (Tokarev et al., 2013) and the densities of the sucrose solutions were taken from published values (Asadi, 2005) (Table 2).

The proboscis was modeled as a conduit consisting of a truncated cone and a straight tube of length L_p–H. We assumed that the point L_p corresponded to the position where the food canal meets the suction pump (i.e. the pressure at this point must be equal to the pressure in the suction pump). The basic Eqns A7 and A12 (see  Appendix) were applied to determine the pressure at the conjunction point H and at the point L_p. The following materials parameters of the proboscis were used to calculate the pressure differentials at different regions: H=1.5 mm, L_p=14 mm, R₀=5 μm, R_p=30 μm and tanφ=0.0167. The pressure needed to pump fluid through a tapered proboscis was greater than possible at surface atmosphere, whereas the pressure needed in a straight tube was considerably less and within the realm of possibility (Fig. 5).

We observed that butterflies, while feeding, altered the configuration of the proboscis in four ways (Table 3, Fig. 6): (1) apically spreading the galeae (‘galeal splaying’); (2) shifting the galeae along one another in antiparallel movements (‘galeal sliding’); (3) radially expanding and contracting each galea (‘galeal pulsing’); and (4) forcing the proboscis against a surface (‘galeal pressing’). Each butterfly performed at least one of these behaviors while feeding on two to four droplets of 15% sucrose solution.

During galeal splaying, the two galeae separated slightly at their apices over a variable portion of the drinking region, whereas during galeal sliding, the galeae remained paired but moved along one another in antiparallel fashion for a distance of up to three proboscis diameters. During galeal sliding, one galea shifted toward the head, opening the end of the proboscis; the inner face of the food canal of the steady galea remained open for 0.1–90.0 s. Galeal pulsing involved rapid (0.05–0.30 s) expansion and contraction of each galea. Galeal sliding and pulsing were performed by individual butterflies independently or sequentially in the same feeding trial. Butterflies feeding on large drops pressed their proboscises to the substrate, alternately increasing and decreasing the proboscis diameter by as much as 5–8%.

In experiments on monarchs feeding from large droplets intended to simulate pools of liquid, the flow rates vary from 0.2×10⁻⁹ to 0.5×10⁻⁹ m³ s⁻¹. Similar flow rates have been obtained for other species of butterflies (May, 1985). The sucrose solutions that we tested (25–56%) include sugar concentrations in flowers visited by Lepidoptera (Heinrich, 1975; Adler, 1987). These experiments set the metrics for the flow rates of interest. Using theoretical models of proboscises with tapered and smooth channels, we estimated the pressure required by a suction pump to support these, and greater, flow rates. Based on the model that a tapered tube more accurately approximates actual proboscis structure, we found that the pressure differential in the suction pump at the observed flow rates should be greater than 1 atm. Estimates for blood- and sap-feeding bugs support the need for high pressure differentials (Bennet-Clark, 1963; Malone et al., 1999). Even for dilute sucrose solutions (e.g. 10%), the pressure differential is expected to be greater than 1 atm. However, no vacuum pump can produce a pressure differential greater than 1 atm in surface atmosphere (i.e. in an open system). Kingsolver and Daniel also point out that pressure differentials of more than 1 atm would be a mechanical limitation to butterfly feeding (Kingsolver and Daniel, 1979). In the drinking region where the food canal tapers, the pressure drops significantly, and the proximal portion of the proboscis makes a minor contribution to the pressure differential, as indicated (Fig. 5) by the close approximation of paired lines for pressure at the drinking region (P_H) and in the cibarial pump (P_p). Thus, more than 1 atm of pressure differential would need to be generated by the pump or another mechanism(s) to overcome the restriction of the tapered food canal in the drinking region; less force would be needed in the absence of a taper.

A tapered proboscis and food canal are characteristic of Lepidoptera (Krenn and Muhlberger, 2002); thus, the role of the taper in influencing the pressure differential is likely to be widespread among butterflies and moths. Moreover, a tapered food canal might be characteristic of most, if not all, fluid-feeding insects with an elongated proboscis, regardless of fluid source or type. Thus, insects such as blood-sucking true bugs and mosquitoes, sap-feeding planthoppers and nectar-feeding flies all have a tapered food canal (Christophers, 1960; Bennet-Clark, 1963; Malone et al., 1999; Karolyi et al., 2013). Butterflies, however, have a distinct feature; the proboscis has pores along its length that provide opportunities for air to enter or cavitation to occur. When butterflies use the cibarial pump to move liquid up the food canal, menisci in the interlegular slits deform to follow the pressure gradient. A similar effect can be observed by stretching a sponge completely filled with water; the water moves from the sides of the sponge, reflecting the change of pressure in the liquid column. When suction pressure is high, an air bubble can enter the food canal through the interlegular slits, supporting the partitioning of the liquid column. Also, to obtain feeding rates, we submersed the butterfly proboscis in fluid to avoid air in the food canal. However, under natural feeding conditions, air would enter the porous proboscis. Thus, the butterfly proboscis is not a closed system.

We recently showed that structural features of the drinking region, including tapering of the food canal, facilitate fluid acquisition by enhancing capillary action, allowing butterflies to drink from porous surfaces, such as damp soil (Monaenkova et al., 2012; Lehnert et al., 2013). Additional benefits of a tapered proboscis, with a concomitantly tapered food canal, include reduced costs associated with cuticular thickening (Bauder et al., 2013) and the ability to reach fluid sequestered in small recesses. The benefits of a tapered food canal, however, are countered by increased viscous friction (Batchelor, 2000) that hinders flow. However, the required pressure can be significantly reduced when the taper is ignored, as in previous models (e.g. Kingsolver and Daniel, 1979); in most cases the required pressure drops below atmospheric pressure for the same flow rate.

Optimizing uptake from liquid films and menisci, versus pools, therefore, is contradictory; a small lumen enhances capillarity (Monaenkova et al., 2012), whereas a large lumen enhances flow (Kingsolver and Daniel, 1995; Vogel, 2003). In other words, fluid uptake by the butterfly proboscis presents a paradox: a simple drinking-straw model that ignores structural features of the proboscis avoids the catastrophic pressure differential, whereas incorporating actual proboscis structure – the taper – into the model causes the required pressure to skyrocket.

We suggest that the mechanism of fluid uptake is more complex than a strict drinking-straw analogy and that the paradox can be resolved by a suite of behavioral strategies (Table 3). Galeal sliding could adjust the fluid–pressure differential by changing the size of the interlegular pores and terminal opening and by reducing the active, tapered length of the food canal. The ability to slide the galeae in antiparallel movements (Krenn, 1997) is well documented for moths that pierce animal and plant tissues (Büttiker et al., 1996); it also occurs in nectar-feeding Lepidoptera (Kwauk, 2012) and could serve to adjust the pressure differential. Galeal sliding might facilitate meniscus formation and transport if the amount of fluid is minute and a droplet is trapped in the food canal. Galeal sliding also could facilitate debris removal from the legular linkage. Galeal splaying opens the distal tip of the proboscis and should function to reduce the pressure differential by increasing the diameter in the tapered region. Although we observed this behavior in the monarchs in only two instances, we have observed it regularly in Gulf fritillaries, Agraulis vanillae. Galeal pulsing might be controlled by processes similar to those that drive coiling and uncoiling of the proboscis. Uncoiling, for example, is achieved by increased hemolymph pressure in each galea, brought about by contractions of the maxillary stipital muscles, whereas coiling is achieved by contractions of intrinsic galeal muscles (Wannenmacher and Wasserthal, 2003). When hemolymph is forced from the head into the galeal lumen, it would be expected to travel in a rapid wave, supporting peristaltic pumping of fluid and increasing interlegular spacing and the diameter of the food canal. Galeal pressing would alter the food canal diameter, the legular spacing and perhaps also the surface contact area for capillarity.

We previously showed that the full cibarial pump cycle takes 0.45–0.70 s at 25°C (Monaenkova et al., 2012). Galeal sliding can be slower, lasting 0.1–90 s, and can, therefore, be independent of the pump; the proboscis would be able to remain open for multiple pump cycles. Galeal pulsing occurs faster than the rate of contraction and expansion of the suction pump and, therefore, might facilitate flow within the first half of the cycle when the pump is open. More experiments are required to test this hypothesis.

Proboscises of unfed monarch butterflies (Shady Oak Butterfly Farm, Brooker, FL, USA) for scanning electron microscopy (Fig. 1) were straightened with crisscrossed pins on foam, dehydrated through an ethanol series (80–100%), dried in hexamethyldisilazane, mounted with double-sided conductive adhesive tape on aluminium stubs, and sputter coated with platinum for 3 min. Imaging was done with a Hitachi TM3000 (Hitachi High Technologies America Inc., Alpharetta, GA, USA) at 15 kV, composite image mode and full vacuum.

Coiled proboscises of seven monarch butterflies were soaked in deionized water for 12 h to soften and uncoil them; deionized water was used to maintain consistency across measurements and instruments. They were straightened several millimeters every 2 h and fixed in position with pins. Straightened proboscises were examined with an optical microscope to confirm that the galeae did not separate apically and to measure the diameter of the proboscis.

To understand fluid uptake from pools of liquid, feeding behavior was observed under a stereomicroscope at 22±3°C. Monarch butterflies (N=5) were held by their wings, and their proboscises were threaded into glass capillary tubes (internal diameter=0.4 mm). A 15% sucrose solution was introduced into the opposite end of the capillary tube via flexible tubing. Butterflies were allowed to feed for 2–3 min and the behavior was video recorded (Dalsa Falcon 1.4M100 XDR). The drinking region of the proboscis was submersed in fluid throughout observations to maintain fluid in the food canal.

We also used an inverted microscope to observe feeding behavior of butterflies (N=5) from droplets (1–2 ml each) of 15% sucrose solution placed on the microscope stage. Each butterfly was exposed to the droplets for 5–10 min. The drinking region of the proboscis remained submersed during feeding. Within a period of 5–10 min, each time a droplet was taken up by the butterfly, an additional droplet was added; each butterfly took up a total of two to four droplets.

To estimate uptake rate, butterflies were fed from large droplets (radius r_d=3–4 mm, h_d=2–3 mm) of sucrose solution (Fig. 7A). The droplets were modeled as hemispherical caps with volume V_d=(πh_d/6)(3r_d²+h_d²). We therefore could minimize the effect of confinement and associated counter-pressure caused by viscous drag typically present (Cohn, 1954; Cohn, 1955; Rashevsky, 1960) when a butterfly is fed from a tube. Once the butterflies began drinking, they were not restrained at the stage. The feeding process was filmed with a high-speed camera (Motion ProX3, Redlake). The images were analyzed with ImageJ software (NIH), and the change in droplet volume was plotted as a function of time; the results were fitted with a straight line, with the slope indicating the uptake rate (Fig. 7B).

The Cahn DCA-322 allowed incremental changes in the sample mass to be detected with 1 μg accuracy. Each straightened proboscis was cut with a razor blade (single edge, Stanley) 5 mm proximal to its tip, and the cut end was inserted into a capillary tube. The inserted portion was ~3 mm long; the remaining (distal) 2 mm, which included the drinking region, protruded from the capillary tube. The tube with the proboscis was placed in a rectangular vessel (polystyrene, 12.5×12.5×45 mm, Plastibrand) and capped (Cuvette cap square, Fisher Scientific). A 3 mm diameter hole in the cap allowed the capillary tube to hang freely in the container, but permitted the Cahn balance arm to connect to it (Fig. 2A). The tip of the proboscis was suspended above the water, without touching it (Fig. 2B). A drop of motor oil (Castrol, SAE 5W-30) was used to seal the space between the hole edges and external wall of the tube, preventing evaporation and serving as a lubricant to enable the tube to move during wicking experiments. The tip of the proboscis was brought in contact with the water by raising the stage with the water vessel at 20 μm s⁻¹ (Fig. 2C). From the control experiments, we found that the trapped air bubble separating the top of the sealed vessel from the water surface required about 1 h to reach full saturation with water vapor (99% relative humidity, RH) when the water filled the vessel to a height of y=30 mm.

Two loops were used for force measurements (loop a and loop b; Fig. 2A). Loop a could measure a force up to 1.5 mN; loop b was less sensitive and could measure a force up to 7.5 mN. A reference weight on loop c was used to counterbalance the sample weight, allowing maximum sensitivity. The ratio of the applied masses on the three loops (a:b:c) was 1:5:1, meaning that a 100 mg sample on loop a or loop c created the same torque as a 500 mg sample on loop b.

A special function of the Cahn DCA-322 – the zero depth of immersion (ZDOI) – can set the starting moment for weight measurements. The moment when the proboscis tip first touched the water was chosen as the ZDOI point; we experimentally found that this point could be distinguished by setting a minimum force threshold of F_min=5 μN. With this choice of the ZDOI point, if the measured force was less than 5 μN, the stage continued upward movement. The balance was zeroed; when the stage moved up, the force became negative due to friction and wiggling of the capillary tube (Miller et al., 1983). However, this background noise was less than 5 μN, and was not recorded (Fig. 8). When the proboscis touched the water, the force rapidly increased, reflecting the action of the wetting force, which was significantly larger than the ZDOI threshold (Miller et al., 1983). The friction on the capillary tube exerted by the lubricating layer of oil was always smaller than the threshold value F_min.

When the tip of the proboscis touched the water and the measured force became greater than F_min, the stage continued to rise up to 0.1 mm at 20 μm s⁻¹, confirming that the proboscis tip was immersed in water. A negative slope in Fig. 8 was associated with the immersion process and was caused by buoyancy and increased viscous friction forces at the meniscus when the proboscis became immersed (Miller et al., 1983). The stage was then stopped. The entire setup was allowed 1 min to stabilize before acquiring the force change for the next 60 min (red line, Fig. 8). After the stage was stopped, a meniscus inside the capillary tube was observed, and all incremental changes of force detected by the analyzer were attributed to the incremental change of weight of the water column invading the tube as a result of capillary action.

The surface tension of deionized water was measured using the Wilhelmy method with the Cahn DCA-322 (Adamson and Gast, 1997). A platinum wire (250 μm diameter) was used as a standard probe (Miller et al., 1983). The wire was cleaned with ethanol and heated to red-hot with an oxidizing flame. The Wilhelmy equation F=σpcosθ was used, where F is the wetting force and p is the perimeter of the probe. The contact angle was assumed to be zero, θ=0 deg; hence, cosθ=1 because of the high surface energy of the platinum (Miller et al., 1983). Deionized water was measured three times, yielding an average surface tension of σ=71.4±0.5 mN m⁻¹.

The contact angle of the internal meniscus was measured indirectly by analyzing the Jurin height (Z_c), defined as the maximum possible height of the liquid column co-existing with the liquid reservoir (Jurin, 1917–1919): Z_c=P_c/ρg=2σcosθ/(ρgr). Deionized water (η: 1 mPa s, ρ: 1000 kg m⁻³) in a glass capillary tube with a 250 μm radius (r) was used to determine the Jurin length at room temperature (20–21°C). Three experiments were performed, and the average Jurin height was calculated as Z_c=0.029±0.001 m.

We thank Bethany Kauffman, Steven Rea, and Taras Andrukh for helping with high-speed imaging of butterfly feeding behavior.