The fangs of the spitting cobra were placed in a small plastic vessel and stabilized with cotton watting. The fangs were scanned from tip to base with a micro-computer tomograph (MCT, μCT 20, Scanco, Bassersdorf, Germany) and visualized in three-dimensions with the software Amira® (Amirasoft ltd., Germany). Also, scanning electron microscopy (SEM) was used as a control for the resolution of the MCT data. For scanning electron microscopy, we prepared a parasagittal section of dried fangs by using a diamond drill to expose the venom channel. The fangs were placed on aluminum stabs using a liquid conductant graphite. Afterwards fangs were sputter-coated with silver and scanned in a Cambridge Stereoscan Microscope (Cambridge Instruments, Oxford, England).

The surface tension of the venom was measured in a tensiometer (OCA 30, DataPhysics Instruments GmbH, Filderstadt, Germany) at 20°C. About 100 µl of venom was filled into a syringe connected to a cannula (radius 1 mm). Small droplets of venom were pumped out of the cannula to create a hanging droplet. The droplet was photographed with the OCA camera and its surface tension was calculated with the OCA software. Fifteen measurements were made for each of two individuals. In addition, the venom was weighed with a high precision scale (Bp 110 S, Sartorius AG, Germany). Thereafter, the density ρ of the venom was calculated according to the equation ρ = G/V, with G = weight and V = volume. All measurements were conducted at 20°C room temperature and normal air pressure. Density was expressed in g cm −3 . Ten measurements were made for each individual (N = 2).

Adult spitting cobras (Naja pallida, N = 7) were kept in glass containers at a temperature of 20–27°C and a humidity of at least 70%. Naja pallida were captive bred. All snakes were regularly fed with small to medium sized live rodents and given water ad libitum. An authorization to house the cobras has been obtained. All animals were housed at the Institute of Zoology of the University of Bonn in accordance with regional laws to the keeping of venomous snakes as well as applying rules for laboratory animals. We did not have IACUC approval of experiments which is neither required nor a common procedure for experiments in Europe. All experiments were according to the Principles of Animal Care. Animals were not anaesthetized. Snakes were gently held behind the neck before a jar covered with a para-film was presented in front of their mouth. The snakes readily bit through the para-film injected their venom into the jar. After milking, the venom is immediately transferred into small plastic vessels (Eppendorf GmbH, Germany). The volume of venom yielded in each milking process is measured. Plastic vessels are stored at 10°C to prevent any decay of the venom until measurement. Venomous snakes substitute their fangs every 6–8 weeks. Thus, the snakes' mouths were inspected every 4–6 weeks in order to pick the substituted fang. The substituted fang normally gets lost out of the fang membranes with the snakes next meal. We picked the loose fang out of the membranes with a forceps, cleaned in an ultrasonic cleaner and air-dried for the morphological investigations. For each individual, the viscosity of the venom is measured in a rotational rheometer (Bohlin Gemini 2, Bohlin Ltd., USA). The venom is transferred directly into the specimen chamber of the rheometer. The specimen chamber is immediately closed and sealed with a special solvent trap to prevent dehydration of the venom. For each measurement, a volume of about 150 µl venom liquid is used. Measurements were conducted at a temperature of 20°C and at continuously increasing shear. Measurements lasted for about 15 minutes. They were repeated three times (with breaks of five minutes in between two measurements) to verify that the values were reproducible.

The fluid-dynamical model of the venom channel

Venom-gland contraction provides the only force for venom expulsion [13], [14]. Young et al. [15] measured the venom pressure at the fang tips of a spitting cobra (N. pallida). While this has been done successfully in the past, it is impossible to measure in vivo the pressure build-up at the entrance of the venom channel. This information – which is important for the analysis of the flow in the fang model – can, however, be obtained with a numerical simulation, provided that the geometry of the venom channel and the flow rates of the venom are known. Therefore, the real venom channel was transferred into a model with the aid of computer micro-tomography. The 3D structure of the channel in the model was first reconstructed from the images of the cross-sections of a cobra fang and then smoothed mathematically. Due to its complex geometry the channel was subdivided along its long axis into three parts (cf. results section). The 3D computer-aided design model of the venom channel was created and transferred into a computational grid using a grid generation tool (ANSYS 12.1 ICEM CFD, see Appendix S1). The venom was treated as incompressible non-Newtonian fluid. A standard approach to describe the rheological behavior of non-Newtonian media with a shear-thinning behavior is the power-law model [16], which was applied to the current data (see below and Eq. 1) both with lower (μ venom min ) and upper (μ venom max ) bounds for the dynamic viscosity. (1)Herein, is the shear rate. The parameters of the model are adapted from the rheological measurements as follows: the minimum and the maximum dynamic viscosity bounds are and , the consistency index is and the power-law index is .

The flow regime was assumed to be laminar because the channel geometry was of micro-scale. This is justified by estimation of the maximum Reynolds number defined for a hypothetical Newtonian case when the minimum value of dynamic viscosity μ min is used and the characteristic streamwise velocity u inlet at the channel inlet with an equivalent diameter of d inlet . The Reynolds number, which defines the ratio of inertial forces to viscous forces in the fluid [17] reads as follows: (2)with the characteristic velocity in the channel inlet given by . Herein, Δt is the total venom expelling period, ΔV is the venom volume during one spit, and d inlet is the inlet diameter of the channel when the cross-sectional area is calculated with a circular shape. The parameter ρ is the density of the venom. The resulting Reynolds number, Re max , attains values of less than 100 which is well below the critical Reynolds number of Re crit = 2300, where turbulence is observed to start in channel flows [17]. Therefore, no turbulence model needs to be taken into account in the flow simulations.

A further dimensionless number to be taken into account is the so-called Strouhal number which is defined as the ratio of the characteristic time scale of the fluid, the time a fluid element needs to travel along the channel relative to the total expelling time period: (3)where L channel is the length of the venom channel. When the Strouhal number is well below unity [17] the flow process can be regarded as quasi-steady. The Strouhal number for the case of the venom channel flow has a value about Sr = 0.02. Therefore, steady-state simulations of the flow were justified. As a consequence, each phase in the flow pulse can be simulated independently. In our simulations we concentrated only on the peak flow situation where the maximum velocity is reached in the venom channel during the spitting process.

An a-priori estimation of the possible existence of secondary flow structures in the venom channel due to the strong curvature of the bend at the distal end can be discussed by means of the so-called Dean number, which has been deduced from the centrifugal flow instability in curved pipe flows [12]. The non-dimensional Dean number (Dn) characterizes the influence of these instabilities on the generation of secondary flows in a curved bend (4)where R curv denotes the curvature of the bend. The Dean number, in the case of curved venom channel flow, is on the order of 100 when we use the curvature radius of the sharp bend at the distal end of the channel as a representative value (compare Table 1, see below). Because the Dean number is not low, we expect to see secondary flow structures in the results of the simulations.

For a validation of the numerical simulations, a transparent experimental model was created. The model was scaled up 56∶1 to ease visualization of flow features. A water/glycerine mixture was chosen to match the refractive index of the transparent material of the model. The fluid exhibited Newtonian behaviour; therefore, the numerical model described in the last section was validated for the Newtonian case. In order to ensure similarity of the flow structures in the model experiment and the validation simulations, the Reynolds number was set equal. The resulting parameters of the flow in the scaled-up model are summarized in Table 2.

The steps for the generation of the transparent model are given in Fig. 1. With the aid of the MCT-data, a negative form was created out of wax. In a further step, silicon was casted around the wax form and the wax then removed, resulting in a transparent model of the cobra's venom channel. The experimental measurements were carried out in the test facility described in Fig. 2 and below. The facility consisted of an upper and a lower reservoir, which were interconnected on one side by the feed flow and on the other side by the return flow. The silicone model was integrated into the lower reservoir and supplied by the liquid from the upper reservoir. To assure constant inflow and outflow conditions, the height difference Δh between the two reservoirs was kept constant. A light sheet (about 2 mm thick) was generated by a laser (New Wave, Pegasus, high-speed, dual cavity, 10 mJ @1 kHz) and light sheet optics. The particles (Vestosint, Evonik Degussa GmbH, mean diameter 20 µm) in the flow were illuminated by the laser sheet and filmed with a high-speed camera (Photron, APX RS , 1024×1024pix2 @ max 3000 fps), which was arranged perpendicular to the light sheet. An area of about 50×50 mm was captured with a separation time of 200 µs at 1000 Hz. The post-processing of all numerical and experimental results was carried out in TECPLOT 360 (Tecplot Inc.).