Table 1.
Parameters used for the CFD study.
Table 2.
Parameters of the scaled-up (56∶1) model case.
Figure 1.
Steps for the generation of the model: mold for wax model (a), cast-wax model (b), Plexiglas casing (c), transparent-silicone model (d).
Figure 2.
Flow circuit (left) arrangement for flow measurements inside the model of the fang (right).
Figure 3.
Average viscosities of the venom of N. pallida (dots) as function of shear rate (s−1) expressed on a logarithmic scale.
Note that the viscosity decreased with increasing shear rate and remained nearly constant for shear rates >3.7 101 s−1.
Figure 4.
SEM image of a parasagittal section (d = dentin) of a N. pallida fang.
(A) The exit orifice (e) as well as the symmetrical ridges (r) are displayed. (B) SEM image of the inner surface of the channel in high magnification. The surface is smooth in the micron dimension. No microstructures are visible that might affect the venom flow.
Figure 5.
3d-reconstruction of a N. pallida fang obtained from MCT data.
(A) Lateral view into the venom channel (v). The cutting planes and viewing angles of images B and C are indicated. (B) Dorsal view towards the exit orifice (e). Note the symmetrical ridges (r) above the exit orifice. (C) View from the middle of the venom channel towards the exit orifice, which is oriented downwards in this view. Scale bars: 500 µm (A, B) and 200 µm (C).
Figure 6.
Computational domain and mesh topology in the region of interest (ROI) of the venom channel.
Table 3.
Boundary conditions used for the simulations.
Figure 7.
Cross-section positions at various downstream locations: lateral (top) and top view (bottom).
S indicates the midline of the channel. Note the curvature of the midline in the top graph.
Figure 8.
Normalized cross sectional area along the midline (s) of the channel.
Solid line/dots: venom channel with ridges; crosses: venom channel without ridges (reference case); Ainlet = 1.963e-07 m2; a to p: Positions of cross sections are indicated in Fig. 7.
Figure 9.
PIV measurements of the flow (A) and CFD results of the venom flow (B).
Graphs show sectional streamlines in the mid-coronal cross-section and the contour of the velocity magnitude. (C) CFD result: vectors indicate the streamwise velocity profiles. A transformation of the velocity profile along the venom channel is visible.
Table 4.
Calculated pressure and velocity values for Cases 1 and 2.
Figure 10.
Case 1: pressure distribution and streamlines in the frontal midplane for the Newtonian (A) and the non-Newtonian case (B). (C) Integral pressure in the sections along the midline s of the channel for the Newtonian case (cf. Fig. 7). Reference case: pressure distribution and streamlines in the frontal midplane for the Newtonian (Case 2 = reference) case (D). (E) Integral pressure in sections along the midline s of the venom channel (cf. Fig. 7).
Figure 11.
Isosurface plots of regions of concentrated helicity indicating the pre-conditioning and generation of secondary flow structures for Case 1 (top), and 2 (bottom).
The normalized helicity is +0.05 (red) and −0.05 (blue).
Figure 12.
Cross-sectional distribution of helicity with sectional streamlines at various downstream locations (cf. Fig. 7): blue −0.05, red +0.05.
Min. and maximum values of relative helicity are given. Case 1 (A) and reference case (B).
Figure 13.
Case 1: (A) Flow structures at the outlet.
The velocity magnitude is color-coded. (B) Velocity profile plots in sections A and B from (A). Contours of velocity components (color-coded) ux (C) and uz (D) at the outlet plane.
Figure 14.
Mean velocity (arrow length) of the liquid in the sections given in Fig. 7 for Case 1 (top) and reference case (bottom).