Dermal Denticles of Three Slowly Swimming Shark Species: Microscopy and Flow Visualization

Shark skin has for many years inspired engineers to produce biomimetic structures reducing surface drag or acting as an anti-fouling layer. Both effects are presumed to be consequences of the structure of shark skin that is composed of arrays of so-called dermal denticles. However, the understanding of the full functional role of the dermal denticles is still a topic of research. We report optical microscopy and scanning electron microscopy of dermal denticles from three slowly swimming shark species for which the functional role of the dermal denticles is suggested as one of defense (possibly understood as anti-fouling) and/or abrasion strength. The three species are Greenland shark (Somnosius microcephalus), small-spotted catshark (Scyliorhinus canicula) and spiny dogfish (Squalus acanthias). Samples were taken at over 30 different positions on the bodies of the sharks. In addition, we demonstrate that the flow pattern near natural shark skin can be measured by micro-PIV (particle image velocimetry). The microfluidic experiments are complemented by numerical flow simulations. Both visualize unsteady flow, small eddies, and recirculation bubbles behind the natural dermal denticles.

. Map of skin sample positions on a generic shark.
. Figure S2. SEM images of dermal denticles from area c1 of a small spotted catshark (female, TL 59 cm). Scalebars are 500 µm (left image) and 200 µm (right image). Images courtesy of Thomas Erik Bohn Smitshuysen and Emil Christian Jensen. For the Greenland shark, the areal density is found by counting the number of denticles in a 15mm x 15mm area, visualized by optical microscopy. For the sections with multiple lengths measured, the mean of the lengths are calculated. These results are shown in Fig. S6(a). Even though the points do not form a perfect line they appear in a clear tendency of large denticles associated with low density.

Supplementary information
For the small spotted catshark, detailed images of the dermal denticles were obtained by SEM. From the microscope images of the denticles, the length of a few denticles and the total number of denticles in each frame was noted. Fig. S6(b) shows Figure S3. SEM pictures of a denticle from the Greenland shark (female, TL 470cm). This denticle was positioned right in front of the pectoral fin, position pj. In the closeup in (b) it appears that the denticle has a smooth and a rough side. Scalebars are 1mm in (a) and 200µm in (b). The shape of the dermal denticle is quite typical for all areas (other than the nose) investigated.
the areal density versus the length of denticles in a semi-logarithmic coordinate system. As one could expect, the longer the denticles, the lower their areal density, yet we cannot conclude a specific power law dependence.
The dermal denticles of the spiny dogfish were also investigated by SEM. Results are collected to extract the areal density as displayed in Fig. S7.
We searched for signs of bristling in the small-spotted catshark during a single microscopy session, conducted on an alive, adult shark of a length of about 70 cm, generously made available to us by The Øresund Aquarium. The shark was positioned under a stereomicroscope in dry conditions for a brief amount of time, during which we visualized a region on the tail and a region of the dorsal fin. Bending the fin was attempted, in order to possibly induce a condition that would force the dermal denticles to bristle should they have a natural tendency to do so. No sign of bristling was observed, however.
One µ-PIV recording is shown in Fig. S8. As explained in the main text, the flow was kept at 5ml/min throughout the whole experiment through the chamber with a crosssection of 3mm × 4mm, corresponding to a flow velocity of approximately 7 mm/s along the chamber. With a typical length of 600 µm of the dermal denticle as the length scale, this flow velocity corresponds to a Reynolds number of 4. Fluorescent seeding particles with a diameter of 0.86 µm were added to the water used in the flow experiment. Measurements where conducted with the 20× objective. In all of these, 30 picture pairs were taken with a time delay of 8 ms, 10 ms and 12 ms between the paired images. A vector field is calculated for each of the 30 picture pairs using standard PIV processing tools, thus creating a short movie of 30 frames. The relatively low number of picture pairs was a compromise that ensured constancy in the overall imposed flow while still obtaining trustworthy micro-PIV vector fields. A time averaged vector field of the 30 frames was then calculated. At this relatively low flow speed, the streamlines point almost straight away from the skin but vortices appear under the tips of the denticles Figure S4. Examples of optical microscopy images of dermal denticles from a Greenland shark (female, TL 470 cm), most images have only one dermal denticle within the field of view. Scale bar is 1mm in all cases. Upper line: Dermal denticles from area b1, b2, and b4. Second line: Dermal denticles from area b5, b6, and b9. Third line: Dermal denticles from area b10, b11, and b12. Fourth line: Dermal denticles from area c3, c4, and c5. Figure S5. Examples of optical microscopy images of dermal denticles from a Greenland shark (female, TL 470 cm), most images have only one dermal denticle within the field of view. Scale bar is 1mm in all cases. Upper line: Dermal denticles from area d1, d2, and d3. Second line: Dermal denticles from area g2, p1, and p3. Third line: Dermal denticles from area p4, p5, and p6. Fourth line: Dermal denticle from area pj.   Figure S6. Plot of areal density of denticles around the body of different sharks against their average length in the measurement area. Part (a) gives results for a greenland shark (female, TL 470 cm). Notice that the y-axis is logarithmic. The errorbars for the length goes from the smallest measured to the highest measured length in the specific section. When assigning errorbars for the density itself, we assume that counting statistics is Poissonian, i.e., the error in the count number is assigned to be equal to the square-root of the count. In the main plot, errorbars are shown as a box connected to the corresponding point, insert shows the same data without the error-box. The colours represent different areas of the shark; blue is the body, green is the caudal fin, orange is the dorsal fin, grey is by the gills and purple is the pectoral fin. Darker colour signify a higher number in the area name e.g. b12 is pictured in darker blue than b4. Note that pj is in a lighter purple than p1. Part b) shows results for denticles of a small spotted catshark (male, TL 72 cm), with a similar color coding. Horizontal error bars go from smallest measured to longest measured length. Vertical error bars are too small to see in the plot.

Elements analysis
The composition of elements in the dermal denticles of any shark is crucial for the drag reduction of the skin. If the denticles are too soft, they will bend when experiencing the force from the Figure S7. The mean length and mean width of the dermal denticles of the spiny dogfish (female, TL 76 cm) plotted versus the density. The relation is fitted with a 1st degree polynomial. Both axes are on logarithmic scale. Figure S8. Vector field of flow near denticles from the small spotted catshark (male, TL 72 cm, denticle from pectoral fin) with a 20× objective. A reference vector of speed 0.01m/s is shown in top corner. Denticles are shown upside down and pointing to the right, a microscope image of a denticle from the same area, scaled to match the dimensions of the field of view, is overlaid to roughly illustrate the position of the denticle which is otherwise hardly visible in the image. The water is flowing to the right and is illustrated by vector arrows in colours between blue (slow) and red (fast), ranging between 0 µm/s and 3 µm/s, as indicated in the color map. The field of view covers an area of width 285 µm and height 215 µm.