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First published online October 18, 2006
Journal of Experimental Biology 209, 4398-4408 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02506
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Air-flow sensitive hairs: boundary layers in oscillatory flows around arthropod appendages

T. Steinmann1, J. Casas1,*, G. Krijnen2 and O. Dangles1

1 Institut de Recherche sur la Biologie de l'Insecte-UMR CNRS 6035, Faculté des Sciences et Techniques, Université François Rabelais, Parc de Grandmont Avenue Monge, 37200 Tours, France
2 MESA+ Research Institute, Transducers Science and Technology group Faculty of Electrical Engineering, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands


Figure 1
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  		Fig. 1. (A) Longitudinal, circumferential and radial components of an oscillating flow acting on a hair perpendicular to a cylindrical substrate. (B) Principle of stroboscopic measurement of a flow oscillating at high frequency with a low-frequency sampling device. In this example, we take pairs of images (separated by 500 µs) at a frequency of 30 Hz of a flow oscillating at 33 Hz. The pseudo time increment is 3 ms and we need 10 pairs to sample a full period of the flow oscillations. We repeat this procedure five times and proceed then to a phase average.

 

Figure 2
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  		Fig. 2. Vector field of velocity amplitude around a cylinder of 1 mm diameter at four frequencies in transverse flow. Vectors are of constant length.

 

Figure 3
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  		Fig. 3. Velocity profiles for longitudinal and transverse flows at four frequencies around a cylinder of 1 mm diameter. Holtsmark solutions for transverse flow (lines) and particle image velocimetry (PIV) measurements (points) at angles of 90° (red circles), 60° (black circles), 45° (green circles), 30° (orange circles) and 15° (blue circles). Humphrey solution for longitudinal flow (grey line) and corresponding PIV measurement (squares). The distance above the cylinder at which both components are equal is highlighted (arrow).

 

Figure 4
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  		Fig. 4. Temporal evolution of the velocity field around a cylinder of 1 mm diameter in a 120 Hz transverse flow. The phase interval separating each vector field is 0.06 rad.

 

Figure 5
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  		Fig. 5. Temporal evolution of the instantaneous velocity in longitudinal and transverse flows over a cylinder of 1 mm diameter at 120 Hz. Humphrey solution for longitudinal flow (dotted line) and particle image velocimetry (PIV) measurement (grey circles). Holtsmark solutions for transverse flow (lines) and PIV measurements (points) at angles of 90° (red circles) and 45° (black circles).

 

Figure 6
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  		Fig. 6. Phase shift between far field and boundary layer flow as a function of distance from the cylinder at 120 Hz. Analytical solution (Eqn 3) of the phase displacement (dotted line) and particle image velocimetry (PIV) measurement (open circles) for a longitudinal flow. Numerical solution (line) and PIV measurement (filled circles) for a transverse flow at a circumferential angle of 90°.

 

Figure 7
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  		Fig. 7. Viscous drag torque for short and long hairs in transverse and longitudinal flows. Flow oscillations, f=120 Hz; flow velocity, V=35 mm s-1; hair lengths, 1500 µm and 300 µm.

 

Figure 8
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  		Fig. 8. Maximal hair displacement as a function of flow frequency (fflow) and circumferential angle ({theta}). (A) Maximal hair displacement of long hairs positioned on a cylinder of 1 mm diameter, for attack angles of 90° (squares, transverse flow), 50° (triangles), 30° (circles) and 0° (broken line, longitudinal flow). (B) Maximal hair displacement of short hairs positioned on a cylinder of 1 mm diameter, for impact angles of 90° (squares, transverse flow), 37° (triangles), 30° (circles) and 0° (dotted line, longitudinal flow). For both computations, U0=35 mm s-1.

 

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© The Company of Biologists Ltd 2006