The use of the dimensionless Womersley number to characterize the unsteady nature of internal flow

Journal of Theoretical Biology

Volumn 191, Issue 1, 1998, Pages 63-78

  Loudon, Catherine ^a   Tordesillas, Antoinette ^b  

^a UNIVERSITY OF KANSAS   (United States)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; FLOW; MATHEMATICAL MODEL; PRIORITY JOURNAL;

EID: 0344222187     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0564     Document Type: Article

References (77)

1. AL TAWEEL, A. M. & LANDAU, J. (1976). Mass transfer between solid spheres and oscillating fluids. A critical review. Can. J. Chem. Engin. 54, 533-539.
2. ALTNER, H. & PRILLINGER, L. (1980). Ultrastructure of invertebrate chemo-, thermo-, and hygroreceptors and its functional significance. Int. Rev. Cytol. 67, 69-139.
3. ATEMA, J. (1985). Chemoreception in the sea: adaptations of chemoreceptors and behavior to aquatic stimulus conditions. Soc. Exp. Biol. Symp. 39, 387-423.
4. ATEMA, J. (1987). Temporal aspects of chemical stimuli: natural stimulus distributions, receptor cell adaptation, and behavioral function. In: Olfaction and Taste IX. Annals of the New York Academy of Sciences, vol. 510 (Roper, S. D. & Atema, J., eds), pp. 130-132. New York: New York Academy of Sciences.
5. ATEMA, J. (1988). Distribution of chemical stimuli. In: Sensory Biology of Aquatic Animals (Atema, J., Fay, R. R., Popper, A. N. & Tavolga, W. N., eds), pp. 29-56. New York: Springer-Verlag.
6. CAMHI, J. M. (1984). Auditory worlds. In: Neuroethology: Nerve Cells and the Natural Behavior of Animals, pp. 157-210. Sunderland: Sinauer Associates, Inc.
7. CARO, C. G., PEDLEY, T. J., SCHROTER, R. C. & SEED, W. A. (1978). The Mechanics of the Circulation. Oxford: Oxford University Press.
8. CHOI, Y. & WROBLEWSKI, D. E. (1993). Visualization of transition to turbulence in oscillatory flow through a rigid cast model of the central airways. Adv. Bioeng. 26, 169-172.
9. CHRISTENSEN, T. A. & HILDEBRAND, J. G. (1988). Frequency coding by central olfactory neurons in the sphinx moth Manduca sexta. Chem. Senses 13, 123-130.
10. CONDORET, J. S., RIBA, J. P. & ANGELINO, H. (1989). Mass transfer in a particle bed with oscillating flow. Chem. Engng Sci. 44, 2107-2111.
11. COOPER, W. E. (1994). Chemical discrimination by tongue-flicking in lizards: a review with hypotheses on its origin and its ecological and phylogenetic relationships. J. Chem. Ecol. 20, 439-487.
12. DANIEL, T. L. (1984). Unsteady aspects of aquatic locomotion. Am. Zool. 24, 121-124.
13. DANIEL, T. L., KINGSOLVER, J. G. & MEYHOFER, E. (1989). Mechanical determinants of nectar feeding energetics in butterflies: muscle mechanics, feeding geometry,and functional equivalence. Oecologia 79, 66-75.
14. DENNY, M. W. (1988). Biology and the Mechanics of the Wave-swept Environment. Princeton: Princeton University Press.
15. DENNY, M. W. (1993). Air and Water: The Biology and Physics of Life's Media. Princeton: Princeton University Press.
16. DENTON, E. J. & GRAY, J. A. B. (1989). Some observations on the forces acting on neuromasts in fish lateral line canals. In: The Mechanosensory Lateral Line: Neurobiology and Evolution (Coombs, S., Görner, P. & Münz, H., eds), pp. 229-246. New York: Springer-Verlag.
17. DESIMONE, J. A. (1981). Physicochemical principles in taste and olfaction. In: Biochemistry of Taste and Olfaction, pp. 213-229. New York: Academic Press.
18. DUSENBERY, D. B. (1992). Sensory Ecology; How Organisms Acquire and Respond to Information. New York: W.H. Freeman.
19. ELLINGTON, C. P. (1984). The aerodynamics of flapping animal flight. Am. Zool. 24, 95-105.
20. 2 transfer in Ringer-perfused gills of the eel, Anguilla austrails. J. Exp. Zool. 227, 371-380.
21. FEI, D.-Y., KRAFT, K. A. & FATOUROS, P. P. (1990). Model studies of unsteady flow using magnetic resonance imaging. J. Biomechanical Engr. 112, 93-99.
22. FLETCHER, N. H. (1992). Acoustic Systems in Biology. New York: Oxford University Press.
23. Fox, R. W. & MCDONALD, A. T. (1978). Introduction to Fluid Mechanics, 2nd Edn. New York: John Wiley & Sons.
24. FUNG, Y. C. (1997). Biomechanics: Circulation, 2nd Edn. New York: Springer-Verlag.
25. GHIRADELLA, H. T., CASE, J. F. & CRONSHAW, J. (1968). Structure of aesthetascs in selected marine and terrestrial decapods: chemoreceptor morphology and environment. Am. Zool. 8, 603-621.
26. GLEESON, R. A., CARR, W. E. S. & TRAPIDO-ROSENTHAL, H. G. (1993). Morphological characteristics facilitating stimulus access and removal in the olfactory organ of the spiny lobster, Panulirus argus: insight from the design. Chem. Senses 18, 67-75.
27. GOLDSCHMIED, F. R. (1974). Experimental study of pulsating viscous incompressible flow in rigid pipes. In: Flow: Its Measurement and Control in Science and Industry, vol. 1 (Dowdell, R. B., ed.), pp. 185-195. New York: Instrument Society of America.
28. HAHN, I., SCHERER, P. W. & MOZELL, M. M. (1994). A mass transport model of olfaction. J. theor. Biol. 167, 115-128.
29. HAPPEL, J. & BRENNER, H. (1965). Low Reynolds Number Hydrodynamics. Englewood Cliffs, NJ: Prentice Hall.
30. HARA, T. J. (1975). Olfaction in fish. Prog. Neurobiol. 5, 271-335.
31. HOLETON, G. F. & JONES, D. R. (1975). Water flow dynamics in the respiratory tract of the carp (Cyprinus carpio L.). J. Exp. Biol. 63, 537-549.
32. HUGHES, G. M. (1966). The dimensions of fish gills in relation to their function. J. Exp. Biol. 45, 177-195.
33. HUGHES, G. M. (1984). General anatomy of the gills. In: Fish Physiology, vol. 10A (Hoar, W. S. & Randall, D. J., eds), pp. 1-72. Orlando: Academic Press, Inc.
34. HUMPHREY, J. C., DEVARAKONDA, R., IGLESIAS, I. & BARTH, F. G. (1993). Dynamics of arthropod filiform hairs. I. Mathematical modelling of the hair and air motions. Phil. Trans. Roy. Soc. London B 340, 423-444.
35. INOUCHI, J., SHIBUYA, T., MATSUZAKI, O. & HATANAKA, T. (1987). Distribution and fine structure of antennal olfactory sensilla in Japanese dung beetles, Geotrupes auratus Mtos. (Coleoptera: Geotrupidae) and Copris pecuarius Lew. (Coleoptera: Scarabaeidae). Int. J. Insect Morphol. Embryol. 16, 177-187.
36. JOSHI, C. H., KAMM, R. D., DRAZEN, J. M. & SLUTSKY, A. S. (1983). An experimental study of gas exchange in laminar oscillatory flow. J. Fluid Mech. 133, 245-254.
37. KAPOOR, N. N. (1985). External morphology and distribution of the antennal sensilla of the stonefly, Paragnetina media (Walker) (Plecoptera: Perlidae). Int. J. Insect Morphol. Embryol. 14, 273-280.
38. KIM, S. Y., KANG, B. H. & HYUN, J. M. (1994). Heat transfer from pulsating flow in a channel filled with porous media. Int. J. Heat Mass Transfer 37, 2025-2033.
39. KLEEREKOPER, H. (1969). Olfaction in Fishes. Bloomington: Indiana University Press.
40. KOEHL, M. A. R. (1996). Small-scale fluid dynamics of olfactory antennae. Mar. Fresh. Behav. Physiol. 27, 127-141.
41. KURZWEG, U. H. (1985). Enhanced heat conduction in oscillating viscous flows within parallel-plate channels. J. Fluid Mech. 156, 291-300.
42. KURZWEG, U. H., LINDGREN, E. R. & LOTHRUP, B. (1989). Onset of turbulence in oscillating flow at low Womersley number. Phys. Fluids A 1, 1972-1975.
43. LANDAU, L. D. & LIFSHITZ, E. M. (1959). Fluid Mechanics. Reading, MA: Pergamon Press.
44. MACRIDES, F. & CHOROVER, S. L. (1972). Olfactory bulb units: activity correlated with inhalation cycles and odor quality. Science 175, 84-87.
45. MCDONALD, D. A. (1955). The relation of pulsatile pressure to flow in arteries. J. Physiol. 127, 533-552.
46. McMAHON, T. A. & BONNER, J. T. (1983). On Size and Life. New York: W. H. Freeman.
47. MERKLI, P. & THOMANN, H. (1975). Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567-575.
48. MURRAY, J. D. (1977). Reduction of dimensionality in diffusion processes: antenna receptors of moths. In: Lectures on Nonlinear-differential-equation Models in Biology, pp. 83-127. Oxford: Oxford University Press.
49. NEREM, R. M. & SEED, W. A. (1972). An in vivo study of aortic flow disturbances. Cardiovasc. Res. 6, 1-14.
50. NEVITT, G. A. (1991). Do fish sniff? A new mechanism of olfactory sampling in pleuronectid flounders. J. Exp. Biol. 157, 1-18.
51. NISHIMURA, T., ARAKAWA, S., MURAKAMI, S. & KAWAMURA, Y. (1989). Oscillatory viscous flow in symmetric wavy-walled channels. Chem. Engng Sci. 44, 2137-2148.
52. OLSON, D. M. & ANDOW, D. A. (1993). Antennal sensilla of female Trichogramma nubilale (Ertle and Davis) (Hymenoptera: Trichogrammatidae) and comparisons with other parasitic Hymenoptera. Int. J. Insect Morphol. Embryo!. 22, 507-520.
53. PAYNE, T. L., MOECK, H. A., WILLSON, C. D., COULSON, R. N. & HUMPHREYS, W. J. (1973). Bark beetle olfaction. II. Antennal morphology of sixteen species of Scolytidae (Coleoptera). Int. J. Insect Morphol. Embryol. 2, 177-192.
54. PEDLEY, T. J. (1995). High Reynolds number flow in tubes of complex geometry with application to wall shear stress in arteries. In: Biological Fluid Dynamics (Ellington, C. P. & Pedley, T. J., eds), pp. 219-241. Cambridge: The Company of Biologists, Limited.
55. PEDLEY, T. J., SCHROTER, R. C. & SUDLOW, M. F. (1977). Gas flow and mixing in airways. In: Bioengineering Aspects of the Lung (West, J. B., ed.). New York: Marcel Dekker, Inc.
56. PENNYCUICK, C. J. (1992). Newton Rules Biology; A Physical Approach to Biological Problems. Oxford: Oxford University Press.
57. PIIPER, J. & SCHEID, P. (1984). Model analysis of gas transfer in fish gills. In: Fish Physiology, Volume 10: Gills. Part A. Anatomy, Gas Transfer, and Acid-Base Regulation, pp. 229-262. Orlando: Academic Press, Inc.
58. RANDALL, D. & DAXBOECK, C. (1984). Oxygen and carbon dioxide transfer across fish gills. In: Fish Physiology, vol. 10A (Hoar, W. S. & Randall, D. J., eds), pp. 263-314. New York: Academic Press.
59. SARPKAYA, T. (1986). Force on a circular cylinder in viscous oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech. 165, 61-71.
60. SCHLICHTING, H. (1979). Boundary-Layer Theory, 7th Edn. New York: McGraw-Hill.
61. SCHMITT, B. C. & ACHE, B. W. (1979). Olfaction: responses of a decapod crustacean are enhanced by flicking. Science 205, 204-206.
62. SCHNEIDER, D. (1964). Insect antennae. Ann. Rev. Entomol. 9, 103-122.
63. SCHWENK, K. (1994). Why snakes have forked tongues. Science 263, 1573-1577.
64. SOBEY, I. J. (1983). The occurrence of separation in oscillatory flow. J. Fluid Mech. 134, 247-257.
65. STUART, J. T. (1966). Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673-687.
66. TATSUNO, M. & BEARMAN, P. W. (1990). A visual study of the flow around an oscillating circular cylinder at low Keulgan-Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157-182.
67. VAN DER PERS, J. N. C., CUPERUS, P. L. & DEN OTTER, C. J. (1980). Distribution of sense organs on male antennae of small ermine moths, Yponomeuta spp. (Lepidoptera: Yponomeutidae). Int. J. Insect Morphol. Embryol. 9, 15-23.
68. VOGEL, S. (1992). Vital Circuits: On Pumps, Pipes, and the Workings of Circulatory Systems. New York: Oxford University Press.
69. VOGEL, S. (1994a). Life in Moving Fluids: The Physical Biology of Flow, 2nd Edn. Princeton: Princeton University Press.
70. VOGEL, S. (1994b). Nature's pumps. Am. Sci. 82, 464-471.
71. WANG, C.-Y. (1968). On high-frequency oscillatory viscous flows. J. Fluid Mech. 32, 55-68.
72. WANG, Z., ISHIZAWA, S. & TAKAHASHI, K. (1990). Unsteady viscous flow between two parallel disks with a time-varying gap width and central fluid source (the case in which the rate of flow from the source is forcibly varied with time). JSME Int. J. 33, 446-453.
73. WATSON, E. J. (1983). Diffusion in oscillatory pipe flow. J. Fluid Mech. 133, 233-244.
74. WEIS-FOGH, T. (1973). Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biol. 59, 169-230.
75. WHITE, F. M. (1991). Viscous Fluid Flow. 2nd Edn. New York: McGraw-Hill.
76. WOMERSLEY, J. R. (1955). Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553-563.
77. ZAGZOULE, M., KHALID-NACIRI, J. & MAUSS, J. (1991). Unsteady wall shear stress in a distensible tube. J. Biomechanics 24, 435-439.