Abstract
Since the turn of the century, when Ludwig Prandtl formulated the theoretical concept of the boundary layer, the phenomenon of boundary layer or flow separation has been associated mostly with trouble, i.e., energy losses, reverse flow, vortex formation, wakes, stalling, increased drag, decreased lift, wall scouring effects, etc. One of the more serious problems with which flow separation has been associated in recent years is cardiovascular disease. There is an ever increasing abundance of evidence which suggests indirectly that the pathogenesis, localization and/or aggravation of certain forms of cardiovascular disease may be related to the incidence, persistence and consequences of internal, unsteady, laminar-flow separation. This very same evidence, because of its indirect speculative nature, has also brought to light an area of fluid mechanics that has hitherto been conspicuously neglected.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Prandtl, L., “Uber Flussigkeitsbewegung bei sehr kleiner Reibung,” Verhandlung des III Intern. Math. — Kongresses, Heidelberg, zur Hydrodynamik u. Aerodynamik, Gottingen, 1927, pp. 1–8, and Edwards Bros., Ann Arbor, Mich., 1943.
Blasius, H. Von., “Laminare Stromung in Kanalen Wechselnder Breite,” Zeitschr. F. Math. u. Phys., 58: 225–233, 1910.
Patterson, G.N., “Flow Forms in a Channel of Small Exponential Divergence,” Canad. J. Res., 11: 770–779, 1934.
Patterson, G.N., “Viscosity Effects in a Channel of Small Exponential Divergence,” Canad. J. Res., 12: 676–685, 1935.
Gutstein, W.H., and Schneck, D.J., “In Vitro Boundary Layer Studies of Blood Flow in Branched Tubes,” J. Atheroscler. Res., 7 (No. 3): 295–299, June, 1967.
Forrester, J.H., and Young, D.F., “Flow Through a Converging-Diverging Tube and its Implications in Occlusive Vascular Disease — I. Theoretical Development,” J. Biomechanics, 3: 297–305, 1970.
Bentz, J.C., and Evans, N.A., “Hemodynamic Flow in the Region of a Simulated Stenosis,” ASME Paper Number 75-WA/Bio-10, December, 1975.
Manton, M.J., “Low Reynolds Number Flow in Slowly Varying Axisymmetric Tubes,” J. Fluid Mech., 49: 451–459, 1971.
Kandarpa, K., and Davids, N., “Analysis of the Fluid Dynamic Effects on Atherogenesis at Branching Sites,” J. Biomechanics, 9: 735–741, 1976.
Lee, J.S., and Fung, Y.C., “Flow in Locally Constricted Tubes at Low Reynolds Numbers,” J. App. Mech., 37: 9–16, 1970.
Young, D.F., and Tsai, F.Y., “Flow Characteristics in Models of Arterial Stenoses — I. Steady Flow,” J. Biomech., 6: 395–410, 1973.
Young, D.F., “Effect of a Time-Dependent Stenosis on Flow Through a Tube,” J. Engng. Ind. Trans. ASME, 90: 248–254, 1968.
Rott, N., “Unsteady Viscous Flow in the Vicinity of Stagnation Point,” Quart. Appl. Math., 13: 444–451, 1956.
Sears, W.R., “Some Recent Developments in Airfoil Theory,” J. Aero. Sci., 23: 490–499, 1956.
Moore, F.K., “On the Separation of the Unsteady Laminar Boundary Layer,” in: Gortler, J., (ed.), Boundary Layer Research, Proc. Symp. of Int. Union of Theoret. and Appl. Mech., Berlin, Springer, 1958, pp. 296–311.
Sears, W.R., and Telionis, D.P., “Boundary-Layer Separation in Unsteady Flow,” SIAM J. Appl. Math., 28 (no. 1): 215–235, January, 1975.
Telionis, D.P., “Calculations of Time-Dependent Boundary Layers,” in: Kinney, R.B., (ed.), Unsteady Aerodynamics, Proc. Symp. Univ. Ariz., The Arizona Board of Regents, 1975, pp. 155–190.
Despard, R.A. and Miller, J.A., “Separation in Oscillating Laminar Boundary-Layer Flows,” J. Fluid Mech., 47 (Part 1): 21–31, 1971.
Schneck, D.J., and Ostrach, S., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -- I. The Linear Approximation for Low Mean Reynolds Number,” ASME Paper Number 74-WA/Bio-14, Trans. ASME, J. Fluids Eng., 97 (Ser. 1, No. 3): 353–360, Sept., 1975.
Schneck, D.J., and Walburn, F.J., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -II. Steady Streaming Due to the Interaction of Viscous Effects With Convected Inertia,” Trans. ASME, J. Fluids Eng., 98: 707–714, December, 1976.
Schneck, D.J., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -- III. Unsteady Flow Separation,” Trans. ASME, J. Fluids Eng., 99: 333–338, June, 1977.
Schneck, D.J., and Ostrach, S., “Pulsatile Blood Flow in a Diverging Circular Channel,” Case Western Reserve University, Division of Fluid, Thermal and Aerospace Sciences, Technical Report Number FTAS/TR73–86, Cleveland, Ohio, January, 1973.
Schneck, D.J., and Ostrach, S., “Oscillating Blood Flow in a Cylindrical Channel of Small Exponential Divergence,” Proc. 3rd Ann. Meeting Biomed. Eng. Soc., p. 40, April, 1972.
Schneck, D.J., and Ostrach, S., “Dependence of Unsteady Flow Separation on Frequency of Oscillation,” Proc. 26th Ann. Conf. Eng. Med. Biol., 15: 309, October, 1973.
Tsahalis, D.T., “Unsteady Boundary Layers and Separation,” Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, August, 1974.
Tsahalis, D.T., and Telionis, D.P.,“ Oscillating Laminar Boundary Layers and Unsteady Separation,” AIAA Journal, 12 (#11): 1469–1476, November, 1974.
Walburn, F.J., and Schneck, D.J., “An Experimental Technique for Quantifying Unsteady Flow Separation in Diverging Circular Channels. Schneck, D.J. (ed.), Proc. First Mid-Atlantic Conf. on Bio-Fluid Mech., Blacksburg, Virginia, Virginia Polytechnic Institute and State University, 1978, pp. 161–170.
Schneck, D.J., and Walburn, F.J., “Unsteady Laminar-Flow Separation in Tubes -- II. The Effect of Variatiions in the Frequency and Amplitude of Flow Oscillations”, Virginia Polytechnic Institute and State University Technical Report #VPI-E-79–21, June, 1979.
Koromilas, C., “Experimental Investigation of Unsteady Separation,” Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, August, 1978.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer Science+Business Media New York
About this chapter
Cite this chapter
Walburn, F.J., Schneck, D.J. (1980). An Experimental Investigation of Pulsatile Laminar Flow Separation in Exponentially Diverging Tubes. In: Schneck, D.J. (eds) Biofluid Mechanics · 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4610-5_23
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4610-5_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-4612-9
Online ISBN: 978-1-4757-4610-5
eBook Packages: Springer Book Archive