Micropolar Fluids

  • Vijay Kumar Stokes

Abstract

The theory of micro fluids, which has been presented in Chapter 5, is very general and allows for a wide variety of microstructures through the gyration tensor v ij . The simplest subclass of micro fluids in which microstructure is still present, and which is obtained by restricting the form of the gyration tensor, is the class of micropolar fluids of A. C. Eringen.

Keywords

Convection Vorticity Congo Suspen Kirwan 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Eringen, A. C. (1965). Theory of Micropolar Continua, Dey. Mech. (“Proc. Ninth Midwest. Mech. Conf., Madison”), (T. C. Huang, and M. W. Johnson, Jr., Eds ), John Wiley, 23–40.Google Scholar
  2. 2.
    Eringen, A. C. (1966). Theory of Micropolar Fluids, J. Math. Mech. 16, 1–18.MathSciNetGoogle Scholar
  3. 3.
    Eringen, A. C. (1966). Mechanics of Micromorphic Materials, Proc. 11 th Int. Cong. Appl. Mech. (H. Görtler, Ed. ), Springer Verlag, 131–138.Google Scholar
  4. 4.
    Eringen, A. C. (1969). Micropolar Fluids with Stretch, Int. J. Eng. Sci. 7, 115–127.MATHCrossRefGoogle Scholar
  5. 5.
    Ariman, T., Cakmak, A. S., and Hill, L. R. (1967). Flow of Micropolar Fluids Between Two Concentric Cylinders, Phys. Fluids 10, 2546–2550.ADSGoogle Scholar
  6. 6.
    Cowin, S. C., and Pennington, C. J. (1970). On the Steady Rotational Motion of Polar Fluids, Rheol. Acta 8, 307–312.CrossRefGoogle Scholar
  7. 7.
    Ariman, T., Turk, M. A., and Sylvester, N. D. (1973). Microcontinuum Fluid Mechanics–A Review, Int. J. Eng. Sci. 11, 905–930.MATHCrossRefGoogle Scholar
  8. 8.
    Ariman, T., Turk, M. A., and Sylvester, N. D. (1974). Review Article: Applications of Microcontinuum Fluid Mechanics, Int. J. Eng. Sci. 12, 273–293.MATHCrossRefGoogle Scholar
  9. 9.
    Bleustein, J. L., and Green, A. E. (1966). Dipolar Fluids, Int. J. Eng. Sci. 5, 323–340.CrossRefGoogle Scholar
  10. 10.
    Cowin, S. C. (1974). The Theory of Polar Fluids, “Advances in Applied Mechanics,” (Chia-Shun Yih, Ed.), Vol. 14, Academic Press, New York, 279–347.Google Scholar
  11. 11.
    Eringen, A. C. (Editor), (1976). “Continuum Physics, Vol. IV: Polar and Non-Local Field Theories,” Academic Press, New York.Google Scholar
  12. 12.
    Eringen, A. C. (1980). Theory of Anisotropic Micropolar Fluids, Int. J. Eng. Sci. 18, 5–17.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Peddieson, J., Jr., and McNitt, P. R. (1968). Boundary-Layer Theory for a Micropolar Fluid, “Recent Advances in Engineering Science,” (A. C. Eringen, Ed.), Vol. 5/1, Gordon and Breach, New York, 405–426.Google Scholar
  14. 14.
    Eringen, A. C. (1968). Mechanics of Micromorphic Continua, “Mechanics of Generalized Continua,” (E. Kröner, Ed.), Springer-Verlag, Berlin, 18–35.Google Scholar
  15. 15.
    Eringen, A. C., and Chang, T. S. (1968). A Micropolar Description of Hydrodynamic Turbulence, “Recent Advances in Engineering Science,” (A. C. Eringen, Ed.), Vol. 5/2, Gordon and Breach, New York, 1–8.Google Scholar
  16. 16.
    Grot, R. A. (1969). Thermodynamics of a Continuum with Microstructures, Int. J. Eng. Sci. 7, 801–814.MATHCrossRefGoogle Scholar
  17. 17.
    Eringen, A. C. (1970). Balance Laws of Micromorphic Mechanics, Int. J. Eng. Sci. 8, 819–828.MATHCrossRefGoogle Scholar
  18. 18.
    Eringen, A. C. (1970). Mechanics of Micropolar Continua, “Contributions to Mechanics,” (D. Abir, Ed ), Pergamon Press, 23–40.Google Scholar
  19. 19.
    Liu, C. Y. (1970). On Turbulent Flow of Micropolar Fluids, Int. J. Eng. Sci. 8, 457–466.MATHCrossRefGoogle Scholar
  20. 20.
    Rao, S. K. L. (1970). Stability of Micropolar Fluid Motions, Int. J. Eng. Sci. 8, 753–762.MATHCrossRefGoogle Scholar
  21. 21.
    Tokuoka, T. (1970). Optical Properties of Polarizable Linear Micropolar Fluids, Int. J. Eng. Sci. 8, 31–37.CrossRefGoogle Scholar
  22. 22.
    Wilson, A. J. (1970). Boundary Layers in Micropolar Liquids, Proc. Cambridge Philos. Soc. 67, 469–476.ADSCrossRefGoogle Scholar
  23. 23.
    Allen, S. J., and Kline, K. A. (1971). Lubrication Theory of Micropolar Fluids, J. Appl. Mech. 38, 646–649.Google Scholar
  24. 24.
    Ariman, T. (1971). On the Analysis of Blood Flow, J. Biomech. 4, 185–192.CrossRefGoogle Scholar
  25. 25.
    Kafadar, C. B., and Eringen, A. C. (1971). Micropolar Media–I. The Classical Theory, Int. J. Eng. Sci. 9, 271–305.Google Scholar
  26. 26.
    Kafadar, C. B. and Eringen, A. C. (1971). Micropolar Media - II. The Relativistic Theory, Int. J. Eng. Sci. 9, 307–329 Google Scholar
  27. 27.
    Rao, S. K. L. (1971). Existence of Periodic Solutions of the Equations of Incompressible Micropolar Fluid Flow, Int. J. Eng. Sci 9, 1143–1150.MATHCrossRefGoogle Scholar
  28. 28.
    Eringen, A. C. (1972). Theory of Thermomicrofluids, J. Math. Anal. Appl 39, 253–266.MATHCrossRefGoogle Scholar
  29. 29.
    Eringen, A. C. (1972). Continuum Foundations of Rheology - New Adventures, “Heat and Mass Transfer,” (W. R. Schowalter, et al., Eds.), Vol. 5, Pergamon Press, 1–18.Google Scholar
  30. 30.
    Kirwan, A. D., Jr., and Newman, N. (1972). Time Dependent Channel Flow of a Micropolar Fluid, Int. J. Eng. Sci 10, 137–146.MATHCrossRefGoogle Scholar
  31. 31.
    Peddieson, J., Jr. (1972). An Application of the Micropolar Fluid Model to the Calculation of a Turbulent Shear Flow, Int. J. Eng. Sci. 10, 23–32.Google Scholar
  32. 32.
    Eringen, A. C. (1973). On Non Local Microfluid Mechanics, Mt. J. Eng. Sci 11, 291–306.MathSciNetMATHGoogle Scholar
  33. 33.
    Turk, M. A., Sylvester, N. D., and Ariman, T. (1973). On Pulsatile Blood Flow, Trans. Soc. Rheol. 17, 1–21.MATHCrossRefGoogle Scholar
  34. 34.
    Ariman, T., Turk, N. A., and Sylvester, N. D. (1974). On Steady Pul-salite Flow of Blood, J. Appl. Mech. 41, 1–7.ADSCrossRefGoogle Scholar
  35. 35.
    Ariman, T., Turk, M. A., and Sylvester, N. D. (1974). On Time Dependent Blood Flow, Lett. Appl. Eng. Sci. 2, 21–36.Google Scholar
  36. 36.
    Ahmadi, G. (1975). Optical Properties of Polarizable Linear MagnetoMicropolar Fluid, Int. J. Eng. Sci. 13, 209–215.MathSciNetCrossRefGoogle Scholar
  37. 37.
    Ahmadi, G. (1975). Turbulent Shear Flow of Micropolar Fluids, Int. J. Eng. Sci. 13, 959–964.MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Prakash, J., and Sinha, P. (1975). Lubrication Theory of Micropolar Fluids and Its Application to a Journal Bearing, Int. J. Eng. Sci. 13, 217–232.MATHCrossRefGoogle Scholar
  39. 39.
    Ramkissoon, H., and Majumdar, S. R. (1975). Creeping Flow of a Micropolar Fluid Past a Sphere, Leu. Appl. Eng. Sci. 3, 133–142.Google Scholar
  40. 40.
    Ahmadi, G. (1976). Stability of Micropolar Fluid Layer Heated from Below, Int. J. Eng. Sci. 14, 81–89.MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Avudainayagam, A. (1976). The Effective Viscosity of a Dilute Suspension of Micropolar Fluid Particles in a Viscous Fluid, Int. J. Eng. Sci. 14, 703–712.MATHCrossRefGoogle Scholar
  42. 42.
    Datta, A. B., and Sastry, V. U. K. (1976). Thermal Instability of a Horizontal Layer of Micropolar Fluid Heated from Below, Int. J. Eng. Sci. 14, 769–788.CrossRefGoogle Scholar
  43. 43.
    Kirwan, A. D., Jr., and Chang, M. S. (1976). On the Micropolar Ekman Problem, Int. J. Eng. Sci. 14, 685–692.MATHCrossRefGoogle Scholar
  44. 44.
    Kirwan, A. D., Jr., Newman, N., and Chang, M. S. (1976). On Microdeformable Fluids: A Special Case of Microfluids, Int. J. Eng. Sci. 14, 673–684.MATHCrossRefGoogle Scholar
  45. 45.
    Prakash, J., and Sinha, P. (1976). Squeeze Film Theory for Micropolar Fluids, J. Lubr. Technol. 98, 139–144.CrossRefGoogle Scholar
  46. 46.
    Prakash, J., and Christensen, H. (1977). Microcontinuum Theory for the Elastohydrodynamic Inlet Zone, J. Lubr. Technol. 99, 24–29.CrossRefGoogle Scholar
  47. 47.
    Tözeren, A., and Skalak, R. (1977). Micropolar Fluids as Models for Suspensions of Rigid Spheres, Int. J. Eng. Sci. 15, 511–523.MATHCrossRefGoogle Scholar
  48. 48.
    Kuemmerer, H. (1978). Stability of Laminar Flows of Micropolar Fluids Between Parallel Walls, Phys. Fluids 21, 1688–1693.ADSMATHCrossRefGoogle Scholar
  49. 49.
    Sava, V. A. (1978). Initial-Boundary-Value Problems in Theory of Micropolar Fluids, Z. Angew. Math. Mech. 58, 511–518.MathSciNetMATHCrossRefGoogle Scholar
  50. 50.
    Rao, S. K. L., and Raju, K. V. (1979). Stability of Microstretch Fluid Motions, Int. J. Eng. Sci. 17, 465–473.MathSciNetCrossRefGoogle Scholar
  51. 51.
    Niefer, R., and Kaloni, P. N. (1980). On the Motion of a Micropolar Fluid Drop in a Viscous Fluid, J. Eng. Math. 14, 107–116.MATHCrossRefGoogle Scholar
  52. 52.
    Migun, N. P. (1981). Experimental Method of Determining Parameters Characterizing the Microstructure of Micropolar Liquids, J. Eng. Phys. (USSR) 41, 832–835.CrossRefGoogle Scholar
  53. 53.
    Mizukami, A. (1981). Nonsteady Shear Flow of Micropolar Films, Ina. J. Eng. Sci. 19, 75–82.MATHCrossRefGoogle Scholar
  54. 54.
    Sinha, P., Singh, C., and Prasad, K. R. (1982). Microcontinuum Analysis of the Self Propulsion of the Spermatozoa in Cervical Canal, Int. J. Eng. Sci. 20, 1037–1048.MATHCrossRefGoogle Scholar
  55. 55.
    Sinha, P., Singh, C., and Prasad, K. R. (1982). Lubrication of Human Joints–A Microcontinuum Approach, Wear 80, 159–181.CrossRefGoogle Scholar
  56. 56.
    Kolpashchikov, V. L., Migun, N. P., and Prokhorenko, P. P. (1983). Experimental Determination of Material Micropolar Fluid Constants, Int. J. Eng. Sci. 21, 405–411.CrossRefGoogle Scholar
  57. 57.
    Olmstead, W. E., and Majumdar, S. R. (1983). Fundamental Oseen Solution for the 2-Dimensional Flow of a Micropolar Fluid, Int. J. Eng. Sci. 21, 423–430.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1984

Authors and Affiliations

  • Vijay Kumar Stokes
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KanpurIndia
  2. 2.Corporate Research and DevelopmentGeneral Electric CompanySchenectadyUSA

Personalised recommendations