Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-20T04:55:04.524Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag on spheres in micropolar fluids with non-zero boundary conditions for microrotations

Published online by Cambridge University Press:  15 October 2007

KARL-HEINZ HOFFMANN ,
DAVID MARX  and
NIKOLAI D. BOTKIN
KARL-HEINZ HOFFMANN
Affiliation:
Department of Applied Mathematics, Technical University of Munich, Boltzmann Street 3, 85747 Garching/Munich, Germany
DAVID MARX
Affiliation:
DFG Research Center Matheon, Humboldt-University of Berlin, Unter den Linden 6, 10099 Berlin, Germany
NIKOLAI D. BOTKIN
Affiliation:
Department of Applied Mathematics, Technical University of Munich, Boltzmann Street 3, 85747 Garching/Munich, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The Stokes formula for the resistance force exerted on a sphere moving with constant velocity in a fluid is extended to the case of micropolar fluids. A non-homogeneous boundary condition for the micro-rotation vector is used: the micro-rotation on the boundary of the sphere is assumed proportional to the rotation rate of the velocity field on the boundary.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 319 - 330
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Erdogan, M. E. 1972 Dynamics of polar fluids. Act. Mech. 15, 233–253.CrossRefGoogle Scholar
Eringen, A. C. 1964 a Simple microfluids Intl J. Engng Sci. 2, 205–217.CrossRefGoogle Scholar
Eringen, A. C. 1964 b Theory of micropolar fluids. J. Math. Mech. 16, 1–18.Google Scholar
Hayakawa, H. 2000 Slow viscous flows in micropolar fluids. Phys. Rev. E 61, 5477–5492.CrossRefGoogle ScholarPubMed
Kolpashchikov, V. L., Mingun, N. P. & Prokhorenko, P. P. 1983 Experimental determination of material micropolar fluid constants. Intl J. Engng Sci. 21, 405–411.CrossRefGoogle Scholar
Lakshmana Rao, S. K. & BhujangaRao, P. Rao, P. 1970 The slow stationary flow of a micropolar liquid past a sphere. J. Engng Maths 4 (3), 209–217.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1995 Fluid Mechanics: Course of Theoretical Physics, vol. 6. Butterworth–Heinemann.Google Scholar
Loitsyanskii, L. G. 1996 Mechanics of Liquids and Gases. Begell Hause.Google Scholar
Lukaszewicz, G. 1999 Micropolar Fluids: Theory and Applications. Birkhäuser.CrossRefGoogle Scholar
Papautsky, I., Brazzle, J., Ameel, T. et al. 1999 Laminar fluid behaviour in microchannels using micropolar fluid behaviour, Sensors Actuate. 73, 101–108.CrossRefGoogle Scholar
Ramkissoon, H. 1985 Flow of a micropolar fluid past a Newtonian fluid sphere. Z. Angew. Math. Mech. 65 (12), 635–637.CrossRefGoogle Scholar
Ramkissoon, H. & Majumdar, S. R. 1976 Drag on axially symmetric body in the Stokes' flow of micropolar fluid. Phys. Fluids 19 (1), 16–21.CrossRefGoogle Scholar
Stokes, V. K. 1984 Theories of Fluids with Microstructure. Springer.CrossRefGoogle Scholar
Straughan, B. 2004 The Energy Method, Stability and Nonlinear Convection, 2nd edn. Springer.CrossRefGoogle Scholar