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Slow motion of a sphere away from a wall: Effect of surface roughness on the viscous force

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Abstract

An asymptotic analysis is given for the effect of roughness exhibited through the slip parameter β on the motion of the sphere, moving away from a plane surface with velocityV. The method replaces the no-slip condition at the rough surface by slip condition and employs the method of inner and outer regions on the sphere surface. For β > 0, we have the classical slip boundary condition and the results of the paper are then of interest in the microprocessor industry.

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References

  1. Basset A B,A treatise on hydrodynamics, 2, (New York: Dover Publications Inc.) (1961)

    Google Scholar 

  2. Cooley M D A and O’Neill M E, On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere,Mathematika 16 (1969) 37–49

    Article  Google Scholar 

  3. Happel J and Brenner H,Low Reynolds number hydrodynamics (Prentice Hall) (1965)

  4. Higdon J J L, Stokes flw in arbitrary two-dimensional shear flow over ridges and cavities,J. Fluid. Mech. 159 (1985) 195–226

    Article  MATH  MathSciNet  Google Scholar 

  5. Hocking L M, A moving fluid interface on a rough surface,J. Fluid Mech. 76(4) (1976) 801–817

    Article  MATH  Google Scholar 

  6. Miksis M J and Davis S H, Slip over rough and coated surfaces,J. Fluid Mech. 273 (1994)125–139

    Article  MATH  Google Scholar 

  7. O’Brien S B G and Van Den Brule B H A A, A Mathematical model for the cleansing of silicon substrates by fluid immersion,J. Colloid Interface Sci. 144(1) (June 1991) 210–221

    Article  Google Scholar 

  8. O’Neill M E and Ranger K B, The approach of a sphere to an interface,J. Phys. Fluids 26(8) (August 1983)

  9. O’Neill M E and Stewartson K, On the slow motion of a sphere parallel to a nearby plane wall,J. Fluid Mech. 27(4) (1967) 705–724

    Article  MATH  MathSciNet  Google Scholar 

  10. Scheneel E, Slippage of water over nonwettable surfaces,J. Appl. Phys. 27 (1956) 1149–1152

    Article  Google Scholar 

  11. Tsien H S, Superaerodynamics, Mechanics of rarefied gases,J. Aeronaut. Sci. 13 (1946) 653–664

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Astronomy, Lucknow University, 226 007, Lucknow, India

    Sunil Datta & Manju Shukla

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  1. Sunil Datta
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  2. Manju Shukla
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Datta, S., Shukla, M. Slow motion of a sphere away from a wall: Effect of surface roughness on the viscous force. Proc. Indian Acad. Sci. (Math. Sci.) 112, 641–654 (2002). https://doi.org/10.1007/BF02829694

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  • DOI: https://doi.org/10.1007/BF02829694

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