Experimental Results of Boundary Slip

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Experimental Results of Boundary Slip

• Cindy Christensen
• 1/28/2003

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Hydrodynamic/drainage force

• Proportional to approaching velocity
• Inversely proportional to distance between
  surfaces

Vinogradova, 1995
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What is slip length?

• Distance behind interface at which the liquid
  velocity extrapolates to zero (Brochard and de
  Gennes, 1992)
• Slip length (b)
• f
• Correction Factor
• 0 lt f lt 1
• f 1 corresponds to no slip

D spacing between two surfaces
Vinogradova, 1995
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When do we have to consider the slip length?

• When the slip length is on the order of the
  length scale of velocity changes
• When fluid highly confined
• MEMS
• Microfluidics
• MD simulations

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m-PIV measurements of slip length
Hydrophilic
Hydrophobic ( )
u(0) 0.10U b 1 mm
Tretheway and Meinhart, 2001
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Slip dependence on contact angle
0 lt b lt 2.5 mm
Zhu and Granick, 2001
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Slip as a function of surface roughness
Smooth
2 nm
3.5 nm
6 nm
Zhu and Granick, 2002
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Slip as a function of viscosity and driving rate
80.3 mPa s
38.9 mPa s
19.2 mPa s
Craig, Neto, and Williams, 2001
Slip length b
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Summary

• Slip causes a shift in the velocity profile
• Slip increases with the contact angle
• Slip decreases with increasing surface roughness
• Slip increases with viscosity and driving rate

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References

• F. Brochard and P.G. de Gennes, Shear-dependent
  slippage at a polymer/solid interface, Langmuir
  8, 3033 (1992)
• S.J. Craig, C. Neto, and D.R.M. Williams,
  Shear-dependent boundary slip in an aqueous
  Newtonian liquid, Phys. Rev. Lett. 87 054504
  (2001)
• D.C. Tretheway and C.D. Meinhart, Apparent fluid
  slip at hydrophobic microchannel walls, Phys. of
  Fluids 14 L9 (2001)
• Vinogradova, 199
• Y. Zhu and S. Granick, Rate-dependent slip of
  Newtonian liquid at smooth surfaces, Phy. Rev.
  Lett. 87 096105 (2001)
• Y. Zhu and S. Granick, Limits of the hydrodynamic
  no-slip boundary condition, Phy. Rev. Lett. 88
  106102 (2002)