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Nayaz Khalid Ahmed and Martin Hecht National Institute of Technology, Tiruchirappalli, INDIA – 620 015 Institute for Computational Physics, Pfaffenwaldring 27,  70569 Stuttgart, GERMANY A lattice Boltzmann study of flow along patterned surfaces and through channels with alternating slip length
Outline Introduction ,[object Object]
Slip Flows
Lattice Boltzmann Method (LBM)Boundary Conditions ,[object Object],Results and Discussion ,[object Object]
Continuously varying  striped devices,[object Object]
Slip Flows Presence of slip during interaction between solid and fluid interface General assumption of no-slip condition in macro flows fails in micro fluidics λ – slip length
Lattice Boltzmann Method (LBM) At the microscopic level – Velocity distribution of particles, Brownian motion, huge number of particles/degree of freedom Describe motion of particles by distribution functions –
Lattice Boltzmann Method (LBM) Boltzmann’s equation – time evolution of the distribution functions
LBM solves this equation on a discrete lattice (D3Q19) 19 discrete lattice vectors	         for velocities   Lattice Boltzmann Method (LBM) ,[object Object]
   Equilibrium distribution:,[object Object]
 Macroscopic Variables:,[object Object]
Micro mixers Flow in micro fluidics – low Re, no mixing Flow past surfaces on which slip length is modulated in stripes Simulation Setup: ,[object Object]
y , z direction – periodic boundaries

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Icmens 2009 L100

  • 1. Nayaz Khalid Ahmed and Martin Hecht National Institute of Technology, Tiruchirappalli, INDIA – 620 015 Institute for Computational Physics, Pfaffenwaldring 27, 70569 Stuttgart, GERMANY A lattice Boltzmann study of flow along patterned surfaces and through channels with alternating slip length
  • 2.
  • 4.
  • 5.
  • 6. Slip Flows Presence of slip during interaction between solid and fluid interface General assumption of no-slip condition in macro flows fails in micro fluidics λ – slip length
  • 7. Lattice Boltzmann Method (LBM) At the microscopic level – Velocity distribution of particles, Brownian motion, huge number of particles/degree of freedom Describe motion of particles by distribution functions –
  • 8. Lattice Boltzmann Method (LBM) Boltzmann’s equation – time evolution of the distribution functions
  • 9.
  • 10.
  • 11.
  • 12.
  • 13. y , z direction – periodic boundaries
  • 14. x direction – slip flow with stripes
  • 15.
  • 16. Continuously varying striped walls Slip parameter varies as a continuous periodic function along the wall: where the wave vector k defines the frequency and direction of the variation of slip parameter ζ. Amplitude and mean ζ = 0.5 and wave vector points in the diagonal direction Velocity along the x boundary wall. (Colour coding: y component)
  • 17. Continuously varying striped walls Fluid arriving is a region of smaller slip has to go aside: - Vortice in the plane perpendicular to the direction of accelerating force occurs. Averaged projection of velocity vectors on the xy plane. Homogeneous rotation about the centre is observed. Velocity at the centre is aligned with the channel. Curl of the z-component velocity field, averaged along the z-direction. Homogeneous rotation is more clearly observed.
  • 18. Conclusion Study confirms tensorial nature of slip proposed by M.Z. Bazant and O.I. Vinogradova, Journal of Fluid Mechanics, 613, 125-134, 2008. Generation of vortex – surface wall pattern can be exploited for designing Micro mixer devices. Heartfelt thanks to the DAAD for the WISE 2009 Scholarship to carry out my work. We also wish to thank the German Research Foundation (DFG) for financial support within grant EAMatWerk. Thank YOU