Nayaz Khalid Ahmed and Martin Hecht<br />National Institute of Technology,<br />Tiruchirappalli, INDIA – 620 015<br />Inst...
Outline<br />Introduction<br /><ul><li>Microfluidics
Slip Flows
Lattice Boltzmann Method (LBM)</li></ul>Boundary Conditions<br /><ul><li>For alternating  slip and no-slip conditions</li>...
Continuously varying  striped devices</li></li></ul><li>Micro fluidics<br />Flow through channels of 10 – 1000 nm in dia.<...
Slip Flows<br />Presence of slip during interaction between solid and fluid interface<br />General assumption of no-slip c...
Lattice Boltzmann Method (LBM)<br />At the microscopic level – Velocity distribution of particles, Brownian motion, huge n...
Lattice Boltzmann Method (LBM)<br />Boltzmann’s equation – time evolution of the distribution functions<br />
LBM solves this equation on a discrete lattice (D3Q19)<br />19 discrete lattice vectors	         for velocities  <br />Lat...
   Equilibrium distribution:</li></li></ul><li>Two alternating steps:<br />Advection:   move the populations      to the n...
 Macroscopic Variables:</li></li></ul><li>Boundary Conditions<br />On wall boundary nodes – <br />distributions pointing o...
Micro mixers<br />Flow in micro fluidics – low Re, no mixing<br />Flow past surfaces on which slip length is modulated in ...
y , z direction – periodic boundaries
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Icmens 2009 L100

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Presentation made on Simulations conducted for a microfluidic mixer at the 5th International Conference for MEMS, NANO and Smart Systems 2009, held at Dubai, UAE.

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Icmens 2009 L100

  1. 1. Nayaz Khalid Ahmed and Martin Hecht<br />National Institute of Technology,<br />Tiruchirappalli, INDIA – 620 015<br />Institute for Computational Physics,<br />Pfaffenwaldring 27, <br />70569 Stuttgart, GERMANY<br />A lattice Boltzmann study of flow along patterned surfaces and through channels with alternating slip length<br />
  2. 2. Outline<br />Introduction<br /><ul><li>Microfluidics
  3. 3. Slip Flows
  4. 4. Lattice Boltzmann Method (LBM)</li></ul>Boundary Conditions<br /><ul><li>For alternating slip and no-slip conditions</li></ul>Results and Discussion<br /><ul><li>Textured walls with alternating stripes
  5. 5. Continuously varying striped devices</li></li></ul><li>Micro fluidics<br />Flow through channels of 10 – 1000 nm in dia.<br />Surface interactions dominate at this scale.<br />Colloidal micro pumps using 3 micron silica microspheres<br />6 micron channel, motion due to optical traps. Courtesy – D. Marr<br />
  6. 6. Slip Flows<br />Presence of slip during interaction between solid and fluid interface<br />General assumption of no-slip condition in macro flows fails in micro fluidics<br />λ – slip length<br />
  7. 7. Lattice Boltzmann Method (LBM)<br />At the microscopic level – Velocity distribution of particles, Brownian motion, huge number of particles/degree of freedom<br />Describe motion of particles by distribution functions –<br />
  8. 8. Lattice Boltzmann Method (LBM)<br />Boltzmann’s equation – time evolution of the distribution functions<br />
  9. 9. LBM solves this equation on a discrete lattice (D3Q19)<br />19 discrete lattice vectors for velocities <br />Lattice Boltzmann Method (LBM)<br /><ul><li> Discretized Boltzmann equation:
  10. 10. Equilibrium distribution:</li></li></ul><li>Two alternating steps:<br />Advection: move the populations to the next lattice<br />Lattice Boltzmann Method (LBM)<br /><ul><li> Collision: relax the on each lattice site towards
  11. 11. Macroscopic Variables:</li></li></ul><li>Boundary Conditions<br />On wall boundary nodes – <br />distributions pointing out of the lattice move out of computational domain<br />incoming distributions from the wall are undetermined<br />For slip flows, following boundary condition is used*<br /> where, - distribution function at wall node for partial slip <br /> - distribution function at wall node for full slip <br /> - distribution function at wall node for no slip<br /> - slip parameter depending on the material<br />* N. K. Ahmed and M. Hecht, Journal of Statistical Mechanics, P09017, 2009<br />
  12. 12. Micro mixers<br />Flow in micro fluidics – low Re, no mixing<br />Flow past surfaces on which slip length is modulated in stripes<br />Simulation Setup:<br /><ul><li> Cubic box of 32 nodes
  13. 13. y , z direction – periodic boundaries
  14. 14. x direction – slip flow with stripes
  15. 15. Constant accelerating force parallel to yzplane.</li></li></ul><li>Textured Walls with alternating stripes<br />Stripes made of alternating slip parameters ζ1 and ζ2<br />where b1 and b2 are the slip lengths corresponding to ζ1 and ζ2, according to * :<br />Parameters A,B,C,D,E depend on the orientation of strips with respect to direction of accelerating force.<br /><ul><li> Slip – a tensorial quantity – analytically proven by</li></ul> M.Z. Bazant and O. I. Vinogradova, Journal of Fluid Mechanics, vol 613, 2008 <br />3rd degree polynomial fit for orientation of stripes perpendicular to direction of accelerating force<br />3rd degree polynomial fit for orientation of stripes parallel to direction of accelerating force<br />Stripes at four different orientations of the stripes wrt direction of accelerating force. Relative error of 10-3 %<br />* N. K. Ahmed and M. Hecht, Journal of Statistical Mechanics, P09017, 2009<br />
  16. 16. Continuously varying striped walls<br />Slip parameter varies as a continuous periodic function along the wall:<br /> where the wave vector k defines the frequency and direction of the variation of slip parameter ζ.<br />Amplitude and mean ζ = 0.5 and wave vector points in the diagonal direction<br />Velocity along the x boundary wall. (Colour coding: y component)<br />
  17. 17. Continuously varying striped walls<br />Fluid arriving is a region of smaller slip has to go aside:<br /> - Vortice in the plane perpendicular to the direction of accelerating force occurs.<br />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.<br />Curl of the z-component velocity field, averaged along the z-direction. Homogeneous rotation is more clearly observed.<br />
  18. 18. Conclusion<br />Study confirms tensorial nature of slip proposed by M.Z. Bazant and O.I. Vinogradova, Journal of Fluid Mechanics, 613, 125-134, 2008.<br />Generation of vortex – surface wall pattern can be exploited for designing Micro mixer devices.<br />Heartfelt thanks to the DAAD for the WISE 2009 Scholarship to carry out my work. <br />We also wish to thank the German Research Foundation (DFG) for financial support within grant EAMatWerk.<br />Thank YOU<br />

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