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Optimal Frequency for Microfluidic Mixing across a Fluid Interface

Optimal Frequency for Microfluidic Mixing across a Fluid Interface. Ivo Matthijssen (0614966) Lennart Swartjes (0618701). Table of contents. Problem description Fluid mixing Hamilton dynamics Perturbation Melnikov function Fluid sloshing Example: T-mixer Conclusion.

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Optimal Frequency for Microfluidic Mixing across a Fluid Interface

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  1. Optimal Frequency for Microfluidic Mixing across a Fluid Interface Ivo Matthijssen (0614966) Lennart Swartjes (0618701)

  2. Table of contents • Problem description • Fluid mixing • Hamilton dynamics • Perturbation • Melnikov function • Fluid sloshing • Example: T-mixer • Conclusion / department of Mechanical Engineering

  3. Problem description • Determine the optimum frequency to mix fluids on micro scale • 2 different ways: • Numerically: Long calculation times • A structured approach without difficult formula’s or difficult calculations / department of Mechanical Engineering

  4. Fluid mixing • Hamilton equations: • Poincaré–Bendixson theorem • 2D • Time independent • No mixing • To mix the fluids a time dependent perturbation is needed / department of Mechanical Engineering

  5. Time dependent perturbation Next step: Determine the magnitude or the degree of mixing / department of Mechanical Engineering

  6. Homoclinic (and perturbed) manifold / department of Mechanical Engineering Due to the perturbation there will be an unstable and a stable manifold

  7. Perturbed manifold Broken homoclinic manifold Wu – Ws is an estimate for the transversal distance between the unstable and stable manifold each time instance / department of Mechanical Engineering

  8. Melnikov function / name of department

  9. Melnikov function frequency domain / department of Mechanical Engineering

  10. Melnikov function frequency domain (cntd) / department of Mechanical Engineering

  11. Melnikov function frequency domain (cntd) / department of Mechanical Engineering

  12. Fluid sloshing Fluid sloshing back and forth across the homoclinic manifold Average flux is the area of lobes crossing this homoclinic manifold Independent of initial conditions / department of Mechanical Engineering

  13. Example: T-mixer / department of Mechanical Engineering

  14. Time dependent perturbation / department of Mechanical Engineering

  15. Sloshing function (T-mixer) / department of Mechanical Engineering

  16. Sloshing function (ω = 4π) / department of Mechanical Engineering

  17. Sloshing function (ω = 4.7) / department of Mechanical Engineering

  18. Conclusion • With a structured approach the degree of mixing at a particular frequency can be predicted • The optimal frequency of the T-mixer • ω = 4π / department of Mechanical Engineering

  19. Questions? / department of Mechanical Engineering

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