1 / 21

An Accurate Mode-Selection Mechanism for Magnetic Fluids in a Hele-Shaw Cell

An Accurate Mode-Selection Mechanism for Magnetic Fluids in a Hele-Shaw Cell. Slide 2. David P. Jackson Dickinson College, Carlisle, PA USA José A. Miranda Universidade Federal de Pernambuco, Recife, Brazil. The Birthday Girl!. What is a Ferrofluid?.

ramona
Télécharger la présentation

An Accurate Mode-Selection Mechanism for Magnetic Fluids in a Hele-Shaw Cell

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An Accurate Mode-Selection Mechanism for Magnetic Fluids in a Hele-Shaw Cell Slide 2 David P. Jackson Dickinson College, Carlisle, PA USA José A. Miranda Universidade Federal de Pernambuco, Recife, Brazil

  2. The Birthday Girl! Mar del Plata, Argentina

  3. What is a Ferrofluid? • Colloidal suspension of tiny magnets (10 nm) coated with a molecular surfactant • Thermal motion keeps the dipoles uniformly distributed and randomly oriented unless there is a magnetic field present • The dipoles align in a magnetic field For details, see Ferrohydrodynamics, Ronald E. Rosensweig (Cambridge University Press, 1985), (Dover, 1997) Mar del Plata, Argentina

  4. Basic Physical Situation Ferrofluid is confined between two closely spaced glass plates and placed in a perpendicular magnetic field Mar del Plata, Argentina

  5. Video Camera Hele-Shaw cell Helmholtz Coils Light Experimental Setup Mar del Plata, Argentina

  6. Qualitative Description No magnetic field Uniform magnetization collinear with field Parallel-plate capacitor Current Ribbon Uniform magnetic field Outward magnetic pressure competes with surface tension that results in a fingering instability Mar del Plata, Argentina

  7. Sample Evolution Single drop experimental example Mar del Plata, Argentina

  8. Controlling the Instability • How can we control the fingering instability? • Add an azimuthal field that falls off with distance Mar del Plata, Argentina

  9. Essential Physics • Outward force caused by a magnetic pressure due to dipole alignment from normal field • Inward force caused by surface tension that tends to minimize surface area • Inward force caused by the radial gradient of the azimuthal field Mar del Plata, Argentina

  10. Governing Equations Navier-Stokes: Hele-Shaw Approximations: Laplace’s Equation: Interfacial BC: Mar del Plata, Argentina

  11. plane plane Conformal Mapping • Solve Laplace’s Eq. on unit disk (Poisson integral formula) • Map exists from complex (simply connected) domain to unit disk • Interfacial BC gives evolution equation for domain boundary • Equation looks like: Bensimon et. al., Rev. Mod. Phys. 58, 977 (1986) Mar del Plata, Argentina

  12. Numerical Evolution Destabilizing (normal) field only! Mar del Plata, Argentina

  13. Linear Stability Analysis Specifying and linearizing the equation of motion leads to growth rates where Mar del Plata, Argentina

  14. Unstable Stable Growth Rates I Destabilizing (normal) field only! Mar del Plata, Argentina

  15. Single unstable mode! Unstable Stable Growth Rates II Possible mode-selection mechanism! Mar del Plata, Argentina

  16. n=5 n=4 n=3 Single Unstable Modes n=2 Stability Phase Portrait • Solid lines are neutral stability curves • Gray areas denote regions where a particular mode is the fastest growing • Diamonds denote specific values used for simulations Mar del Plata, Argentina

  17. Precisely Selected Modes Simulations run with identical initial conditions - Bond numbers chosen so that there is only a single unstable mode Mar del Plata, Argentina

  18. Simulations with NB=1.5 • Simulations with NB=1.5 • Initial condition is left-right n=2 mode • As NB increases, more modes become stable • When only a single mode is unstable, the initial condition is drown out Mar del Plata, Argentina

  19. Simulations with NB=2.5 Mar del Plata, Argentina

  20. Summary • An azimuthal magnetic field can be used to control the normal field fingering instability of a magnetic fluid in a Hele-Shaw cell • By tuning the azimuthal and normal fields, one can produce a situation in which a single unstable mode exists • Numerical simulations demonstrate that mode growth can be accurately selected • Large enough azimuthal fields completely stabilize the interface Mar del Plata, Argentina

  21. An Accurate Mode-Selection Mechanism for Magnetic Fluids in a Hele-Shaw Cell Slide 2 David P. Jackson Dickinson College, Carlisle, PA USA José A. Miranda Universidade Federal de Pernambuco, Recife, Brazil

More Related