Surface Only Ferrofluids Libo Huang, Dominik L. Michels KAUST VCC - - PowerPoint PPT Presentation

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Surface Only Ferrofluids Libo Huang, Dominik L. Michels KAUST VCC - - PowerPoint PPT Presentation

Jun 08, 2023 206 likes •486 views

Surface Only Ferrofluids Libo Huang, Dominik L. Michels KAUST VCC Overview Introduction (10%) Related Ferrofluid Simulation (10%) Surface Only Liquids (20%) Make It Magnetic! (30%) Results (25%) Conclusion (5%)

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SLIDE 1

Surface Only Ferrofluids

Libo Huang, Dominik L. Michels KAUST VCC

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SLIDE 2

Overview

  • Introduction (10%)
  • Related Ferrofluid Simulation (10%)
  • Surface Only Liquids (20%)
  • Make It Magnetic! (30%)
  • Results (25%)
  • Conclusion (5%)
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SLIDE 3

Introduction: What?

  • Ferrofluid: magnetic fluid
  • Spikes: minima of
  • Surface tension
  • Gravity energy
  • Magnetic energy
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SLIDE 4

Introduction: How?

  • How to solve magnetic

fields?

  • How to apply magnetic

forces?

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SLIDE 5

Related Ferrofluid Simulation

  • Huang et al. 2019

Radial basis functions Inter-particle forces Surface tension?

  • Ni et al. 2020

Cartesian grids Pressure boundary condition Extra air DOF?

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SLIDE 6

Surface Only Liquids

  • Origin: Da et al. 2016 “Surface-only Liquids”
  • Key assumptions: curl-free and divergence-free
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SLIDE 7

Surface Only Liquids

  • Origin: Da et al. 2016 “Surface-only Liquids”
  • Key assumptions: curl-free and divergence-free
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SLIDE 8

Surface Only Liquids

  • Key assumptions: curl-free and divergence free
  • The interior velocity is uniquely defined by the

boundary velocity.

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SLIDE 9

Surface Only Liquids

  • Main steps:
  • 1. Move boundaries to new positions
  • 2. Make new velocity fields harmonic (curl-free and div-free)
  • 3. Add forces as harmonic vector fields.
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SLIDE 10

Make It Magnetic!

  • Basis: add forces as gradient of harmonic function
  • Example: gravity (top pressure=0), constant gradient

solve boundary value problem->

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SLIDE 11

Make It Magnetic!

  • Still gravity, but in a real simulation:
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SLIDE 12

Make It Magnetic!

  • Gravity energy = negative integral of gravity body forces

𝑔

𝑕𝑠𝑏𝑤𝑗𝑢𝑧 = 𝜍𝑕

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SLIDE 13

Make It Magnetic!

  • Surface tension energy = negative integral of surface forces

𝑔

𝑇𝑣𝑠𝑔𝑏𝑑𝑓 = 𝜏𝐼

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SLIDE 14

Make It Magnetic!

  • Magnetic energy = negative integral of magnetic body + surface forces
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SLIDE 15

Make It Magnetic!

  • 𝐹 = 𝐹𝑇𝑣𝑠𝑔𝑏𝑑𝑓 + 𝐹𝐻𝑠𝑏𝑤𝑗𝑢𝑧 + 𝐹𝑁𝑏𝑕𝑜𝑓𝑢𝑗𝑑
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SLIDE 16

Make It Magnetic!

Put it all together: 1. Solve the magnetic field (BEM) 2. Get magnetic energy on surface 3. Add gravity, surface tension 4. Solve the gradient with BEM 5. Add the gradient to the velocity

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SLIDE 17

Results

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SLIDE 18

Results

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SLIDE 19

Results

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SLIDE 20

Results

Field Strength Surface Tension

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SLIDE 21

Results

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SLIDE 22

Results

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SLIDE 23

Results

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SLIDE 24

Conclusion

  • Incorporate magnetic effects by adding magnetic

energy on the surface using BEM

  • Benefits:
  • Less unknowns
  • Accurate surface tension
  • Drawbacks:
  • Limited to linear material
  • Complex boundary handling
  • Difficult implementation

KAUST Computational Sciences Group

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SLIDE 25