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Cam v15 november 2018

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Cambridge Nov 2018

Publicada em: Ciências
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Cam v15 november 2018

  1. 1. 1 Cambridge, November 2018 The effect of Viscosity, Yield Stress, and Surface Tension on the Deformation and Breakup profiles of fluid filaments stretched at very high velocities. by, Malcolm Mackley and Simon Butler Department of Chemical Engineering and Biotechnology, University of Cambridge and Rudy Valette, Elie Hachem, Mehdi Khalloufi and Anselmo Pereira Mines ParisTech, CEMEF - Centre for Material Forming, Sophia-Antipolis, France
  2. 2. The People Malcolm Simon Rudy Elie Mehdi Anselmo 2 Thierry Coupez
  3. 3. The effect of Viscosity, Yield Stress, and Surface Tension on the Deformation and Breakup profiles of fluid filaments Stretched at very high Velocities Newtonian Viscosity 10−4 - 103 Pas Typically, 1- 103 mPas Bingham Yield Stress 1 - 103 Pa Surface Tension 20 – 500 mN/m Extensional Flows 𝜀 ≈ 1000 𝑠−1 1970 Twin jet PhD Bristol Rayleigh instability Extensional viscosity , Trouton Capillary number, Grace Hinch, Rallison and Leal The Title 3
  4. 4. 4 Drive belt Piston Linear traverse Motor drive a b The Trimaster Family, 2006 - 2018 Tri Tuladhar Damien Vadillo MPR Mk1 Trimaster MK2 Trimaster Mk3 Trimaster
  5. 5. 5 Cambridge HB4 Trimaster, 2010s Stuart Huxley
  6. 6. 6
  7. 7. 7 Strain Rate 𝜀 = −2 1 𝐷 𝑑𝐷 𝑑𝑡 Hencky strain 𝜀 = 𝛾𝑑𝑡 = −2 𝑑𝐷 𝐷 = 2 𝑙𝑛 𝐷0 𝐷 0.00ms 0.72ms 1.83ms 2.33ms 3.11ms 4.17ms Water based buffer solution Hencky Strain Normalised centre line diameter Piston Amplitude / mm Strain rate / 𝑠−1
  8. 8. 8 0.00 ms 1.00 ms 3.00 ms 15 ms 25 ms 45 ms Silicone oil 492 mPas
  9. 9. CIMLIB-CFD finite element library Parallel environment Flow solver: Navier-Stokes (Variational MultiScale technique) Multiphase: Level-Set method Surface tension: Continuum Surface Force Mesh: anisotropic mesh adaptation Extended to non-linear constitutive models Rudy Valette, Elie Hachem, Anselmo Pererio and Mehdi Khalloufi. CEMEF Sophia Antipolis
  10. 10. 10 Maths Stuff 𝝈𝒄 = −𝑝𝐈 + 𝝉, 𝝉 = 𝟐𝜼 𝒆 𝑫 𝒖 , 𝜼 𝒆 = 𝜼∞ + 𝜼 𝟎 − 𝜼∞ 𝟏 + 𝝀 𝜸 𝒂 −(𝒏−𝟏) 𝒂 , 𝜼 𝒆 = 𝒌 + 𝝉 𝟎 𝜸 𝟏 − 𝒆−𝒎 𝜸 , Carreau-Yasuda (C-Y) Papanastasiou regularization 𝜌 𝜕𝒖 𝜕𝑡 + 𝒖. 𝛻𝒖 − 𝒈 = −𝛻𝑝 + 𝛻. 𝝉 + 𝒇 𝑆𝑇, 𝒇 𝑆𝑇 = −𝜎𝐾𝛿𝒏 Momentum Equation Surface Tension 0 20 40 60 80 100 120 1 21 41 61 81 101 Stress Strain rate 0 20 40 60 80 100 3 30 300 viscosity Strain rate
  11. 11. 11 Water 𝜎 = 70 mN/mh = 1.0 mPas
  12. 12. 12 Silicone oil h = 492 mPas 𝜎 = 20 mN/m
  13. 13. 13
  14. 14. 14 Surface Tension (h = 1 mPa s; 𝜏0 = 0 Pa ) 𝜎 = 0 mN/m 𝜎 = 35 mN/m
  15. 15. 15 Bingham Yield Stress (h = 1.0 mPas, 𝜎 = 70 mN/m). 𝜏0 = 1 Pa 𝜏0 = 100 Pa. 𝜏0 = 1000 Pa
  16. 16. 16 (Carreau-Yasuda) 𝜂∞ = 0.3 Pa s, 𝜂0 = 6 105Pa s, 𝜆 = 2104 s, 𝑎 = 0.75, 𝑛 = 1.89, 𝜎 = 0 mN/m). Carbopol (ClearGlide)
  17. 17. 17 Hellmann’s Mayonnaise (Carreau-Yasuda) 𝜂∞ = 0.3 Pa s, 𝜂0 = 13500 Pas, 𝜆 = 115 s, 𝑎 = 1, 𝑛 = 1.93, 𝜎 =300mN/m. Bingham: k = 0,001 Pa s, 𝜏0 = 140 Pa, 𝜎 = 300 mN/m.
  18. 18. 18 C-Y: 𝜂∞ = 0.3 Pas, 𝜂0 = 107 Pas, 𝜆 = 105 s, 𝑎 = 1, 𝑛 = 1.85, 𝜎 = 0 mN/m Bingham: k = 1 mPa s, 𝜏0 = 500 Pa, 𝜎 = 0 mN/m. Whipped Cream
  19. 19. 19 Conclusions • The HB4 fast filament stretching apparatus is an apparatus that generates high precision stretch and breakup data. • The CEMEF solver is a high precision simulation that can capture HB4 behaviour for different fluids. • Solver validated against high and low viscosity Newtonian fluids. • The effect of surface tension and yield stress has been systematically explored using the solver. • The effect of surface tension on droplet formation has been demonstrated. • Solver matched with experimental behaviour for certain yield stress fluids.
  20. 20. “This could be the last time, this could be the last time, maybe the last time, I don’t know.” (Is this MRM’s last ever CEB presentation 2018?)

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