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Day 2. Interfacial forces acting on phases situated at (or close to) the interface of other phases and driving them in s

Kaptay / Day 2 / 1. See J 96. Day 2. Interfacial forces acting on phases situated at (or close to) the interface of other phases and driving them in space . George Kaptay kaptay@hotmail.com. A 4-day short course. Kaptay / Day 2 / 2. Modeling algorithm. Interfacial energies.

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Day 2. Interfacial forces acting on phases situated at (or close to) the interface of other phases and driving them in s

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  1. Kaptay / Day 2 / 1 See J96 Day 2. Interfacial forces acting on phases situated at (or close to) the interface of other phases and driving them in space George Kaptay kaptay@hotmail.com A 4-day short course

  2. Kaptay / Day 2 / 2 Modeling algorithm Interfacial energies Interfacial forces Interfacial phenomena Complex phenomena

  3. Kaptay / Day 2 / 3 x B A Deriving equations for interfacial forces

  4. Kaptay / Day 2 / 4 A B The curvature induced interfacial force For a spherical B: The Laplace equation for spheres

  5. Kaptay / Day 2 / 5 The general Laplace equation For cylinders: Generally: For a cylinder:

  6. Kaptay / Day 2 / 6 Summary The curvature induced interfacial force The Laplace equation: In equilibrium: P2:atmosphere + gravity +...

  7. Kaptay / Day 2 / 7 Laplace  Kelvin The Laplace equation The Gibbs energy change Kelvin equation (Day 1 / 17):

  8. Kaptay / Day 2 / 8 x A B The interfacial gradient force (1)

  9. Kaptay / Day 2 / 9 See J64 Bubbles in a concentration gradient k=0.5 comes from fluid dynamics for bubbles moving in a C-gradient Measured: Mukai and Lin

  10. Kaptay / Day 2 / 10 See J101 Droplets moving in a T-gradient Pötschke J., Rogge V., 1989: Hadamard, Rybczinski:

  11. Kaptay / Day 2 / 11 Can you produce monotectic alloys in space (g=0)? NO Even in space you can not. Sorry.. Droplets do not sediment But they coalesce too quickly

  12. Kaptay / Day 2 / 12 Interf. gradient force Marangoni force Bubble movement Liquid convection

  13. Kaptay / Day 2 / 13 2 3 x 1 The interfacial capillary force (1) For a solid particle at a liquid/gas interface:

  14. Kaptay / Day 2 / 14 The interfacial capillary force (2) The Young-Laplace equation Wetting liquids penetrate into empty cylinders (see also Day 1 / 15)

  15. Kaptay / Day 2 / 15 See J23 The interfacial capillary force (3)

  16. Kaptay / Day 2 / 16 See J23 equilibrium Particle equilibrium at interface For a spherical particle of radius r:

  17. Kaptay / Day 2 / 17 Wettability versus particle position at interface

  18. Kaptay / Day 2 / 18 The interfacial capillary force in physical metallurgy If solid particles (droplets) are dragged by the grain boundary, its movement is slowed down by the particles (droplets) (the “Zenner force”) and its size stabilizes at a certain value of Req

  19. Kaptay / Day 2 / 19 How to make nano-crystalline alloys? If the grains are identical: The maximum force at x = 2r: Equilibrium if: The equilibrium grain-size: For better properties (low Req) precipitate many nano-particles

  20. Kaptay / Day 2 / 20 The condition of flat meniscus around a sphere (1) Depends on the dimensionless density:

  21. Kaptay / Day 2 / 21 The condition of flat meniscus around a sphere (2) The equilibrium condition for interfacial capillary force, only: The equilibrium condition for gravity + buoyancy forces, only: The two equals, if:

  22. Kaptay / Day 2 / 22 The interfacial meniscus force (1) Chan et al, 1980 (exact solution: Paunov et al, 1993)

  23. Kaptay / Day 2 / 23 The interfacial meniscus force (2) Flat meniscus  no interfacial force

  24. Kaptay / Day 2 / 24 The interfacial meniscus force (3) Similarly curved menisci  attracting interfacial force

  25. Kaptay / Day 2 / 25 The interfacial meniscus force (4) Oppositely curved menisci  repulsing interfacial force

  26. Kaptay / Day 2 / 26 The liquid bridge induced interfacial force (1) Valid at x  0, V  0, same as interfacial capillary force for cylinders (see Today, slide 14)

  27. Kaptay / Day 2 / 27 The liquid bridge induced interfacial force (2) (1/2 = 1 J/m2, 3/2/1 = 4/2/1 = 30o, V2/V3 = V2/V4 = 0.01, r = 10 m, Fmax= -54.4 N).)

  28. Kaptay / Day 2 / 28 x 2 1 3 The interfacial adhesion force (1)

  29. Kaptay / Day 2 / 29 A simplified derivation x 1 2 3

  30. Kaptay / Day 2 / 30 ij = f (interface separation) Boundary condition 1: If x: 13(x)  13, 23(x)  23 Boundary condition 2:If x 0: 13(x)  12, 23(x)  12

  31. Kaptay / Day 2 / 31 See J24 Substituting…. Literature

  32. Kaptay / Day 2 / 32 Summary 2 1 1 1 3 3 Hamaker, 1937: Neumann, 1973: Kaptay, 1996: See J24

  33. Kaptay / Day 2 / 33 Conclusions Equations have been obtained for the interfacial forces: The “curvature induced interfacial force” (Laplace) The “interfacial gradient force” (Marangoni) The “interfacial capillary force” (Young-Laplace, Carman, Zener) The “interfacial meniscus force” (Nicolson, Denkov, White) The “liquid bridge induced interfacial force” (Naidich) The “interfacial adhesion force” (Derjaguin, Hamaker)

  34. Kaptay / Day 2 / 34 Conditions for the trial calculations Liquid: steel at 1600 oC, l/g = 1.7 J/m2, 1 = 7000 kg/m3 Solid particle: Al2O3, r = 10 m, s/g = 0.9 J/m2, s = 3600 kg/m3, m = 1.5.10-11 kg, Fg = m.g = 1,5.10-10 N. Contact angle: 120o. From the Young equation: s/l = 1.75 J/m2, Derivatives by T and weight % of oxygen, dissolved in liquid steel: dc/l/dT = –2.10-4 J/Km2 and dc/l/dCO = –10 J/m2w%. Temperature gradient: dT/dx = 10K/mm Gradient of the oxygen concentration: dCO/dx = 0.01 w%/mm For capillary force, the depth of immersion: x = 20m For meniscus force between two, equal particles: x = 10 m. From the densities: * = 0.51, flat* = 0.16, i.e. (* - flat*) = 0.35. For the liquid bridge induced interfacial force we suppose that the particles are in contact (x = 0), the volume of liquid is negligible.

  35. Kaptay / Day 2 / 35 The curvature induced interfacial force -4.4.10-4 N >> gravity force

  36. Kaptay / Day 2 / 36 x A B The interfacial gradient force T-induced: 2.5.10-9 N > gravity force O-concentration induced: 1.3.10-7 N >> gravity

  37. Kaptay / Day 2 / 37 The interfacial capillary force F = -1.6.10-4 N >> gravity force

  38. Kaptay / Day 2 / 38 The interfacial meniscus force F = -1.3.10-16 N << gravity force (but perpendicular to gravity)

  39. Kaptay / Day 2 / 39 The liquid bridge induced interfacial force (1) F = 5.3.10-5 N >> gravity force

  40. Kaptay / Day 2 / 40 x 2 1 3 The interfacial adhesion force F = 1.1.10-4 N (x = 0) >> gravity force F = 1.10-12 N (x = 1 micron) < gravity force

  41. Thank you for your attention so far If not too tired, please, come again (tomorrow morning…)

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