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Surface Adhesion (Adsorption) in LBM

Surface Adhesion (Adsorption) in LBM. Key Papers. Martys, N. and H. Chen, 1996, PRE 53, 743-750 Raiskinmäki, P., A. Koponen, J. Merikoski, and J. Timonen, 2000, Comp. Materials Sci. 18, 7 – 12. Key Books.

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Surface Adhesion (Adsorption) in LBM

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  1. Surface Adhesion (Adsorption) in LBM

  2. Key Papers • Martys, N. and H. Chen, 1996, PRE 53, 743-750 • Raiskinmäki, P., A. Koponen, J. Merikoski, and J. Timonen, 2000, Comp. Materials Sci. 18, 7 – 12

  3. Key Books • Adamson, A. W., and A.P. Gast, Physical Chemistry of Surfaces, New York, John Wiley & Sons, Inc., 1997. • Israelachvili, J. N., Intermolecular and Surface Forces, 2nd ed. Academic Press, London, 1992.

  4. Wetting http://www.hdm-stuttgart.de/projekte/printing-inks/b_sel42.jpg

  5. Wetting http://psii.kist.re.kr/Teams/psii/research/Con_4.jpg

  6. Geometrically-controlled Superhydrophobic surfaces http://www.nature.com/nmat/journal/v1/n1/images/nmat715-f1.jpg

  7. LBM Adhesive Force Formula • s is a ‘switch’ that takes on value 1 if the site at x + eaDt is a solid and is 0 otherwise • We seem to have flexibility in the choice of the pre-sum factor; the papers cited use r or Y

  8. Computation of y • // Compute psi, Eq. (61). • for( j=0; j<LY; j++) • for( i=0; i<LX; i++) • if( !is_solid_node[j][i]) • { • psi[j][i] = 4.*exp( -200. / ( rho[j][i])); • }

  9. // Compute interaction force, Eq. (66). for( j=0; j<LY; j++) { jp = ( j<LY-1)?( j+1):( 0 ); jn = ( j>0 )?( j-1):( LY-1); for( i=0; i<LX; i++) { ip = ( i<LX-1)?( i+1):( 0 ); in = ( i>0 )?( i-1):( LX-1); if( !is_solid_node[j][i]) { sum_x=0.; sum_y=0.; if( is_solid_node[j ][ip]) // neighbor 1 { sum_x = sum_x + WM*ex[1]; sum_y = sum_y + WM*ey[1]; } if( is_solid_node[jp][i ]) // neighbor 2 { sum_x = sum_x + WM*ex[2]; sum_y = sum_y + WM*ey[2]; } if( is_solid_node[j ][in]) // neighbor 3 { sum_x = sum_x + WM*ex[3]; sum_y = sum_y + WM*ey[3]; } Sforce

  10. if( is_solid_node[jn][i ]) // neighbor 4 { sum_x = sum_x + WM*ex[4]; sum_y = sum_y + WM*ey[4]; } if( is_solid_node[jp][ip]) // neighbor 5 { sum_x = sum_x + WD*ex[5]; sum_y = sum_y + WD*ey[5]; } if( is_solid_node[jp][in]) // neighbor 6 { sum_x = sum_x + WD*ex[6]; sum_y = sum_y + WD*ey[6]; } if( is_solid_node[jn][in]) // neighbor 7 { sum_x = sum_x + WD*ex[7]; sum_y = sum_y + WD*ey[7]; } if( is_solid_node[jn][ip]) // neighbor 8 { sum_x = sum_x + WD*ex[8]; sum_y = sum_y + WD*ey[8]; } sforce_x[j][i] = -Gads * psi[j][i] * sum_x; sforce_y[j][i] = -Gads * psi[j][i] * sum_y; } } } Sforce

  11. Contact Angles in SCMP LBM • Cohesive force: • Adhesive force: Interplay between these forces will determine wetting

  12. Young’s Equation?

  13. Contact Angles in SCMP LBM Assume uniform liquid or vapor surroundings:

  14. Contact Angles in LBM • Assume uniform surroundings: Liquid Vapor

  15. Contact Angles in LBM • Assume uniform surroundings: Liquid surrounded by solid Vapor surrounded by solid

  16. Contact Angles in LBM • Zero degree contact angle: • Adhesive force equal to cohesive force for liquid Liquid Liquid surrounded by solid

  17. Contact Angles in LBM • 180 degree contact angle: • Adhesive force on vapor equal to cohesive force for vapor Vapor Vapor surrounded by solid

  18. Contact Angles in LBM • 90 degree contact angle: • Adhesive force on vapor equal to cohesive force for ‘interface’ y (= [yl + yv]/2) Interface Interface surrounded by solid

  19. Adsorption • Asvl: Hamaker constant for interaction of solid with vapor through liquid • P: Disjoining pressure (P relative to flat, free interface)

  20. Adsorption rvap=85.7 rvap=85.7857 rvap=86.1285

  21. Capillary Condensation • Avll: Hamaker constant for interaction of liquid with liquid through vapor • P: Disjoining pressure (P relative to flat, free interface)

  22. Capillary Condensation rvap=86.557

  23. Adsorption/Capillary Condensation

  24. Hysteretic Wetting/Drying of Angular Pores (Tuller, Or, and Dudley,1999 WRR) Filled cross-sectional area Young-Laplace (zero contact angle) Shape factor Imbibition radius Drainage radius Saturation as a function of p at high tension p as a function of saturation at high tension

  25. Hysteretic Wetting and Drying

  26. Hysteretic Wetting and Drying

  27. Hysteritic Wetting and Drying

  28. Invasion Percolation

  29. Capillary Number • v inlet/outlet velocity • m viscosity of injected fluid • n porosity • g interfacial tension between fluids • q contact angle Friedman, 1999. J. Adhesion Sci Technol. 13(12), 1495-1518.

  30. Pore Selection and Impact of Ca on Pore Penetration v 10-3 v 10-4 Ca  2 x 10-4 Ca  2 x 10-5 r = 7.5 r = 5 r = 6.5 2,500 ts/movie step

  31. Viscosity Ratio • For D2Q9 LBM:

  32. Phase Diagram Air/Viscous Oil Glucose Soln./ Oil Lenormand et al. 1988. J. Fluid Mech. 189, 165-187. Air/Viscous Oil

  33. Viscosity-Matched Fluids Monolayer of 0.7 mm beads Frette et al., 1997. PRE 55(3) 2969-2975.

  34. Drainage and gravity stabilization No Gravity Gravity

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