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 + e a  t is a solid and is 0 otherwise We seem to have flexibility in the choice of the pre-sum factor; the papers cited use  or 

8. Computation of  // 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. Sforce // 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]; }

10. Sforce 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; }

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

12. Young’s Equation?

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

14. Contact Angles in LBM Assume uniform surroundings: LiquidVapor

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

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

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

18. Contact Angles in LBM 90 degree contact angle: –Adhesive force on vapor equal to cohesive force for ‘interface’  (= [  l +  v  ) Interface surrounded by solidInterface

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

20. Adsorption  vap =85.7  vap =85.7857  vap =86.1285

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

22. Capillary Condensation  vap =86.557

23. Adsorption/Capillary Condensation

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

25. Hysteretic Wetting and Drying

27. Hysteritic Wetting and Drying

28. Invasion Percolation

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

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

31. Viscosity Ratio For D2Q9 LBM:

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

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

34. No Gravity Gravity Drainage and gravity stabilization