! Particle Detachment Mechanisms ! Particle Detachment Mechanisms ! JKR Adhesion Model ! JKR Adhesion Model ! DMT Adhesion Model ! DMT Adhesion Model ! Maugis ! Maugis- -Pollock Model Pollock Model ! Maximum Moment Resistance ! Maximum Moment Resistance ME 437/537 Ahmadi ME 437/537 Ahmadi Sphere Attached Sphere Attached Johnson- Johnson -Kandall Kandall- -Roberts (1971) Roberts (1971) P to a Surface to a Surface ⎡ ⎤ ⎛ π 2 ⎞ d 3 3 W d ⎢ ⎥ = + π + π + ⎜ ⎟ 3 A a P W d 3 W dP a = Contact a = Contact d ⎢ A A ⎥ ⎝ ⎠ 2 K 2 2 ⎣ ⎦ P = Exerted Force P = Exerted Force − 1 ⎡ − υ − υ ⎤ 2 2 1 1 O 4 = + K ⎢ 1 2 ⎥ 3 ⎣ E E ⎦ 1 2 a F a 3 = F ad = Adhesion Force dP F ad = Adhesion Force ad Hertz Model Hertz Model 2 K ME 437/537 Ahmadi ME 437/537 Ahmadi 1
Derjaguin- -Muller Muller- -Toporov Toporov (1975) (1975) Derjaguin 3 = π Pull- Pull -Off Force Off Force JKR F W d = π DMT po A F W d 4 Pull- -Off Force Off Force Pull Po A 1 4 Contact Radius ⎛ π ⎞ = Contact Radius DMT JKR 2 3 W d F F 3 ⎜ ⎟ = Po Po A a 3 ⎜ ⎟ at Zero Force at Zero Force 0 ⎝ 2 K ⎠ Contact Radius Contact Radius 1 ⎛ π ⎞ 2 W d 3 ⎜ ⎟ = A a ⎜ ⎟ at Zero Force at Zero Force 1 0 ⎝ ⎠ ⎛ π ⎞ 2 K Contact Radius 2 Contact Radius 3 W d a 3 = ⎜ ⎟ = a A 0 ⎜ ⎟ 1 / 3 ⎝ ⎠ 8 K 4 at Separation at Separation a = Contact Radius at Contact Radius at 0 Separation Separation ME 437/537 Ahmadi ME 437/537 Ahmadi Polystyrene on Polyurethane Rimai et al. et al. Rimai + π = π H = 2 3 Y P W d a H A High elastic High elastic modulus spherical modulus spherical 2 particles on particles on Elastic Elastic a ~ d 3 elastomeric elastomeric 0 substrates. substrates. 1 Plastic Plastic a ~ d 2 0 ME 437/537 Ahmadi ME 437/537 Ahmadi 2
Polystyrene particles on a silicon wafer Rimai et al. et al. Rimai Rimai et al. et al. Rimai ME 437/537 Ahmadi ME 437/537 Ahmadi Rimai et al. et al. Rimai 0.6 A Conntact Radius (microns) = W 0.5 π A 2 12 z 0.4 0 0.3 0.2 0.1 0.0 0 1 2 R 0.5 ( µ m 0.5 ) ME 437/537 Ahmadi ME 437/537 Ahmadi 3
3 = − + − * * * = = − + − * JKR * * * * * 1 / 3 a 1 P 1 2 P M P a P ( 1 P 1 2 P ) P a max = Maximum = − = Maximum * M JKR * * P a 0 . 42 1 3 ⎛ π ⎞ π 2 Moment 3 W d 3 Moment W d ⎜ ⎟ A ⎜ ⎟ A 2 ⎝ ⎠ 4 K JKR F = = = * * JKR = P F 0 . 5 M JKR * 0 = π 0 . 397 a * max po 3 1 . 26 W d A 2 = * * P a 0 . 63 max 0 ME 437/537 Ahmadi ME 437/537 Ahmadi d ( ) DMT F 2 ≈ + π = = = = * * DMT = Contact Radius 3 P F * * Contact Radius M DMT * a P W d P a 0 . 58 π 0 max po 3 3 A max 0 2 K W d A 2 a 2 Nondimensional Nondimensional 3 = = − + * 3 * Maximum Maximum a ( ) P π Contact Radius Contact Radius 2 = = 3 W d / 4 K 3 * JKR * DMT M 0 . 42 1 . 5 M Moments Moments A max max = − * DMT * * 1 / 3 Resistance Moment M P ( 2 / 3 P ) Resistance Moment 4 5 4 5 3 3 W d 3 3 W d = = JKR A DMT M 2 . 63 A M 1 . 83 max 1 max 1 = M DMT * Maximum Moment Maximum Moment 0 . 28 κ κ 3 3 max ME 437/537 Ahmadi ME 437/537 Ahmadi 4
1.3 0.5 1.2 1.1 JKR 0.4 1.0 JKR 0.9 0.3 0.8 M* 0.7 DMT a* DMT 0.6 0.2 0.5 0.4 0.1 0.3 0.2 0.1 0.0 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 P* P* Variations of resistance moment with the exerted force. Variations of resistance moment with the exerted force. Variations of contact radius with the exerted force. Variations of contact radius with the exerted force. ME 437/537 Ahmadi ME 437/537 Ahmadi ! Spherical particles are removed ! Spherical particles are removed by overcoming the adhesion by overcoming the adhesion rolling resistance rolling resistance ! ! JKR, DMT and JKR, DMT and Maugis Maugis- -Pollock Pollock Models Models ! ! Contact radius varies differently Contact radius varies differently with d for elastic and plastic with d for elastic and plastic deformations deformations ME 437/537 Ahmadi ME 437/537 Ahmadi 5
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