a F a 3 = F ad = Adhesion Force dP F ad = Adhesion Force ad - - PowerPoint PPT Presentation

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Ahmadi ME 437/537 Ahmadi ME 437/537

! ! 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

Ahmadi ME 437/537

Sphere Attached Sphere Attached to a Surface to a Surface

ad

F P

O

a

d a = Contact a = Contact F Fad

ad = Adhesion Force

= Adhesion Force P = Exerted Force P = Exerted Force

Ahmadi ME 437/537

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π + π + π + =

2 A A A 3

2 d W 3 dP W 3 d W 2 3 P K 2 d a

Johnson Johnson-

• Kandall

Kandall-

• Roberts (1971)

Roberts (1971)

1 2 2 2 1 2 1

E 1 E 1 3 4 K

−

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ υ − + υ − =

K 2 dP a3 = Hertz Model Hertz Model

2

Ahmadi ME 437/537

d W 4 3 F

A JKR po

π =

3 1 2 A

K 2 d W 3 a ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π =

3 / 1 3 1 2 A

4 a K 8 d W 3 a = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π =

Pull Pull-

• Off Force

Off Force Contact Radius Contact Radius at Separation at Separation Contact Radius Contact Radius at Zero Force at Zero Force

Ahmadi ME 437/537

d W F

A DMT Po

π =

Derjaguin Derjaguin-

• Muller

Muller-

• Toporov

Toporov (1975) (1975)

JKR Po DMT Po

F 3 4 F =

Pull Pull-

• Off Force

Off Force

3 1 2 A

K 2 d W a ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π =

a =

Contact Radius Contact Radius at Zero Force at Zero Force

Contact Radius at Contact Radius at Separation Separation Ahmadi ME 437/537

H a d W P

2 A

π = π +

Y 3 H =

3 2

d ~ a

2 1

d ~ a

Elastic Elastic Plastic Plastic

Ahmadi ME 437/537

High elastic High elastic modulus spherical modulus spherical particles on particles on elastomeric elastomeric substrates. substrates.

Polystyrene on Polyurethane

Rimai Rimai et al. et al.

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Ahmadi ME 437/537

Rimai Rimai et al. et al.

Ahmadi ME 437/537

Polystyrene particles on a silicon wafer

Rimai Rimai et al. et al.

Ahmadi ME 437/537

R0.5 (µm0.5)

1 2

Conntact Radius (microns)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Rimai Rimai et al. et al.

Ahmadi ME 437/537

2 A

z 12 A W π =

4

Ahmadi ME 437/537

* * 3 *

P 2 1 P 1 a − + − =

d W 2 3 P P

A *

π − =

3 1 2 A *

K 4 d W 3 a a ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π =

26 . 1 a*

0 =

Ahmadi ME 437/537

3 / 1 * * * * * JKR *

) P 2 1 P 1 ( P a P M − + − = =

42 . M JKR

* max = 5 . d W 2 3 F F P

A JKR JKR * po * max

= π = =

397 . M JKR

*

=

63 . a P

* * max

=

Maximum Maximum Moment Moment

Ahmadi ME 437/537

Maximum Moment Maximum Moment

( )

d W P K 2 d a

A 3

π + ≈

3 2 P ) K 4 / d W 3 a ( a

* 3 2 A 3 *

+ − = π =

3 / 1 * * DMT *

) P 3 / 2 ( P M − =

28 . M DMT

* max

=

Contact Radius Contact Radius Nondimensional Nondimensional Contact Radius Contact Radius Resistance Moment Resistance Moment

Ahmadi ME 437/537

Maximum Maximum Moments Moments

3 2 d W 2 3 F F P

A DMT DMT * po * max

= π = =

58 . a P

* * max

= M DMT

*

=

DMT * max JKR * max

M 5 . 1 42 . M = =

3 1 3 5 3 4 A JKR max

d W 63 . 2 M κ =

3 1 3 5 3 4 A DMT max

d W 83 . 1 M κ =

5

Ahmadi ME 437/537

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

a*

0.1 0.2 0.3 0.4 0.5 0.6 0.7

P*

JKR DMT

Variations of contact radius with the exerted force. Variations of contact radius with the exerted force.

Ahmadi ME 437/537

0.0 0.1 0.2 0.3 0.4 0.5

M*

0.1 0.2 0.3 0.4 0.5 0.6 0.7

P*

Variations of resistance moment with the exerted force. Variations of resistance moment with the exerted force.

JKR DMT Ahmadi ME 437/537

! ! 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

Ahmadi ME 437/537